{"group":{"group":{"id":97277,"name":"Transforming functions","lockable":false,"created_at":"2026-01-03T10:11:57.000Z","updated_at":"2026-02-14T17:15:09.000Z","description":"Translate and scale functions, among other transformations, by shifting their graphical representations, with an emphasis on polynomials. Knowing critical points is a fundamental step for the resolution of the problems.\nThe presented figures were obtained using software MATLAB version R2025b.\nFor a better understanding of the subject, plot the graphical representations of all functions given in Tests.","is_default":false,"created_by":4993982,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":null,"image_id":7182,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTranslate and scale functions, among other transformations, by shifting their graphical representations, with an emphasis on polynomials. Knowing critical points is a fundamental step for the resolution of the problems.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe presented figures were obtained using software MATLAB version R2025b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a better understanding of the subject, plot the graphical representations of all functions given in Tests.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 360px 61.5px; transform-origin: 360px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 336px 31.5px; text-align: left; transform-origin: 336px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTranslate and scale functions, among other transformations, by shifting their graphical representations, with an emphasis on polynomials. Knowing critical points is a fundamental step for the resolution of the problems.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 336px 10.5px; text-align: left; transform-origin: 336px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe presented figures were obtained using software MATLAB version R2025b.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 336px 10.5px; text-align: left; transform-origin: 336px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a better understanding of the subject, plot the graphical representations of all functions given in Tests.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2026-02-14T17:15:09.000Z"},"current_player":null},"problems":[{"id":61142,"title":"Shifting vertically a function's graph","description":"Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k.\r\nFor a real constant k, you may assume that the translation is given. However, if k = 'mean', you firstly must determine the real constant k such that the translated function has an average value of 0 over the given interval (see figure below).\r\nFind\r\ny_shifted, which is the 1×n vector that stands for the outputs of the translated function;\r\nv, which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\r\nHint. Calculate the mean of a piecewise linear discrete function, represented as an array of x and an array of y values. Be aware to the existence of calculus discrepancies whenever the function f will be continuous, but not piecewise linear.\r\ninput: (x, y, k)\r\noutput: [y_shifted, v]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 563.312px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 281.65px; transform-origin: 408px 281.656px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a real constant \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, you may assume that the translation is given. However, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'mean', you firstly must determine the real constant \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that the translated function has an average value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the given interval (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_shifted,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the translated function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and an array of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be continuous, but not piecewise linear.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_shifted, v]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 259px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 129.5px; text-align: left; transform-origin: 384px 129.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg 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\" alt=\"Vertical shift\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_shifted, v] = v_shifting(x, y, k)\r\n  y_shifted = x;\r\n  v = x;\r\nend","test_suite":"%%\r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 'mean';\r\ny_correct = [1.38   1.98   1.78   0.78   0.48  -0.82  -1.22  -0.62];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];\r\nk = 'mean'; \r\ny_correct = [2.47  2.07  1.87  0.87  0.57 -0.73 -1.13 -1.63];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nfiletext = fileread('v_shifting.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = -(cos(x)).^2;\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nx = -5*pi/12:pi/12:5*pi/12;\r\ny = (tan(x)).^2;\r\nk = 1;\r\ny_correct = (sec(x)).^2;\r\nv_correct = 'up';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 'mean';\r\ny_correct = atan(x);\r\nv_correct = '';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-29T14:41:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-20T13:44:19.000Z","updated_at":"2026-03-24T16:04:22.000Z","published_at":"2025-12-29T14:41:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a real function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, you may assume that the translation is given. However, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'mean', you firstly must determine the real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the translated function has an average value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the given interval (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_shifted,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the translated function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be continuous, but not piecewise linear.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_shifted, v]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"367\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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parabola by its vertex to the origin","description":"Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the parabola by shifting its vertex to the origin (see figure below).\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint: Be careful to the potential computer errors whenever the results will be integer numbers.\r\ninput: p\r\noutput: [d, v, h]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 633.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 316.987px; transform-origin: 408px 316.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a quadratic polynomial, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = ax^2 + bx + c (a ~= 0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, represented by the vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a b c]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider the translation of the parabola by shifting its vertex to the origin (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed (d\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the shifting distance of the above translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Be careful to the potential computer errors whenever the results will be integer numbers.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[d, v, h]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 169.9px; text-align: left; transform-origin: 384px 169.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"480\" height=\"334\" style=\"vertical-align: baseline;width: 480px;height: 334px\" 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alt=\"Shift parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_parabola(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [-1 12 -28];\r\nd_correct = 10;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [1 -3 0.25];\r\nd_correct = 2.5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%% \r\np = [4 -12 9];\r\nd_correct = 1.5;\r\nv_correct = '';\r\nh_correct = 'left';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-5 -2 -1.6];\r\nd_correct = sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-5 -2 1.2];\r\nd_correct = sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_parabola(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-03T10:31:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-03T10:31:42.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-24T12:38:12.000Z","updated_at":"2026-02-27T10:20:46.000Z","published_at":"2026-01-02T10:06:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a quadratic polynomial, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = ax^2 + bx + c (a ~= 0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, represented by the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a b c]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider the translation of the parabola by shifting its vertex to the origin (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the parabola is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the parabola is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Be careful to the potential computer errors whenever the results will be integer numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relation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even-degree polynomial by its vertex to the origin","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint. Compare to the Problem 61143.\r\ninput: p\r\noutput: [d, v, h]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 157.587px; transform-origin: 408px 157.594px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed (d\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the shifting distance of the above translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Compare to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61143\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[d, v, h]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_vertex(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [1 0 0 0 -1];\r\nd_correct = 1;\r\nv_correct = 'up';\r\nh_correct = '';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [1/4 -1/3 -2.5 -3 16.25];\r\nd_correct = 5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.25 -1 0.5 -3 15.25];\r\nd_correct = 5;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_vertex.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 54];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nd_correct = 2;\r\nv_correct = '';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-0.5 -2.4 3 22 -4.5 -54 -25.4];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-04T13:00:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-26T17:29:02.000Z","updated_at":"2026-03-26T10:19:33.000Z","published_at":"2026-01-04T13:00:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Compare to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[d, v, h]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61148,"title":"Shifting vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u0026lt;b\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined such that the endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stand for the least and the greatest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values of the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = y_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the highest local maximum of the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see non-scale figures below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they exist. Otherwise, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb = '' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see Hint 1);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe shifting constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 1. An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomial has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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B34qoqOj77zzTkLIjz/++OWXX9I7hU5p0KBB9DtC6EtHjRo1ZMgQk8kUHx8vfA5DfS0SIpXgatOmzezZs//zn//s2rVryZIlgwYNEj5/Dofj1VdfdQ91e/Xq1aFDB+HpXbp0oQ9mE7HBw/72a665hg7VCL/90qVLdEJMhw4dhg4dKjyrT58+N910U6svnpycTLv+goIC+sWwZ88eOiQgDGCePHmS9t1xcXFCSZg2bdrQ8Ri73f7DDz9wLzt48GBpf+yJEyfoYfTp00eIJtu1a7dly5aSkpLjx4/TIbHRo0efPHmSjlR98803a9aseeihhw4cOCDhN3bq1Gn06NGEkKqqKvoKTU1Nu3btcjgcJpPp7rvvNps9L8eTduZ79uzZrl074UeLxbJhw4aSkpL8/PyIiIiPP/44PT198eLF3p5uMpmSkpJozEEI6dGjBz3VdrudTY1RgwcPFh553XXX0fiJftH6OCHUbbfdJqyACw8Pp/0yIeTkyZO1tbWST5p4wqyyqqqqGTNm0ETtl19++eGHH/qYT8YZMGBAmzZt6G365UEIuemmm6677jrht9AbFy9ebGhoaGho+O9//0vvueWWW4SzFxsbS59SXFx86dIlk8n0l7/8paSk5Pvvv+/Zs2dubu4LL7wwd+5cH2NpvluxR4cOHaJ5zGHDhgkHT5hAsKSk5MSJE4SQnj170kGs0tJSGrAeP368sLCQnoFBgwYRQs6ePUsf3KlTp169etGXMplM9PPjcDjoeBiL+6y6U+Y8+MZ+yKOjo+mH1veHPPBTYTKZJkyYQBdh7N27t66uTkh9mkym++677+qrryaE0EGdkpKSv/3tbyUlJevXr58xY8ZHH30k7S/VGqxSVkJYWBidHjVv3rzGxsZt27ZlZmbW1NTQaxFu7DoyMjLwnlcy37+9qqqKXj1YLBah/6XPYn/05vrrrx86dOi2bduKi4sLCgruuOMOOtosDGASQurr62l+h84Cdn8R2uzZX+27g/Ph1KlT9Eb79u1pa/fI4XAcOnRo2bJlR48eDXyfrJSUlPXr19vt9r179z7wwANlZWU0Wr3++ut9hFzSznzXrl25ey5duvTaa6+9++67YqbXcL/LbDbT7pIQ4l60MJCZItxzhR+F7wBpJ028a6+9dsGCBYsWLaITGmiill7s9u7d22q1CgkjkX+F0Iiuuuoq4btN8PPPP9MT+PPPP9N7hMnvrB9//LGqquraa6+tq6vbtGnTa6+9xs3B9EZCHyI0q969e7MHHBER0b59e8IMH5rN5rvvvvuTTz5pbGzcvHnziBEjcnNz6cfpvvvuo1/e9fX1dITj9OnTHk/d6dOnGxoa2Ebn/ll1p8B58E3Ch1yWU9G3b99+/fodPnz466+//v777zt16kRj3Pj4ePY1i4qKli1blp+fr8xlrZIwphIsS5cupbOvrVYr+/VGxyHnzp1Lf2x1eoeemM3mSZMmhYeH0+lg33zzDb0m69+//w033CDyRbgzFh4eLnx9BsmePXtmzZpFM0EJCQlLly7dsWMHnbQhwU033TRkyBBCyOHDh0+cOHHw4EE6riMk+GXEdax2u33BggVvvPGG3W63WCyTJk3KyspavXq1vL80GBQ4aePGjdu6deuvf/3riIgI9v6ioqLU1FR2Mq9iGhoa6uvrm5qa/vznP2dmZlZUVERERIwbN+7VV19dv369v3WYZCTk477++uvCwkI61cyvCUNCrCZoNQjQ4HmQhZhTIaTO7Xb7/v379+/ff/bsWUJIYmKicC1RWFj40EMP7du3r7m5OTY29vHHH9+1a9dvfvMbRf6IoMOYSrAMHz6czn/cvXv37Nmz6cwmyuFwhGj5k3bt2lkslpqamosXL54/f17ImNTX1wul53wbMmTIgAEDDh8+fPTo0bCwsMbGRpPJNHnyZGHYPCwszGQyORyOxMTENWvWBL6mw4cbb7yR3jhz5gz98nZ/TENDw3vvvUcvtdPT0x977DGahr/qKolRfps2bX79619//vnnNTU127ZtowsowsPDU1JS3C++BYGfeULIN998Q2fhxcbG0smShBAfy3NqamrKysqEWdhNTU3CRBZ5vx7Onz/P/iiM9/zqV7+i68WknTR/9e7de+3atY2NjaWlpXl5eZ988gldZnz58uWPP/6YzpSSkclkEq7416xZQzNc7oqLi+lsqqioqOzsbDrzQPYdW4TERFFREU0r0B8vX7588eJF4jp42alTp7FjxxYVFZ05c2br1q108tDtt98uTBgKCwujf1qPHj3ef/9994l6EgizyoJ6HmQn16lISUl58803y8vLv/zySzoAY7FY7r33XuGdysnJoZOaJ0+e/NJLL9GGI7mb0hqd/BkadMstt9AJ22fOnJk/f35BQQENnC9cuPD6669nZWXRh3lMcMjuypUrsrzOtddeS7/da2pq6Owt6rvvvhO5kjMqKor2+KdOnaJbY9xwww3sxItevXrRiW8lJSXCcu7KykpaMWXgwIFfffWV+AP2vWSjV69e9IqE/V1c6ZeGhgahVgGdTksIuXDhgpA5kiAlJYV+NjZu3EhDB2FCsTeBn3lCyE8//UQ/hF26dKFD+oQQ9xknrI8//li44Dt79iwdWLJYLH379hX5S8UQ5mYSQpqamnJzc+ntAQMGCKPiEk5aq4Q/bdu2bUJploaGht69e8+bN2/Lli0LFy7kHimjtm3b0oEiQshXX30ljLyuX7+efvwWLlzY1NR06dIlGiC2b9+engFCyMmTJ+Udjr311ltppH7w4EFh2jIh5MCBAydPniSE9OvXj33TR40aZbFYHA5HdnZ2fX29yWS69957hcCrR48edLJLZWWlkFeqq6tLTU31WBpEDGXOg1yEnkeuU9GtWzf6aTl06BDNSw4YMKBPnz7CrxOuWHr27EnDlOrqavre6QAilWCJjo6eOXMm/WIrKiqaMWMGrdIzdOjQv/zlL/QavXfv3t4upGTRpUsXeu1rs9kqKyvtdruYJaM+WCyWKVOm0D9q9erVdKSxsLDw2WefFV9WRFg7QCUlJbF52ejoaLr0o6KiIiMjo7y8vLGxcePGjXSie2Jiopipu8IFYmFhYUNDQ3V1tcfEbWxsLF1yWVFRsXTp0vLy8ubm5ry8vB07dhBCOnXqNH78+KuvvppO9SWEfPTRR5cuXaqsrFy+fDkdfZVG6HRqamroJ0GYUOyNLGeeLoIghHz33XdfffVVU1PTzp073377bR9P2blz5z//+c+6urrKysqXX36ZVlIR+S6IR/PrNJBav379rl27yC/nX3iMhJPmkcVioaEwIeTo0aNNTU3V1dUjR46k1wwHDhyg2TFCyOnTp+lXAp1ZLMPf6Wb8+PF02vg777yzadOm5ubmkpIS+o5ERERMmTLFbDZfc801NL957tw5WlHj8OHDK1eulPdIBg4cSP/GM2fOLF269PTp083Nzfv371+2bFljY2NERMScOXPYgTQhH0fFx8fTubRUVFTUpEmTTCZTfX39Cy+8cOzYsebm5s8++4yGmH369BEz74ejzHkIkHvP86tf/UqWUyGkzoV72DJCZrNZSAN99tln5eXldrv9lVdecV8pGaIQqQSLyWRKS0t79NFHvY1OR0dHr1ixQug0g6Fr1650rU1FRcWdd945cODAwNPt995777Rp0wghVVVVaWlp8fHxEydObGxsFP+HCLW8iNsAJnGtQ5Ofnz9q1Kg+ffqsXLmSFgHLyMgQ8kQ+9OvXjzbpTz/9tF+/fhMnTqTjohyz2fzMM8/QDvrgwYOjRo2Kj49/9NFHq6qqIiIirFZr7969r7766unTp9O5Czt27Bg8ePDw4cM/+eQTYXKM+1qkVnGdjsViEZNZCPzMDx48mHaLNTU1aWlpvXv3fvzxx+vr6+mRnD592n2x5YABA1atWtW/f3/6VxNCxL8L4g0aNOijjz665ZZb+vTp86c//YnWyKHnX3iMtJPmkTCQ+cYbb/Tu3Xv+/Pnh4eEvvvhidHS0w+H4xz/+MXDgQFqTlM7bnTZtGq2+JTs6XTciIqK2tnbp0qXx8fF0oZnJZFq8eDFtBUI83djY+Pzzz/fu3Xvy5Mlnz56lp+Knn34KJGgWhIeH//GPf6S/8eDBg0lJSfHx8bNnzy4rK4uIiHj22We5M9CmTZvJkycLLXfs2LHCSj1q6tSp9ONaVFQ0YcKE+Pj43/72t5cvX+7YseNLL73EPVgMZc5DgDz2PHKdCpo6p7fZRe/U5MmT6RXg4cOHR40aNXDgwOzs7IiICOFqOfDVACpCpBJE4eHhS5cu/eCDD+655x4h4I2IiOjXr9/SpUu3b98ufOyCpFOnTitWrLjlllvo0ujrrrtOWGsgWXh4+B/+8IeMjAz6BdmxY8f/9//+38aNG8VPiTWbzUJ0wg5gCmgdmhUrVtDdFoXfkpOTI4z6+jZy5MjMzEx6hGFhYddcc423iUG04hb7u9q1a3fPPfds3bpVWI505513vvXWW3379qU7N/Xt23f16tXr1q2jFzR79uxxr93UKqHWp7eT4C7wM2+xWFavXp2amkpX5LZr127q1Km7d++mX0JnzpwRyswLnnjiiVdffZXOsmrbtu3UqVM3bNgg8l0Qb/78+atWrRI21xw2bNjGjRuF8y+QcNI8euCBB5566inarUdERISHhzc2Ng4YMGD79u0LFiy48cYb6Yezbdu2w4YNW7t27Ysvvshey8pr3LhxH3/88eTJk+kskLCwsFtuueXf//733Llz6WGYzebnnntu6dKl9IDbtm1755137tixY/78+YQQukWALF9CnTp1ysrKWrt27a233kpDc6EtzJo1y/2Ka+jQofSzFxUVJSwsF9Dgj301+vn58MMPpS3XUuw8BMJjzyPXqYiKiqLjzYSQxMREbi75gAED3n333WHDhtGpfjfeeGNGRsZHH31ED4ZL6oUck4pvrd1uf+KJJ+i3KXv/hQsXHn74YfdL1UmTJnGPBI2w2+3z5s2j33M+5gaCgD1jVqt11qxZgb+OXGe+oqLigQceoOVbNPVuynXSACC0qLb2p7m5+e23387Pz6fFvFnnzp07f/5827ZthaI9FPcjaAet7EkIsVgsEsZ1Dai0tJTu1+PX2k53hjrzcp00AAgt6kQqdXV1K1eufOuttzyO6Jw/f/7ixYvPPvvso48+qvyxgW/p6em0xnnHjh3Xrl07aNCghoaGjz76iK5AoTuFqn2M2kVXBPz8889r1qyhaxYSExNFnjHDnvlAThoA6IAKkUpRUdEzzzxz9OjRfv36lZSUuD/g+PHjhBD0RNo0duzY7du3X758uaqqihsPa9u27fz580O9EFNQHTt27OGHHxbWVXbs2PHRRx8VOQfCsGc+kJMGADqg9Ixau91utVoLCwsXLVqUmZnp3t04HI6ioqKOHTvKXq8TZDF69OitW7fec889nTt3Zvd5mTx58kcffaSdOQ3a1LVrV1r6KSIi4tZbb/3nP/8pfkqdYc98ICcNAHRA6Rm1drt91apVU6ZM6d2797fffvvwww/fdddd7DxZu90+Z86cysrKMWPGbNu27cyZM23btp0wYcKCBQtkX3EAAAAAGqf0mIrFYnn22WfZMgmcCxcunD59urS09J133unfv//UqVM7d+68adOmSZMm0fqYAAAAYBya2/enuro6LCxsxIgRq1atoot9mpub16xZs2LFiuXLl3vbCKagoIBuBw8AAAChaPjw4R6L9mqu8ltCQsLnn3/+9ttvC2uSw8LCHn744cGDBxcWFnrbxeDAgQPuRatAmpycnLKyMrWPQg/KyspycnLUPgqdKCgoQBuXC9q4XNDGZeRjxEFzYyoeRUVFxcbGHj58WNjGzF1iYqKwnRgEIicnZ+HChZjRHDja8PCxlBFOpizQxuWCNq4MzY2pEEK8baRHa5krfzwAAACgFs1FKitWrBg4cGBWVhZ7Z2VlZWFhIZYuAwAAGI3mIpWUlBSLxZKTk1NaWkrvoQVti4qKxowZQ3dKAwAAAIPQ3DyVIUOGPPnkk8uXLx83btwdd9xxzTXX5OfnV1RUDBs2bOHChWaz5g4YAAAAgkdzX/wmk2nu3Ll9+vR59dVXc3Nzm5ubr7/++qVLlz744IMe1ycDAACAjqkZqSQkJHgs5mYymZKSkpKSkpQ/JCCErFy5smvXrmofhR4MwjnZPAAAIABJREFUHjx45cqVah+FTtx99934WMoFbVwuaOPK0Nw8FVBdly5d1D4E/cDJlAu+WWWEj6WMcDIVgEgFAAAAtAuRCgAAAGgXIhUAAADQLkQqAAAAoF2IVAAAAEC7EKkAAACAdmmu8hsAAGWzkbw8MngweeUV0tRkaWxsatOGLFlC3nuPZGSofXAAoBREKgCgITQ62bev5QbDTPur7GxCCLFaSUwMSU4mSUkkNVX5wwQA5SBSMYTsbLJvHyGE2GwkI4MkJ6t8PADubDaybh2xWv14fHY2yc4mmZkkNRWjLKBReXkkM5PExJCYGHLjjQispUCkYgjr1jkvT2fPVvNIANz5G6O4P91qbfmHeAW0Zt8+Z/ebnIxIRQpEKoYQE+O8feqUaocB4C4z01eMQlM8hJC6uvrwcLPZbLbbyQcfeH4w4hUAXUKkYjg2m9pHAEAI8T6UIkxAEcIUQsjFi/WEkPbt27PPpQkgjtVK8vJIbm7QjhvAH2yXi8y7NIhUDIEdUwHQgrw8kpbGx800NMnIaP0TGxPTMnCSkeEh3MnLI7GxJCsLXwygPlwcBg71VAzhxhudt9FsQF02G8nMJCkpLh9FGnnk5pKsLP8Ca/rE0lI+WLHZSEqKhxEXABWxXTGIh0jFcBCpgIo8ZnxotEEXHksjBDqctDSSkiLxNQFkwUXkIAEiFUNgmwciFVALHU3hwpTkZJKbK8+CiORkUlrKZ3zy8hCsgJrQ5QYOkYohIJAH1dlsJC3NJR0TE0OsVpKbK+fnMyamJYXEQrACanGfiQUSIFIxBK55IMYHhdEwha05GxNDsrKCtZw4NZXPBCFYAS1ApCINIhUjQqQCSqKTW7kwJTc3uAtzaFKJRRcEASgJk1RkgUjFKDBVBVRBR1O4/lrejI83dNoKdzAYWQEIOYhUjALhPKiC3cmBKBimCL+OC1ZoHRcAZWBMRRaIVIwCBfVBedxKH4XDFOGXcsEK3dcQQAHobGWBSMWIkP0BBeTl8WGKv1Xd5EIjJBY3vRdAARhTkQyRilGgkYCS3GeEpKaqWdvefYItN8kXIBi41CdIg0jFKFBQHxTjHqZoYX/j5GS+6BwmrACEBEQqRoRIBYIqM9PlM5aaqn6YQmVkuIzrYCkQKAmb/kiGSMUosEoZlMHNV6XTU7SDq+OSl4ccEAQR1v7IApGKUaCRgAJo9RSB+1RWLeAiJ25XZwAZ4aMlC0QqRoGC+hBsXJhCCMnI0GKI7HEpEIDssOmPXBCpAIA8uCJvqany7JAcDMnJfA4oM1O1gwGDQKQiGSIVA8FUFQgem81D9RQt42rQWa2YsAIywyQVuSBSMShEKiAj9+kpGg9TKO4gMawC8kI3KxdEKgaCoB6ChFtBo26RN/G4CivIAYG82FL66H4DgUjFQLD1DwSD+4CKRqqniMFVWLFacR0MQYFIJRCIVAwK3THIJRTzPiwursI6IJAL5qnIBZGKgaCpgOy4vA+3piYkJCe7rFFCLTiQCy4I5YJIxUCw9Q/IK0Qn0rrjNnnGsArIDqX0A4FIxaAQqUDg1q1z+SCF0PQUd+zB22yYWgsyQPZHLohUDAT1VEBGXAEVLocScrj1SiivAoFDNysXRCoGgoL6IKPQXe/jDcqrgIxQSl9GiFQMBE0F5KKDibTuuHk2mFoLMkL3GwhEKsaCBBDIgh1vCN2JtO5SU13aCIZVQDJMUpERIhXjQqQC0mRnuww26CDvw2L/nLw8kp2t2pEAAIVIxVgQ2kOAuHUxMTGhPZHWHTe1FsMqIA3GVGSESMVYUFAfApSX59IF6ybvw+JWLGNYBSRABysjRCrGhewP+Isr9aaPibTuuL8LheBAAoypyAiRirGgwUAg1q1z+VFnM1RY2AwIAoRIRUaIVIwFBfUhEGypN24+h85wwypIAEEgUEo/QIhUjAuRCviFK/U2e7Z6h6IIbgoOhlXALxhTkREiFWNBPRWQhptYqtcZKixuWVN2NpoM+AGfFhkhUjEWhPYgDbcyWcczVFiorw/SoJS+vBCpGAu2/gEJ3AdUjNPzYlgFAmec9hIkiFQAoBXGHFChMKwCEmCSirwQqRgO22ywARu0ysgDKhSGVQDUhUgFAHzhBlR0v+THHTeGhGEVaBXGVOSFSMVw2CUbqPcMvhlwyY8790VAAL6ha5UXIhVDwzg2+MbmB405oEJhWAUkw5hK4BCpGA6aDYhkkF1+xOCGVdhavQDukP2RFyIVw0FBfRAJAyosblgFOSDwAV2rvBCpGBqaE3hjs7nsRzh0qHEHVChuWAXF9UEkbPoTOEQqhoOC+iBGXp7LmMoTT6h2JNrBjSphWAW8QfZHXohUDAfNBsRgB1SMPEOFxZ0H9hQBsHARKC9EKoaDgvrQKm5ARYWitHR5dFoaSUkhJhMxmdp36NC+QwfFj4PHDqtwZwmA4jpVRPmBM6t9AKAg2oAwqAKt4aq9KdfV0tkxGg4BUlNJZqbzq2jdOnwPAQQdxlSMITaWmEwkNpbExpLsbBTUBx9sNjUGVGw2kplJUlKI1arxDyV7QlBcH9xhkorsEKkYAwrTgmjcgAq74CUoaIwSG0us1pD42k9Ndfn6QRU44CBSkR0iFeOx2RC3gDfu5fOD/vvoOIo7mnayWkluLikttX/77cXDh4N8NGJhz0LwAZ2q7BCpGIP3wB6dLLC4am/BTf3QoRT3j2BqKo1OSG4uycig2zc3RUdr5/qUOy1YBATeaOYzG9oQqRiDa2FaNB7wiOZhBMnJQe5nuaEUmmrKzSVZWdqfp4ri+uANF+5D4BCpGI/NhoL64JHN5vJ5CHr5fIfDeTsmRv4Yhc4iD878XFSBAzFQoFYWakYqdrt99uzZ6enp7v9VXl6+YMGCvn37xsXFjRw5cv369Y2NjcofoX54L0yLSAUE3ICKEuMaDgeJiSFWKyktlfny02Qi5Jd5MEEIVlAFDrzBjFrZqRapNDc3v/322/n5+e7/9f3330+aNGnnzp1DhgyZNGlSU1OT1WrNyMhAsCIXFNQHd+osTiaEZGUF/ZcFJ1hBFTjwCJ2q7NSJVOrq6l5++eUVK1Y42OFfQgghjY2Nr732WnV19apVqzZs2LBixYrPPvts5MiRmzdvLigoUOVo9cD16jiG2Ngf0a6AqFjtLRi/yWYjY8a43BOEYIVbroxhFSBu3SnGVGShQqRSVFQ0Y8aMt956q1+/fpGRkdz/lpSUFBQUJCYmJv/Sf0VFRS1cuDAiImLr1q3ukQ1IgMYDHG5xctBrqARbTAzZtYuPgYITrAgwVQXcobOVhdKRit1ut1qthYWFixYtyszMDA8P5x5w7NixqqqqoUOHtmnTRrgzNjY2Ojr6u+++++mnn5Q9Xh1xTfkgAQQsbrVC0OfSKiM3N9jBCpe2QrACmKQSDCqMqQwYMGDHjh1PPvlkRESE+/+eO3eOENK3b1/2zoiIiPbt21dXV9vtdoWOUt8wqRZcsZmLmBgd9bC5ufwAkdzBCvvyqFcL6E6DQelIxWKxPPvss7179/b2gFOeyvu1bdu2a9eudru9uro6mEena65fPuxPqKhocOrvnBxUWVl8wZO0NBlfnh1/4mYlgwGx3al+In61aW4vZY8LfEwm01VXtRJU5eTkuE+5feaZZ7p06SLbwYWyDl26CHOC7IWFXbrUE9Jyx7Fj9WfPOtNqFRUVJpMpLCxM8WPUm4aGhqqqKrNZc62M84c/dBK6gujopj59Ks+eVfeIPLh06RIhpK6uTsqT583rsHNnpNA/2GxNo0ZVbtoky4H16UOiozuVlbWcwNdfr+/TR+tJarRxubi38ZqaKEIs9HaXLi5dKwjOnz+/fPly7s7y8vLJkyd7fLzm+lD3mSuEEIfDceXKFd9PHD58eGJiIndnr169ZDuyEGdmTmzk+fNssB8ebo6KihJ+tFgsFotF+9+v2mc2mxsaGthzq0E2G8nPd77XGRlEmwfc3NxMiPRja/rsM3LvvcKIhzk/v9PUqfWffCLLsT33XNP8+S3ncOPGyOefj9L4xTTauFzc2/j5885lIr16mbXZmlQXFRU1ZcoU7s4PPvjA2+M190m90VNJv9ra2nPnzlkslnbt2nl7YnR0tLdwDAghhAnazGZz377O5lRWZrZYLMKPv/rVr9CLycJsNtfX17PnVoMqK523Y2LInDlm4YpQU5qamgghAZ3MrCySkiLMIzDn51v++ldZcl2PPUbmz3f+eOiQZcCAwF81iNDG5eLexsvKnP8bHm62MPExsVp1l1uVzv37uow9d640V02fRionTpxg77x8+fLFixfbtWun8U5f07yX0McUMMOy2cgLLzh/lK2yiTYna9CC/SyrVa5DZb+AHnlElpeEkMR2p0lJrv+H0vpSaS5S6dWr13XXXVdQUMAmpE+ePGmz2fr379+hQwcVjy3kORwt/3JzsUoZiNsMUHkWJ9tsJC2NmEwt9ew1xT1YkWl2LRfkaTNUAwXw3SlWLctBc5FKdHT04MGDCwoKdu/eTeu81dTUrF69+sqVKxMnTjRpsO8LFa5rNdFkgARpo5/MTGfvrMEGm5zsEqzIFKdjGyAgHgvU4kJQDpqLVNq0afP4449HRUUtXrz4oYceSk9Pv+uuu/Lz8ydNmuQ+YRYk4yIVtCYDCsqASna2S/kz5Wry+4MNK+Qre82ewOxstCng9y3BBaJkmotUCCGDBw/etGlTUlLS119/vXnzZrPZbLVaPRa0BbmgVzUgri6tDBX0ad6HfdGsrIBfNDiysloyofLhTiASQAbUSqoHkYpUas79TkhIOHLkiMf/io2NXbt2rcLHYzQxMc52hUjFgNgMhQxjH1yYQgjJyNBu1xycA0tNdY4opaWF/vZJECBMUpGJFsdUQBloOEbG1aWVJ/XDvmJqqgG/qLnTiGEVo9m3z3kbHayMEKkYFwrqGxk7lzYmJuAxFZuNxMa6vKJm8z7BlJzs0qwwr9boMKYiE0QqQAiyPwbDzaWVYewjVKanBB9bWAVbKxsN25EmJ+MSUDaIVIwLIb5hcXNpAy2bmZ3t8oqyLXcOSVzYh2DFUFBMJUgQqRgXWy8RCXVDYbMSgfafNhufSTLwgArFBitIABnWjTciUpENIhXjQplaY+JSP4EOqLB13ghBmEJca6jn5aFxGQgikyBBpGJcaEjGJOdcWpuNr/Nm4LyPIDXVpXGxJxx0zGbzmf3hNwECPyBSMS6UqTUgLrQIaC5tCNV5Uxx7YjFVxZgQtMsIkQqAgXDxaECXee4riDBM9wsup4ZgxQg8pH5w/ScTRCqGxn6zYFKtEci5JSE3oBLohBe9Yc8tWxAMjMLDdoUgESIVQ0PbMRSZtyQsLXXum8PuTqwnAcwxwYaFRsOPqcTEuOwthd42AIhUDCY2lphMLf/y8lCm1lDk35KQEOJw8JVZ9YG2EatVcoiBDQuNxmsXKvdemAaESMXAXLtgXPPpnpxlVFg6G1Cx2YjJ5PwxgGEVFFYxFL5ALcgHkYrBuI6i6O9KGLyRuYyKjnHDTVwFXn+gsIqh4P0NHkQqBuNa7o0tU4tmpm/cgAqu+XzhlltLHQ9BYRXDYrtWCBwiFWiBPLq+cTvzQCusVuftAIZV2FONtcr6hgK1wYNIxWBcGxCak0Hk5cm66scIMjJkGQ/hTjWuB3QMw9LBg0jFYFzzPdy1NVqaXiH1IwU7l4eL9UTj1kVhXq1eoXhKUCFSMTAEJsYgZwV9Q5Fpmgkb8CABpFeIVIIKkYrBuG2gjDK1uselz7Hqxw9yDKtwoSGCFd1DmCI7RCoGg20JjYfbPBn8INOwCirr6x6m0wYVIhWDcWtDbB+KMrX6gzIqgZJjWAWV9XUPnWdQIVIxHrcEkJefQA+4CvqYS+s3OYZVUFlf9zCmElSIVIzNZkOj0rdgVdA3FLlnqyABpD+IVIIKkYrxuDYjlKnVMXlSPykpLvvgGJAcwypsZX0kgPQNBWplh0jFeLxv/YPeU2dkSP0IQwh0b2HDCnhYhYt2kADSGYypBBUiFWPDPBVdY1M/EmeoYOEQxQYaDoe0s8k+CSXgdAadZ1AhUjEe1+8blKnVKy71I6WCPhYOsTIyiMNBHA7JL4CtlfXKQ9k3mjOl/7A1ZcAQqRgPZqYYgwwV9NPSXF7C4NVtA/7zsbWyXnGpH37wEfNWAoZIxXhSU1suDR0OkptLUKZWpwLdPJkbUDF4mCITbK1sFJi3IitEKoB2pEMybJ7MzVAxeOpHJthaWZfYZect3SmGq2WFSAVcIhVUetAHruv0e0yF29UQBeNkgq2VjQjXggFDpAJoRzoUaN6GW98sZUwGPGPfDiSA9IHPtGJjZbkhUgFMsdWbQFM/Npsc03HBMy6NhgSQDmGSitwQqYALRCo6wIUZfneVXKSDGSpyQwJIZ9huk12LDnJBpAI+tiyE0MPNMJGS+uEKxmFARW5s7IcEkA7w3aaHGbYQEEQqgOJvusK9fX5f4WFAJfiwtbKeYFKKAhCpAOhKoDNM/vSnwJ4PoiABpBvl5Wb2x5gY1+AFLUgOiFSAENd+88CBSNWOAwITaOrHZiN79jh/xIBK0CABpEsophIkiFSAEIxY6kWgqR9uQAZ1aYMGCSDdKChoI9z20JGilL4cEKkAIa4NrKwsXLXjgMAEOheWbsInPB+CCVsr6xZWKcsNkQrwysrMrT8ItEe2urJ0TyhUexOPbpnrZxaHPcFIAIUutsNsaXTI/sgNkQoQ4pom4CaIQagINPXDwZiKGCkpxGRque3nwAgSQPrAd5hYCxQEiFSAhzGVEIUyKCpgB0a4Bd4iIAGkA2yHmZTklvpBpCIHRCpACD9PBZFK6MGWgupITQ1kwTESQDqADlMBiFSAkOxsLu5H2ws5Mqd+QDxuwbE/cxS4BBCClZDDdZUxMYQkJ7fM9HI4SGmpSselN4hUjCotrWUaoMlETp3CCGWo++c/nbeR+lFUYPNN2HeKLcIOoQgdaZAgUoGW63G2jWFyX2ix2cj77zt/RME2pbHBSlqaX09FCbiQxo6pIEwJHkQqRoVWpSNYFKkybkW3P5E+N/qFi4TQgsopykCkYlRs5USbjbj2mKdOKXw0EBCs+lEZd9L9nFeLFUChC12lMhCpgIdLclyjhxCs+tGErCznbT/n1WIFUOjCXoTKQKRiVOxIpc1GsFokZGHVjyZwQ//+ZHFQAi504aJOGYhUjIqL/10bHPrKEILUj1YEMK82gJosoBXYizB4EKlAC7dBFggNbFiJMEVNAcyrxQqgEMW+yZhRGzyIVAzMdV0y18wQrISEvDyXdwqpHzUlJ0seG0ECKBRhhx/FIFKBFmhmoYitFRYT48+Yis3m3FoP5BLA2AgSQKEOXWjwIFIxMLd1ySj+FnLYt4m7Lhf1TFqkGOQSQHl8JIBCDoqpKAaRChBCkOwJSdzevf6lftjL9pQUmY4IXIMVJIB0DZGKYhCpGJhb20Lxt9ASUOqH/SZE+X0Z0YCRblCXm+vXU5EACi3oJBWDSMXA3MrUsjDIon3SUz+Zmc7b/sU40JrUVOJwSHsq+z4gAaR9KPumGEQqQAjxsEkhaJ/E1A9X1Na/GAeCiFvmjKsFjcMbpBhEKgbmVkGFHWRBmlzjpA+LcCUgsLJZM7hlzuxbDBrX0nnSKer0H/pQ+SBSMTC3Cioo/hZCpKd+2BkQcXEYttYUJIBCCF/2DfVVggaRioHFxLTM+6P/YmLQskIFNyPWv9QP+8w//EG2YwI5cG8lLhg0q/WwBP2pfBCpgBPK1IYKdljEv9SP9GeCElJTUdYoJPFjKghTZIVIBVwgARQSpO/1g12CNI99W9iF6KApHsIS9JhBg0gFvEK70yYugcMtGPGFKxXnxzNBOWwCKDsbzVCjPLwvbH0VjKnICpEKuEDxN+3j5vEh9aMzSACFhFbCEkQqskKkAi569XLexsWcNnHxhlgooxI6kADSPrZ7HD3a7S5EKrJCpAIumprUPgLwSXodfC7wRBkVDUMCSPvYN6Wl28T7FDSIVMAFir9pnPTUD1tHLDkZqR8tw26F2seGJS2RpYe7QB5ajFQuXLgwfvz4ODfp6elqH5r+Ye2PxklP/WAubUhhgxUkgDTIQ/eIHjNotBipnDt37vz5823bto121aFDB7UPTf+4K200PU2RnvqhVf6E25ikonlcAgg0xUPZNxSoDSaz2gfgwfnz5y9evPjss88++uijah8LgIZwM/b8TuDQYCUlRbYDAr+YTCQ5meTminlsaipJS3P+mJ2N8FJDuJYYE0OIzfURiFRkpcUxlePHjxNC4uLi1D4Qg8IKSc3idiWUSNw3JcgmO7tlyzpCSF6e+IFKrAAKJVj4E0yai1QcDkdRUVHHjh2jo6PVPhaDio52rv9BSRXtwFSTUMUVSBG9RTL7FiMBpCls4Mh2mBAkmotUamtrz5w5ExUVtXnz5pEjR8bFxSUkJCxZsqS8vFztQzOK7t2dDQ/zVLSDey+QCwglkrZI5t5iBCvawTbGlg6TDV4wpiI3zUUqFy5cOH36dGlp6TvvvNO/f/+pU6d27tx506ZNkyZNOnLkiNpHZwi4RNAmdtUPlhiHGG4ETHRWFQkgbWIjFXSYCtDcjNrq6uqwsLARI0asWrWKLvZpbm5es2bNihUrli9fvmbNGovF4vGJOTk5OTk53J0rV67s0qVL0A9aX371q8uEtJzk3bubTp8+q+7xhK6GhoYLFy7I9Wq7d3cTGuwtt9hPn/5JrlcOCdXV1SaTqaamRu0DkaRnz27R0eayMvpT/euvV/bsKeZ5EyZE5uV1orezs8kLL5yW5XDOnj3b3NwcFhYmy6sZUH19J0Ii6e2oqKrTp38ijzxCHnnE+YjT8rxTenX+/PnFixdzd5aVlS1cuNDj400OYe2ihtXU1KSmphYXF7/99tuDBg1yf8Arr7zi8Y/s2rWrIgcYwsx//jOxWuntpocfJllZH3zw44MPOs9bYyOuGCSqr6//8ccfZZlxlZdH7rrLeV3x2WdNRhtWuXjxosPhCN1SBea5c9n8TVNjo8gnhofL/76XlZV17drVbNbclWqoYN+Uf//73JQp16l4MCHq3Llz3D10rMFjsBIan9SoqKjY2NjDhw9XVlZ6ewytuaLkUekEU7fBnJ9PzOYRI1z60LIyM7Ku0pjN5rCwMFm+D/7zH+ftmBgyenRotFwZ0dMYwl+uWVlspGLOzxeZw4uJceYa3n3X3LLFTGDoxzKET6aquBljN97owJmUwK/va83NUyGE2O32hoYG9/tNJhOGK4MLE2i1ip3YgLm0oYoN+dlpRz5JmowLQcRNUsE8FQVoLlJZsWLFwIEDs7Ky2DsrKysLCwuxdDkoPA2YsG0PJVVUx61Pxo4ioYotKiw66ODeblxNgAFpLlJJSUmxWCw5OTmlpaX0nrq6upUrVxYVFY0ZMyY2Nlbdw9MhLlKx2dzvA3Vxe/0YbYaKfkhadsxVY8GVg+pQTEV5motUhgwZ8uSTT5aUlIwbN27evHnp6ekpKSkbN24cNmzYwoULkQ4MCrdtCdk7sDZSdeyXE8KU0CZp2THWKmsWu/k8BI/mIhWTyTR37ty33norISEhNzd38+bNZrN56dKla9eu7dSpk9pHZwA2G0Hz0xKUptUVSXVnud0KkQBSF9seMfysDM1FKoQQk8mUlJT0/vvvFxcXl5SU5Ofnz50711sZFZABe8l26hTB1j9awnWLGFMJbUgA6QsiFWVoMVIBNbllf3ABpy5ukopY2DBZs9hgBQmgEIQxFeUhUgEPrc3TLFtQAZf6YdeOtP40un8v3cIXtINLAIlrXVwCCNTCvV2IVJSBSAVcp6Vg7Y+WcDvJi0394KJPy7h3UdwbhN0KNQKRiioQqYCrX77kkBfXgldfdd72o0+UmDECpaSmEoej5Z8/TxIgAaQFaFuKQaQCnle+ohGqzmYj7J6bYlf9SMwYgYJcK1uKJGnZEMiMjRHRSSoGkQq0XvwNF3Cq4MaZxRbRx2IhneLeSYx0qg6RimIQqQAhxKXNmcvLCRqhBrABoh/xBlI/+sV+DERvHARywhwwVSBSAZ65rIx4mGULSpNSmhapH11DAkhTaCcZuXEjVtgFGyIVIIS4fBOGl5Vx/4lxZuVJ3JUQqR9d4zKAuIRQnvuYSkuHSSsCoI5RcCBSAR4dU+G+49AnKkziroRI/egd+65mZqp2GMbU+hJlNLrgQKQChBBCsrKEZZM//e1vBC1Obeylm9i5tEj9GAAbs+L6QV20k4w8cIC/C+SGSAW8QkkVtSD1A96wH4a8PAQriuIqMXqAzV2DA5EKeIXLA7VIDDnY1A/CFJ3CboUq8lhMxcxO7EOnGRyIVMArlFRRi5SQgxuHEVsnDkIPdivUDnNZmdltCQLIDpEKeIXLA1XIEHIg9aNr3G6FSAAppvXCAWh3wYFIBbxCSRVVSNyVMC3NeRvdpa5xM6yRAFIF7R6R+lEGIhUQBb2hYtilp2K7PqR+DAa7Faqi9Rm1EByIVMArXJkrT2LIERPj3JgXqR8D4BJAoACbzdPQMnYsVAQiFfDK08aFEFwSdyUUOByktFSugwFF0SKnbBbPO+6DgWBFeR4uBxCpBA0iFfCFbXqIVBTw2WfO2xgZMYrsbOfGMaKnyLIfj+Ji2Y8JeJ5TP9ixUBGIVEAsRCoK+OIL523MNjEKSVNk2RLEL70k49GAZ63neVD2LWgQqYAvqNygpLw8XKEZlf9TZLEzlyZgkq0iEKmAL2h6SuIu2pD9MRBJNVKwW6GSPBdTQYSoCEQq4As7nImFysEmZVdC0AdJCSA2lkXzDDY2JmkJLFvfWxnkgUgFfMGMWsVI3JUQdMP/BBD7IfG8hhZk4vn0cqkfRCpBg0gFfEEuXDHYCNno/E8AYbdCtbQ0z+Tk+rq60//7n7oHYwSIVICRkkJMph433GAODxdKNKArVAY2Qja6gBNHnOInAAAgAElEQVRAmPMePK1MnEUdoyBDpAIM7J6sElTDB0ICTQBht8LgQSladSFSAYanJoiLNgVI3JUQdMb/IvnYrRCMoCVSqaurKyoqamxsVPdoQGWedk/GBYQCpOxKCPojqUg+ditUgOclyqCUlkilpqZm7ty5Q4YMefrppw8fPtzc3KzuYYH6folUsFA52JD6ASd23x9JCSAINpSiVV5LpBIZGTlw4MDGxsacnJzJkyfffPPNL7zwQmlpqYPuzgoG4WlRMhYqBxt3VnHFZmh33OG8jQSQZqB4tLpaIpVrrrlm9erV33777bp16379619fvnw5Ozv7zjvvvO222/7617+WlZUhZDEET4uSsVA52Ngr5+Rk9IPGJikBxDZSdhEZyAIF3lTnMqM2PDx81KhRa9eupSHLhAkTLl68+I9//OOOO+4YPXr0m2++WVlZqdaBgoowrBJUUlLgaWnEZHJuwAt64v8kdjZjiASQ7FDgTXWe1/7QkIWOsuTk5Dz44IN1dXXLli1LTEwcM2bMBx98YLfbFT5QUEhr5VMQqchLSmlam835dWQyYccXvfE/7sDeC0GFXQhV18oq5YqKikOHDh0+fJiOpjgcjhMnTvz+97+/7bbb3nzzTawV0iEsVFYWO1Yvdn0yFy2i8L7OCHGHw0FEp92xW2HwnDql9hEYntn9LofDUV5evnHjxi1btpw5c4YQYjKZBgwYMHv27LvuuosQsmvXrr/97W8vv/xybW3tb3/7W6UPGYKK7fCuXHG/D+QlZVdC7Lmse/7PC0xOdo6/5OWRjAx5D8jQsERZdc5IxeFw2Gy2TZs2bdmypaKigt4ZGxs7ffr0KVOmdOjQQXjklClTevToMXfu3E8//RSRip7t308eeYRgoXLQSNyVEHsug5ukJJdIxWbDBUZQYImyKloilcrKytmzZ//www/0x+uvv37GjBn33Xdf9+7dPT4tNja2Q4cODQ0NCh0mKIbt8LBQOcik7EqYl4c9l8FdairJzHQ2z7w8BLGywRJl1bVEKg6Ho7a2tmPHjvfff/+sWbO6d+9u8rmsoLGx8cEHHxw8eLAiBwkq+aWBui9URnOVBTdJRRSkfsALNgG0bx8iFXlgibIWtEQqUVFR7777brdu3cLCwsQ8rXv37o899lgwDwxUIuKbD5GKLLjUj9iJBUj9gBfseGh2NsnKUvNgdANLlLWgZe1PmzZtoqOjRYYpoGdcQ0QCKGik7EoocWILGIKkonHQCs/dnc1GCxpFtmmj8PEYE/ZSBjeeSqqw36NYsycLKbsSSlnTDAaC3Qplx3Z3znbKxC892A0QIDgQqYBPv/R8GFORl8RdCbFcEnzCboWy89zmmE6wKTpauaMxKkQqwDv9+edNjY1c1Sl2bR4ilcBJ2ZUQey5Da7BbYVA5u0EMLCsLkQr4Dd1f4KTsSihlTTMYDnYrlJfnJcrMpUb98OHKHY1RIVIBUbhrNQyrBEhKGkfKmmYwHOxWKCOvS5TRAyoLkQpIgXYaCIm7EkpZ0wyGg4sKGXldosz8R11ionIHZFSIVEAsTKqVS6C7EiL1Az6xTRUJoEB4XaKMHlBZiFRALCxUlouU4m1S1jSDQbFNFbPKAuF5ibIrzFNRACIVkAJXFJJJLN6Wm+tcjYXUD/jEfqjoboUgDZYoawQiFRCL7f7Q90kW6AoehwOpHyMymVr+iZglm5rqsXwjBMS5RBndn+IQqYAU6Pskwwoe8FtKivO2uNKzbDSLYrWSeV6izOSEMKaiDEQqIBbWFAQOK3hACv9XHnPFatFaJRC1RBl7bykCkQpIhL5PAqzgASn8Lz2LYrWBE7NEGZSBSAX8gIXKAcIKHpDI/5XH2K0wQF5PGtv34WpDEYhUwA9IfgcCqR+Qjo07JCWAIBAu1xW4SlMcIhXwA4YBAoHUD0jHzYcQ8WXJJYAQrPir1SXKhKBPVAgiFfADu6MyOj5/YdUPSMftYylu4gkGQQPheeIs+y64zF6BIEKkAq1hSjhwwwAYBPWLlF0JAQT+xx3YrVAyXxXzaQ1Gh4OUlip5SEaGSAW8SEtrqTRFnPUDcP0gGVcqFGsbwW9c3OF/AggrgMRDrlZTEKmACEyrRe1LadhrYHR8IIWkBBB2K5QGA8aagkgFvPBSPB+Zb2mk7EoIwPG/+bHPQAJIPDF7E4JiEKmACF7GVEAkibsSAnD8X3ns/5ohIASzyjQGkQp44aXKG5b/SMCt+kHHBxL5v/IYuxVKg1llmoJIBbzwss4HYyoSSLk+S0lpmc4MwPK/9Cwytv7ytfAH1IBIBcT5peFiobK/pJSmFZ5Dl19h8AoE/ieA/F8zBC4wCKo6RCrgnZcEEAaT/cJtHC9qUAp1MMEbdkzF4RDzDElrhgyNW6IMqkOkAt6xlxLMVHgvd4NnUkrTsmP0ycm4pgMXQuUx0ZAA8gtXUwBUh0gFxPEyZIyRZN8k7kqIhQcgKy5lhGbrG9qf1mg0UikvL1+wYEHfvn3j4uJGjhy5fv36xsZGtQ/KeLxcTbC9HkaSfSsvNwu3xa76wZpmkBu3ZujAgUh1jiMEsasdQS1ajFS+//77SZMm7dy5c8iQIZMmTWpqarJarRkZGQhWlMa2Uea708v0FfDglVc6CLfFDiNjTTMEARusFBS0Ue04NI+7UkD2Rws0F6k0Nja+9tpr1dXVq1at2rBhw4oVKz777LORI0du3ry5oKBA7aMzGC8hCZb/iFRWZi4ocF68IvUDKmLH5nJyLOodSIhBE9QCzUUqJSUlBQUFiYmJyb98QKKiohYuXBgREbF161aHP5PIIFDeQxIsJRCjrCzg1A+7wBQgAFwC6J13zJ4fZ3hY+KNBmotUjh07VlVVNXTo0DZtnOOTsbGx0dHR33333U8//aTisRmdl2EVLP/xJjPTeVtKl4fUD8gKK4DEwMIfDdJcpHLu3DlCSN++fdk7IyIi2rdvX11dbbfbVTouoxIxJwXZH4+4wRGxIUdamvM2ukmQFVcCDjzy2mzz8loqMZpMJDZW4aMyOM1FKqc8XaG3bdu2a9eudru9urpa+UMyNC+DJ142WgYn7rSIWsEjcU0zgChcAgh5W/9gsEU9mktVelzgYzKZrrqqlaCqrKysrKyMu7Nr166yHZlhNDc3NzU10dv089EkvCm/3M9+cvLySJPzfmixb5/zFEVHN40cSVo9SWYmummKjiZinmMYTU1NDocDn7QAxcQ4P2X/+lfTyJFqHow25eU5W+6IEc5PnJmJ7JpGjKBts+kXih5i6KPJE/E0F6mEh4e73+lwOK5cueL7iQcOHJgxYwZ358qVK7t06SLbwRlDRUUFISQsLIwQQl54gbzwAjl7lnvMnXcSQnoIPx46VBkdjbbqYufOToS0LPyZNq3+7NnWp1h1WrrUuVIoJuas22k3surqapPJVF9fr/aBhLYnnoh8+ulO9PY775hfeum0usejNTYbYXu2tm0rz55t6dk61dcLzbO+vv6ns2cJIQ0NDT/99JPZrLlvUu176KGHuHvKysoWLlzo8cGaO783eqqzU1tbe+7cOYvF0q5dO29PnDx5src/EvzVrVu3VtteTIwzwXH8eLfbbgv2QYUSm42wa+rvucfSo0dr60Jdn2N+9NEePXr4eLjRREVFEULat2+v9oGEtvR08vTTzh+bm3sgj8E6edJ5OyaG3HZbN+fPzDCA5Z57LD16EELq6+uvvvpqNFUJPv/8c+6eV155xduDNTdPhUYqJ06cYO+8fPnyxYsX27VrZ7GgDACEAK5ylNj1ySx8gUBwsJ8stsogEB9zUWw2zMhTkeYilV69el133XUFBQV1dXXCnSdPnrTZbP379+/QoYOP54KSsOLRB/YLYO1acc/BroSgiOefd962WlU7DG3yWkyFC1PQPJWluUglOjp68ODBBQUFu3fvpnXeampqVq9efeXKlYkTJ5pMJrUPEFpg+Y833AoeOuGndRkZzg1y0Q9C0PTs6fIjGi9LVNk3jHcqTnPzVNq0afP4448fPnx48eLF//73v6+//vr8/PyKiorp06cnJiaqfXTgGZY7sgLdtweFmMFfwiVcaWmr36PJyS6TzNatw3J4J697g2KJsqo0N6ZCCBk8ePCmTZuSkpK+/vrrzZs3m81mq9WamZnpcVkQqIWrzYArMwHb2Q0fjrUqEGRsFTJxFw3sxxKXGQJfU8XY/8OQp+K0GKkQQmJjY9euXfvDDz+UlJTk5+fPmjULYYoGYfcfd1zqZ8qUGtUOBQzC/yljiYkukQouMygu9eNrngooS6ORCoQETKp1x6Z+oqObMKYCQcdmKbKzxXynTp5cwxZAwmUG5SvDw55VUQWnQU6IVEA6pGvdsZ3+iBGohgfBl5oqYXiTvczAWmXK644/WKKsNkQqIB1bpQ8bnhG31A83lQcgWPwf3mTHBZAAosSOm2CeiuIQqYB0mFTLkVLwDSBwXAJIBEkDMXrma9xE1NplCCJEKhAQdHYsdhQdYQooh7toEBesYJ4Zi4tGXNovliirDZEKyObUKbWPQFVc6mf2bNWOBIwoJcV52/8EkLiZuHomdjotIhU1IFKBgLBXHgbv6ZD6ATXNmuW8jQSQ/7xOpyWIVNSHSAUC4n9+XLe40rQAiuISQP6vAEICSMCuFSCEkNzclp0uHA4U9FUFIhUQwWYjJpPzH4P7SjbysAr71YDeDFTg/y7JSABRXOoWVxpag0gFRPAejyDHQbHjSUj9gDrYAFl0Aohl2ASQr+m0oAGIVEAc7wltpLqJ6xXsLbeodxxgZJJGONlgxbAJIMP+4aECkQqI4308FKlubuj4ySdVOxIwNLpLskDcdQMSQARTZjUPkQqIwzZf13iE7emM2c1JXPWTkuJx6g+AdP5fNyABRLBTsuYhUgFxxF1oGLObk7LqhxuHMeaJA9lJGiExeAKIa4vYf1CDEKmAON73+DF4TX2umxO76gfVVyAYhBopdEmtuMAZCSAW2qIGIVIBcXx2eUaeVCsx5ED1FQiS0lLicPj1DIMngDBJRfsQqYA43Dew62WXkSfVStnrR+I4DECwGDkBhF19tA+RCogmbqGyoUjc6wfVG0BjjJwA8lVHH7QBkQqI5j0e8T6JReckpn4yM12eBqA2I+8BhOm02odIBUTzvlDZsJNqZUj94CIOtMGYOVyus8KFgzYhUgHRMKnWlQypH4KLONAKYyaAuEwsIhVtQqQCorE5HrdghL0gM0hr55bviB0cYS9Xk5MxpgIaYeQEEGWQjisUIVIB0dh27HbBdcMNztvitnENeRJzOEj9gFaxn0eDtGJ2zhjfHG02kp1txJBNexCpgGg+FyrHxjpvG2FSrfTUD+bvgVaxn8e8PEMkgFppjmlpzl0vQD2IVMAf3keHjTapVmLqR+LTAJTAJYB0P6zSynRalITTDEQq4A9a/pL+42ITg02qlSH143YCAVTHfpitVrWOQiFclQE+GkFJOM1ApAKyMc4qx7w8pH5An7gPs74vOVrZ0wJTyjQDkQrIhlvlqGPctZbYTgy7EoLmJScbKwEkQHPUMkQqIBvuokSvU1XoggCBHzkcKXXiAJTGfqR1fMnR+hAnRkA1A5EKyIb78tXruLHN5hKE+dGD5ea2TPEh4jNGAPIRd/XA7Zip44Ys8DDEieK1WoJIBeTEtvZTp1Q7jKDiCjBIGRxxODCmAsqhi2xNJvFBhxEKq7QyXxbFa7UEkQrIyWdxOD3Apj0QYtLSnLdFT3Rnh/z0mgBqpSFj4Y+WIFIBOel+Ui13oYUcDmidpDbJzb7SZVtuZRYKiqloCSIVkJPu67+xqR8MCUMIkBp06LvoQOuzUBCpaAkiFZCZjuu/cakfbuIhgEZJCjq4BJDOrjq4SiqtFFPBwh+1IVIBmen4Ugz1UCAkSZp1wo3F6Oyqg2vLPCz80RhEKiAzHU9VaaWiJYA2SQ062Ofp7KqD5eGSAwt/NAaRCshMr/XfuNRPVpZqRwLgN0l1Z/WaAGq95hsW/mgMIhWQmV7rv7We2AbQLEl1Z7nK+ux08pDWSs030B5EKiA//Q0ao4wKhDZu3ED08Aj7UddNMrf1ERO0do1BpALy0994AxepoIwKhBjX4ZGonByRz9Pl1sqtxyHCxhcOB9b4aQEiFfCfzeasz20yuV+f3Xij87Y+rsO4Miq4yoLQw3xqIw8cEP8knVXWb32SCmgPIhXwX2tjJjqr/4YyKqAHzHdyZEGBuaxM5PP0XVkfVx0hAZEKSNJafTc91X/jSi9wcRhAaEhNldYsdVZZH7UGQhEiFZCktfpueqr/Jrlrixw3rscNN8h9OABSSW2WbLAS6gkgTJYNRYhUQJLWvrF1U/9NeupHeCadzRPqI0ugA1yzFJ2XZZ+XlxfC+VxMjQ9RiFRAktYmzepmxJgbUPHjIgy190FrmGbZ1NgofoSQSxyFbmEVVFIJUYhUQBIRTVwHCSCbzSXG8q9fQz4cNMjhIA7H6f/9z9/n6aOwCmrPhihEKiCJiJr5bNcWuqkP9i/zY6wY64VAX7iPcIgmgDBJJUQhUgGpWltHwCaIbLaQ7NrS0py3ucISfsAoM4Q+7lMcigkgVFIJXYhUQCq23zp1yv3/pS6K1IqAJt+xMQ5GmUEX2GGVUNywEJNUQhciFZCK/QL20mmF9FQVbp6JH2VUsMAA9Ij7ag+5YRWu0jSEEEQqIJWIhcihu1bZZiNWq/NH/y6/uGs3lIoDvZC0JbNWsO0SAyqhBZEKyMTTsEroltXnDtW/YRHm2q0pOlqW4wHQAm5ebQgFK9xUOUxSCS2IVEAq7qrESxgSolNV2IFi/+bSuqZ+7JMny3dQACrjpneEUL1a6YWRQAMQqUAAdDpVJaAlxq7noW74cDmOCEAr2PHFEKpXi/XJIQ2RCgRARBgSilNVuJl3kgu+1ScmIvsDOhOK9WrFznFPS2vZ+wI0BpEKBIANQ7xcW3FTVbSfAAqoLi33ZCTDQY9Cbl4t1zl5bdTC40ym0AjBDAORCsjB4SC5ud7+k70C035im9uux7+5tGJ7RIAQFnLzatkBX19hCgrDaRUiFQhAairdRsT3o0Lr+zqgmXfsk6UXtQXQutCaVytlkgoar5YgUoGgk7rVvAry8gLbrkd63ggglHDzarWc1RU7VsKVQQItQaQCQRdCZfUDmktLWjaqbRlkwugxhBZ/WibXqLU8rMLlc702auyzrGGIVEAJIbFWWc79jx0OjKlAaKCrXUwmf8ONUNkGiEvJeoV1zBqGSAWUEBIJIG5ABUXwQf/YfKWfM2O5BqLNtTJ+7MGF6bQahkgFlKD9BFBAi5MBQlRgVQTYvbG0eQUiNvXDHTqyPxqDSAUUovHFAlyPFlDqByCEBDDfhGsmGmzXYlM/3HRaRCoag0gFFMKOp2qtCLfNRtLSnD8mJ6OnAsPg5pv4iR2UYYdYtMCP1A+m02obIhVQiJYTQNzB+FftDSCkBZYA0nIVOD9qI2E6rbYhUgHlaDMBZLOhYBsYWwAJIC4C0NS8Wj/CD3aMF9NptQeRCihHmwkgORcnA4SiwBJA7LO5mekq8iP1Y7NppTMCLxCpgHK0mQAKtNobQKgLLAHEDUNqZLjUj9QPN50WXYD2aDFSuXDhwvjx4+PcpKenq31oECit9WhcIfCsLNWOBEBNgVWc1WBxfT9SP5hOq3lajFTOnTt3/vz5tm3bRrvq0KGD2ocGgdJaAggDKgCEyLACiP2KV322ih+pH4LptCFAi5HK+fPnL168+Nvf/vZzV88995zahwaB0lQCKDsbM1QACCGBJoCIa/NRfVgloB3RQXu0GKkcP36cEBIXF6f2gUBQsL0GW8VEYdySH5TPB6MLLAGUmqqhpu3fKElurnNvUVyvaJLmIhWHw1FUVNSxY8fo6Gi1jwX8IexzZjL5Tupwc0HUWimAGSoALgJLABHXJIuKi4C4SAVNWwc0F6nU1taeOXMmKipq8+bNI0eOjIuLS0hIWLJkSXl5udqHBj75k9RRfV6t+4CKlPFhLcwbBJBLwAkgblhFrdkq7O9F3kcfNBepXLhw4fTp06Wlpe+8807//v2nTp3auXPnTZs2TZo06ciRI2ofHXg3dqzzNjuX3hPVVwrIM6Cybp1zGAlABwK+hlC9tgrXtJHM0Qez2gfAq66uDgsLGzFixKpVq+hin+bm5jVr1qxYsWL58uVr1qyxWCwen1hQUOCeMLr77ruDfsS68/PPP9vtdrPZv8+GedCgyF9uN+3eXW+3+3jwlCkkM9Mi5Ij+9a+moUPr/T9SicrKzJmZwsGSkSObhg71fbwemMvKIpluuH7Jkqbnn+ceU19fX1tba/f3pcETehr9/ViCR97auHnatEjhez472756tb+vPHQoGTkyMj+/5ZXT0siUKYp+/jMznV8Q0dFSmrZf0MalOXfunPvQQ1lZmbdZH5pr9gkJCZ9//jl7T1hY2MMPP7x79+7CwsKTJ08OGjTI4xPLy8s/+OAD7s6ePXt26dIlWMeqU3a7vW3btmFhYX49q019vfDlby4rq/vhh6bu3X08fuHCpkWL2tPb77xjXriwrnv3JimH67+dO9vYbM5I5Xe/s9fU1Pn7IubCwkjmx/rExLqaGu4xDQ0NP//8c43b/SBBbW0tIcTfjyV45LWN33dft/nzL27ZUjd8OCGESPro/u53Tfn57YUfrVbyu98p1ARsNpKX54xUpk2rD3brQxuXpm3btu7f1+Xl5d4iFZPD4Qj+UXlgt9vnzZtXUFAg3JOYmOhjyCQ9PX3z5s1r1qwZPXq0+/++8sorhJCFCxcG6WgN5fTp0926dZNy8comQbKyWl1Lwz48NVWhiW82G4mNdf6YnExycyW9UEqKc5TZy6vU19dXVlb26NFD0i8AFxcvXiSEtG/fvtVHQqukt3Fx2MZBCCktVaigWmamcz/nmBhSWhr034g2LiMf3+Oam6dCCLHb7Q0NDe73m0wmXFFpGtsbnTrV6sPZSEaxfDa7eDImRmp45F9hKQBj4WaHKLNi2WZzhikEc2n1RbVIxWKxbNiwoYSxYcMGi8WyYsWKgQMHZrl+gVRWVhYWFmLpstaxfYOI6rPK7xfPzbZLTpZ6qce+CiqxALhKTnZpE8rMmud+BS4f9ERzYyopKSkWiyUnJ6f0l5G7urq6lStXFhUVjRkzJpYduAetYUvli4g7FN4v3maTaUCFuJXABABXWVkuLUOBYRW2UXKbJkKo01ykMmTIkCeffLKkpGTcuHHz5s1LT09PSUnZuHHjsGHDFi5ciJn/msYNLYgYVuFKRQX1wmvdOpcjkr58kTtQrIME8IRbsRzUYAWNUt80F6mYTKa5c+e+9dZbCQkJubm5mzdvNpvNS5cuXbt2badOndQ+OmiNn5v6cNsABa8vc89hS8/YcKkfXLsBeMIVguO22ZKR+3ApGqXOaC5SIYSYTKakpKT333+/uLi4pKQkPz9/7ty53tYEgbawPURr9d8odn6+zRaUHJB7RxbQJRdSPwDicAnWIGV4163jlxqBzmgxUoEQ5udUFYoNb6xWMVkj/3AdGXep5x+MMgOIFhPjMpaZlyd/sIIlP0aASAVkxY0xiAs6grqmMS/PpSOTeUAF/SKATxkZ/KWIvDkgOYdLQasQqYCsuG9ucX1ScjJ/4SVXX2azkZQU548yFIPybzt5AODLInJ14QLBzX3xY8lPXh626wohiFRAbmxXIaL+G5WRIf/UWvflBoHWPeFiKFRsABCHvRQhMk1Y4aa1+Vd3gM6io9uLslczoEmIVEBubMThz5QTtpeRZWqt+/SUQEeGT5503kbqB0A0LgeUlydDeBBQ3QEMjoYURCogt6ws4nC0/POntho3chtgPjs7m5+eEui+QjYbmTPH+SPq0gL4IzeXD1YCKUvNNXC/6w6wnQu7DgA0CYXUQEOysly2D0xJ4Xs3kdiNygghMTFStyFkxcQQh8OZ25a1dysoKDhw4ICML6g/9fX1hJDIyMhWH2lAw4cPT0xMVPsoWsc18LQ0cuqUlJHO7OzAJtJyY72oNaB5GFMBDaHBAMvfyXc0bcQlxblJMAGhY0VyF+s+cOAAu684uIuMjESY4pFCYa7JFPj0MfdrBqvV71d1n39WWupnc+SKNyJS0TyMqYDmpKa6DAuLH1mx2ci6dXyYkpUVhESNDEM0vMTERI/bnQOoiR2+yM4OPOpPTiZZWS6hRnY2sdnENimbjXCbv3HtXRQUbww1GFMBzXGPLVJSWk9p0ystrtuyWjGfBCAAXPuRY3lxaio/aSwvjzz4YOvz77OzPYQpgU6Tx3TaUIBIBbQoK4vvQNLSSGys53iFxiixsfyYrgy9GACwwQo7GhHYS3KDKO+9R2JjSVqa53glO5ukpHgoOiClgXNlpjGdNhQg+wMalZvLT1KhEUlmpkvP6bFMHF3pg4slABkkJTkvEWh7k6NpJSe3tHFWdjbJziYxMa23cfeBGbHYUAi1BkIEIhXQrtxc8utf89de3DYf7uisPWSfAeSRmkoyM51f8OvWyfXtnpxMSkv5hA4R0cZjYwMoOsDunIpuIkQg+wOatncvsVrF9ic041Naiv5Hc15//fU4NzfffPOSJUvKy8vVPjpNsNvtM2bMSEpKqqioUPtY3LBDHIFUQXFDl/uJnxVL23hJSQC/EjXfQhAiFdC6jAxSWtpKvCLEKJiYomWjRo2azrjhhhvef//91NRUtYKVioqK5cuXf//996r89lDCtStZgxXCtHEf5GnjmKQSmpD9gdCQkUEyMkhmJsnPJ01NzvuvuorccQcClNAwc+bM0f+/vXuPiyl/HwB+phoazaDU6mZrJlG+RrFNDb+hWqFEqXWZXLZYtSyVyn1RWS+trEvIpUhil7SxGxEioyTlEnIJXXY1bTUpNZOGps7vj7M7xpQoNefM9Lxf+4c+c+bM0+yczjPP5+bkJP0RRdH9+/dv3RTymugAACAASURBVLo1KSlp2bJlio/n1KlTv/322+TJkxX/0srHweHdPZ7H6/I5ddjqbdg1fu0a0tLy7iENDYTD6aJrXG7UPdRUlARkKkCZQEaiSkgkkpOT0+HDh+/cudPQ0KClpYV3RODDvL3f3ea7YmGVD+neaxxWUlFO0PsDAMBNv379KBSKRCJBURRBED6fv3r1altbWwaDYWZm5ujomJCQ0NTUhPw3jCMkJCQuLs7CwoLJZKakpGDtW7ZsYbFYDAaDyWRu3Lixvr4eO3l6ejqDwThz5szOnTuxAzgcTkpKSnNzM4Igy5cvj4yMFAqF7u7us2fPFolErcPDTj5ixAgGg+Hs7Hzx4kUul4sd3GY8zc3Nqamprq6uFhYWWDy+vr4lJSWy8aSkpGzcuNHCwsLMzMzDwyMvL0/uRQsLC7lcrrm5uYWFhb+/P1HG8cgVUTqy+SiByNZU4HuP8oCaCgAE9fm7SePF3v5Ty+rPnz8XCAS2trZaWlrl5eXfffdddXX1jBkzhg8f/tdffyUmJoaHh/fu3XvWrFnY8enp6ffv39+wYUNlZSWTyRQKhUuWLLl+/TqHw/Hw8Lh3715SUtLz58+jo6NpNBr2lJ9++olCoSxduhRBkLi4uBUrVpDJZBcXlzlz5rS0tKSlpQUEBFhbW7deql8kEi1ZsiQ7O9vNzW3s2LGZmZn+/v4oitrY2EiPkYsnLi5u69attra2WNjp6ekXLlz4559/jh49qq2tjT1l06ZNFAplzZo1CILExMTMmzdvz5490k6xsrIyX19fV1fXOXPmXL9+PTk5uby8PD4+Xvrr4CkkBNm27d9/OzrK73xBfHJznaGmojwgUwGAoDqzTDgxhIV9PFNpbm4uKCjYuHFjS0uLm5sbiUS6detWZWXlzp077f8b5zh+/Pi5c+fm5eVJMxWxWLxu3TrpAQkJCVlZWStWrFi0aBGJRJo2bZqtrW1QUNChQ4ekA18YDEZsbCx2p2ez2XPnzr18+bKLi8vIkSNv3rx5+fLl//u//2Myma0jzMjIuHHjxooVK3x9fUkkkru7u5WVVfj7+aNsPLW1tTweb+zYsXv27KFQKAiCuLu7h4eHnz59uqysTJqp9OvXLz4+3sjICPsFvb299+3bZ2dnR/pv88vNmzd7enoiCDJlyhRNTc3Tp0+Xlpa2GaGiTZnyLlNBkK5aWEVxHBzebTIK2/0oFej9Ad2PROqS7c2AsvPz85NOUTY3N/fw8CgqKgoICBg9ejSCIG5ubnfv3rWXmY6hra3dp08f2TPo6+tbWlpi/25oaEhPTzcwMHB1dZXe5seOHTtq1Cgej1dXV4e1cDgcaUFCT09PT0+vqqqqoaGh/VAlEsmFCxeMjIymTp2KnZxEIrm4uJibm38oHm1t7WPHjh06dAhLU7Cn6Ovry5153rx5WJqCIIixsbGLi0tpaemLFy+wFkNDQ+muyCQSyc7OTigUVlZWth+tgshtzNlF69UqGrbJ6H9dckApQE0FdCe57c06v1qTwmE7oSldfZvYxo4dK71Ja2hojBgxYvTo0dIWjEgkev78eWlpaV5eXnZ2dllZGYvFkj5qYGAgzV1ev37N5/O1tLRu3br14MED6TEtLS3V1dXSXERD491fuV69evXv3186LKYdYrG4pqbGwMBAttuFQqHo6OjIHiYbD6a5ubmiouLx48fFxcVZWVl3795VU3vvC6GhoaHcGWpra8vLy7/88ksEQdTU1GQDJpPJ7cepaIoaVwuALMhUQHfy8ZHfNVVZNgzEvi9KC8V4fANTlreqNROTttvlZinLqa2t3bBhw7lz51AUVVdX//LLL0eOHFlTUyN7jOxdH0VRiURSUlKyfPlyuVPRaLSXL192/hf4ZHLxXL58efXq1VjM/fr1YzKZVlZWsllUm0gkkrq6evcG2lXkrujwcGX6+gGUFmQqoJt18zIM3UJuNW+cOuN71C0ARdHdu3dfunRp48aN7u7uVCoVQZCqqqrbt29/6ClaWlomJiYGBgYHDx7EjpfzOZ0mmpqaOjo6Dx8+FAqF0pO/ffv21atX/fv3b/Mpz549+/HHHwcPHhwREfHll19iycf+/fvlMhW5qJ4/f96/f/+BAwd2OlRF8/F5t/Jbj/qMAvzAOBXQzby93/27q5e27C5yMzBlfwXQPRoaGp48eaKnp+fo6IhlBiiK5uTkVFRUvHr16s2bN62foqWlNWrUqPz8/MzMTGkjn8+fMGECl8utra396IuSyWQURVtkVxn7j4aGxqRJk/h8/pkzZ6RdRdevXy8qKvrQ2f7++2+BQMDhcOh0Opam1NbWXr16VSwWSwfNIAhy5swZoVCI/busrOzatWtMJpPeevMbwsIm92KjPQBQCKipAMUqLVWCjm3Z+R1yowhB96BSqba2tjk5OcHBwR4eHgiCpKam3rx5E0XR169fY0uqtPbdd9/duXMnICDAzc3NwcHhxYsXiYmJlZWVwcHB0rk27TAxMRGJREePHq2pqWGz2dKRsBhHR8fRo0dv3bq1sLAQm6Wcnp7eejKz1NChQ42MjGJjY+vr662srAoKCk6fPl1bW9vU1CQWi6WH5ebmzpo1y9vbWyQS7du3j0QiLVu2jEKhtLmgCxFhW/UAoEBQUwHdzMfnvdSk9fbtRCO3MwgsD6Uo33//fUBAQFFR0Zo1azZt2tS3b99z5865u7u/ePHiQwUSGo22Z8+ehQsX3rhxIzAwcNeuXfr6+gkJCc7Ozp/yinZ2dtOmTfvzzz/XrVsnEAjkHqVSqbt37543b97FixdDQkIeP368bds26Uyf1gYNGrRv374hQ4YcPnw4ICAgLS0tKCjo2LFjNBqtoKBAetiSJUvYbHZoaOjWrVutra1//fVXa2vrT4kWgB6L9NEx8EohKioKQZDAwEC8A1EFL168MDAwkJ2A8Lnmz3/X7+PjQ/S+bdloP28srVgsFggEgwYN+uiR8AFWClVVVTNmzGCxWL/88ksnnp6enu7n57dy5cpFixZ1YVSd+PB0/TXeU336NQ4+qp1PMtRUQPeT3bCU4ENVSkvfixD6fXqw2NhYZ2fnZ8+eSVtu3rxZUVExePBgHKMCoAeCTAV0P7n5PkTuAJLbahXG0vZgo0ePfvny5cKFC48cOZKamhoeHr527Vo6ne7m5oZ3aAD0LJCpAIWQHapC2KUtS0vfi83cHGoqPdnw4cP37t2rr68fERHh7+//xx9/zJgx4+TJk3JLtwEAuhv0UwKFCA1VgsVq5cbSrl2LWySAGFgsVmJiYledzcnJqbi4uKvOBkDPATUVoBBK0QEEk5MBAIB4IFMBikLwvc2uXoXJyQAAQECQqQBFIfhitbIFFVNTKKh0ucbGxoSEhMmTJ5ubmzMYjJEjRwYEBDx9+lR6QHp6OoPB2L9//4fOsHz5cnt7+6qqKgRBUBQ9duzYiBEjGAzGt99++9G9kT9q//79n7JHjwKIRKLZs2dLf1MAAGQqQFGI3AEEq711M6FQ+MMPP4SFhdXX17u7u3O5XFNT0/Pnz7u5uZ0/f74TJywoKNi6dSudTt++fXtgYKCamlpiYuJvv/3W5ZEDJXb1KkIi/bvPKFBmMKIWKJDsboVHjhCobiFXUFGKbRSVytWrV69duxYcHLx48WLpvsGPHz+eP39+VFSUjY2Nnp7eR08iu95aZWWlUChctGiRi4sLgiAPHjzYvHnz4sWLuyl+oJSkvcwkEuLggGRk4BoN6DyoqQAFknYAoSixpv/IBkOc/EmFZGdnU6lUe3t7aZqCIIilpeX06dPLy8v5fH7nTksmk7soQKByYBVHFQKZClAgHx/ibsGKBWZqSqwUSlWYmJiIxeJSuU2qEWT58uX379+X3fhGLBbHxsayWCwGg8HhcFJSUpqbm6UH29vbl5aWzp4928/PD0EQPz8/KyuruLg4d3d3oVAYGRkpHWvS1NSUkJDA4XAYDIaFhYW/v79sPoSiaHZ29uTJk83MzJhM5k8//dT+SBeRSLRlyxZsWIyzs/PFixe5XO7s2bNFIhE2rCQkJCQuLs7CwoLJZKakpCAI8vTpU19f35EjRzIYDHNz88mTJ58/fx7bvaSqqsre3j4kJOTMmTNsNpvBYLDZ7ISEBLmNGAsLC7lcrrm5eev4iYtEerceAb7kPmyyK2UDZQO9PwDI+IxdfkA7vv7668OHDwcHByclJU2bNm3MmDEDBw4ktTWAYN++ffr6+kuXLiWTyYcOHQoKCiKRSFOnTpUeQCaTAwICrKysDhw48P33348cOdLExGTlypW7du1ydnZ2dnY2NjZuamoKDQ09ceIEk8n09/cXCATx8fE+Pj7x8fFGRkYIgmDbBw4cOHDDhg0IgsTFxVVUVHxon2SRSLRkyZLs7Gw3NzdsU2V/f38URW1sbKTHpKen379/f8OGDZWVlUwms6CgYP78+X369PH19TUxMSkoKEhKSgoKCtLW1maz2dKn8Hi8qVOnWllZJScnh4WFPX36NCwsDHu0rKzM19fX1dV1zpw5169fT05OLi8vj4+Pp9FoXfO/pGvJ7pZFkAWTYNEBFQKZCgBE1bnvph29SSjkVYYMGXLixImVK1dev349KysLQRAtLS1HR8f58+dbW1vLpizDhg2Li4vT1tZGEOSrr76aO3cudjuXHkAmk9lstkgkwg5wcnJCEOTt27fYPsYTJ05EEITH4yUnJ3/zzTebN2/Geog4HI6vr29kZOS2bdsaGxsPHjw4aNAgaeLi5OTk4+Pzobk2GRkZN27cWLFiha+vL4lEcnd3t7KyCpe9ESKIWCxet26d/X9f3Hfu3NmrV6+YmJihQ4ciCOLq6spms/38/PLz86WZyps3b37++WdsnI2rq+vatWtTUlI8PDywpyAIsnnzZk9PTwRBpkyZoqmpefr06dLSUiaT2aF3XkFCQ9/rapk/H+dkRW6MPKQpSg4yFQCIqnNzuTt6h+jEq3Sq8kSn05OSkgQCQWZm5pUrV3g83tmzZ1NTU728vEJDQ6UjTsaPH4+lKQiCGBkZmZmZlZeXi0QiKpX66a+Vlpamrq4+c+ZM6WmtrKwcHByys7PLy8tra2ufPXvm5+eHpSnYC7m7u8fGxrY+lUQiuXDhgpGR0dSpU7GMikQiubi4yM0z0tfXt7S0lP64bNmyZcuWyR6go6MjV7Nhs9kO/91ByWTyzJkzU1NT8/PzsUzF0NBQmtOQSCQ7O7uEhASsYPPp74PiYOPQZcsqoaHv7aGhYND1o1ogUwGgB3N07MyzPuMOpKen5+np6enpiaLokydPVq9effz4cTs7O2nVREPjvT9KamodHkvX0NDA5/O1tLSKiopkyyTNzc1CobC2tlYgEIhEIgsLC9lnyf0oJRaLa2pqDAwMZLtdKBSKjo6O7GEGBgZ9+vSRe259ff2jR4/++uuvmzdv5uTkCIVC2Ud1dXUpFIr0x/79+1Op1MePH2M/qqmpyb4VSjB2WK6sEh6OZ1kFun5UC2QqAKiQjt4bFLKqDTa2dMyYMREREdJGEolkaWm5adOm1v07nwlFUYlE8vLly7Vt7dwkEAi66oVkyWVUZWVlISEheXl5CIL06tXLzMxs1KhRV65c+eh5lCAj+RDilFXkun5gR3TlB5kKAET13+DKDujoSjCdeImO09XV1dLSunv3rkAgkFs3RVNTs3fv3l17e6ZSqSYmJi9evEhMTGxz3+MHDx7QaLT8/HxsjAvm+fPnbZ5NU1NTR0fn4cOHQqFQ2gP19u3bV69e9e/fv82nNDY2bty4sbi4OCYmZuzYsb1798ZeNDMzU/awV69evXnzBnsUQZDKysq6urrBgwd3/DcmjMOHCVFWkd2sA5ZHUgmQqQBAVApYKlchq/Hq6Oi4ublFRkZGRESEhYX17dsXa29sbIyLi6urqxs3btxnvoS6urqGhoZEIsF+HDNmTHJy8tmzZ7ExsAiCCIXCJUuW8Pn8gwcPmpqaDh48+Pz581wu19jYGEGQ2traCxcutHlmDQ2NSZMmXbx48cyZM9KzXb9+vaio6KuvvmrzKUKhsLCw0MzMjM1mY4lIc3Mzj8cTCoWVlZXSw/Ly8h49ejRy5EgEQZqamv7888++fftyOJzPfCtwhntZpbT0vfwb+n1UAmQqAIBuN2fOnIKCgj/++OPcuXMsFmvQoEEvX77Mzs5+/fq1l5eXbG2jc3R1dalU6rlz54yNje3s7JydnW/cuLFly5br1697eHjU19efOHGisLBw1apVpqamJBJp/fr1vr6+s2bNwtZlaX+WsqOj4+jRo7du3VpYWIjNUk5PT//QwQiC6OjoWFtbnz17duXKlRMnTqyvr09OTn7y5AmJRJIdqiIUCn18fBYsWGBiYnLkyJH79++vWrVqyJAhn7+HEZ5wL6vIdWhC149KgJXfAADdjkajRUVFRUdHDxs2LC8v78SJEzweb9iwYbGxseHh4Z/f+6Onp+fr61tWVhYcHHzz5k0ymbx+/foNGzb8/fffISEhP/30E4Igu3bt+u6777CiiLW19a+//jpo0KBNmzZFRESMGDECW1ilTVQqdffu3fPmzbt48WJISMjjx4+3bdsmO9NHjoaGRlhYGJfLzczMDA4O3rFjx8iRI9PS0uzs7EpKSqTJiq2t7Zo1a44fPx4SEtLQ0CAbnnKTLWnExyt6hy/Zrh8YS6sqSCgxFwztoKioKARBAgMD8Q5EFbx48cLAwEBuCgboBLFYLBAIBg0a9NEj4QOsXKqqqmbMmMFisWS3Iuro042MjGJiYjo0+7pNnfjwdPs1LptvTZqEpKV11wvJuXr1velsGRndnal8+jUOPqqdTzLUVAAAoD2xsbHOzs7Pnj2Ttty8ebOiokK5R792K9myyoULiiuryG01CgUVVQHfmwEAoD2jR4+OiYlZuHDhggULdHV1b9269fvvv9PpdDc3N7xDIypsbRXp8muOjorY7UtucrJCRosDxYCaCuhJCLJ3GlAqw4cP37t3r76+fkREhL+//x9//DFjxoyTJ0+2OQUa/EtuIK0CLj3ZSUYwOVm1QE0FEAaJhJSUdOOcRmwX+Ph4gm7mDAiMxWIlJiZ21dm++OILHo/XVWcjKGw0q7TIER+PeHt3e3cMdmmTSNDvo2KgpgIIgET6dwje+7u+daXS0nff6kgkhE7vrhcCAGDkyioKyx5QlBCbOYOuA5kKwFtQ0Lt/d9+cxqtX3zszVIYB6G6mpu+G1kIhE3wG6P0BeAsMRHbufPdjeHjXf/eSLaggCGJqSsDRdjk5OXiHAJRSTk6OdNdlwgkNJeC1BpQO1FQA3mS/eCEIcvXqe2tcfj65NAXp+DZ+3c/Ozo64NxtiEIvFYrEY7yiIiM1m29nZ4R0FAN0IaiqAAOTmNM6f35W9M0eOyPf7EG+0HZvNhkylfa9evUIQ5EObAgIAVBjUVAAxdNOcxvj49wo2pqYELKgAAABoB2QqgBjkdujokqG1rYenZGR87jkBAAAoFmQqgDDkqh2fOWO5tPS9HUAQBIcN6AEAAHw2yFQAYch1zchtNtYhWDVFOvAFQZCwMJiZDAAAyggyFUAkcsNdO5esYNUU2c4jBweYKgkAAEoKMhVAMHJ9QB1NVrA0RbaaAqNoAVAZspc26DEgUwEEY2qKlJS81/LpycrVqwidLp+mdOteQgAARTpy5N+dN0BPApkKIJ7Wk3Q+cR6Q3EIpMNkHAGVRWoqEh7dXMsHKpdiiA5Cs9DCQqQBCcnB4L8mQq7K0Q7q9CFRTAFAWpaUInY6EhSF0ehv5Cpaj0OnvfWOBTUZ7EshUAFHJJisdSjhQFPHx6UByAwDAl2zageUrcv/JVVVNTWEqX48Cq+kDAnNw6OQWrDCEFgBl0ebKSe10A7UeygZUHdRUAAAA4Cc0FCkpeW/Xiw/BdjOFNKXngUwFAAAArkxNP5KvSHMUWBipR8IzUxGJRN7e3suXL2/9EJ/P9/f3t7CwYDAYHA4nISGhqalJ8RH2TJWVlXiHoCIqKirwDkF1wJvZhQh6jWP5CooiKIpkZLz7D0UJm6PAx1IxcMtUmpubjx49mpWV1fqhR48eeXp6pqWljRo1ytPTUyKRhIWFhYaGQrKiGMHBwXD5dYmKioo5c+bgHYWKuHDhwpEjR/COQkUowTWObVkqt3Ep8cA1rhj4jKhtbGzcvn17XFwc2mq8ZFNT0759++rq6nbt2uXi4oIgiFAoXLJkyalTp1xcXMaOHYtHvAAAAADABw41ladPn86ePTsuLs7S0lJTU1Pu0eLi4pycHDab7fBfKk2j0QIDA3v16pWSktI6swEAAACAClN0piISicLCwgoKCoKCgsLDw8lkstwBjx8/fvnypY2NDYVCkTbS6XRjY+OHDx/W1tYqNl4AAAAA4AmHmsrw4cNTU1OXLl3aq1ev1o9ivacWFhayjb169erfv39dXZ1IJFJQlAAAAAAgAEWPU6FSqWvXrm3ngL/++qt1o5aWlr6+/sOHD+vq6rotNAAAAAAQDuHWqG1zgg+JRFJT+0j5Jycnp3si6nHKysqSk5PxjkIVlJWVlZWVRUVF4R2IKoALvAvBNd5V4BrvQtgQ1TYfIlym0nrkCoIgKIq2tLS08yw7O7tui6jHCQwMxDsEFWFsbAxvZlf50J8w0AnwsewqcI13ITab/aFbeXdlKunp6X5+frItMTExTk5OH32iiYlJ68aGhoaKigoqldqvX782n8Vms+EPGQAAAKB6CLeaPpapPH/+XLbx7du3r1696tevH5VKxSkuAAAAAOCgu2oqTk5OxcXFnXji4MGDdXV1c3JyvL29pROVi4qKSktLXV1dtbW1uzRMAAAAABAa4WoqxsbG1tbWOTk56enp2DpvQqFw9+7dLS0tbm5uJBIJ7wABAAAAoDiEG1FLoVB++OGHu3fvBgcHHz9+3NDQMCsrq6qqisvlwkgUAAAAoKchXE0FQRBra+uTJ0/a29vfuXPn1KlTGhoaYWFhbS5oCwAAAADVRoKddAAAAABAWESsqQAAAAAAYCBTAQAAAABxQaYCAAAAAOJSzUzlzJkzQ4cO3b9/P96BKKv6+votW7awWCwGg2FhYTFr1qzc3FwY0vTpnj59yuVyzc3NzczMJk6ceP78eXj3OgdF0dzc3BkzZpibmzMYjDFjxmzZsqW+vh7vuJSeUCjkcrn29vZVVVV4x6KU+Hz+6tWrmUwmg8FgsVjwsew02WvczMzM0dExJSWlublZ9hgVzFRKSkq2bNnS5k6H4FPw+fxvvvnmwIEDffv2nTlz5qhRo+7cufPtt9+mpaXhHZpySE9P/+abb/Lz8x0dHSdPnlxRUbF06dLY2FhIVjoKRdHY2FgvL68HDx44Ojp6enq2tLQcOHBg6dKlQqEQ7+iUGIqiMTExubm5eAeirAoKCry8vJKSkhgMxsyZM/v27Qsfy05LTEycM2cOdo17eHgIhcJly5atX7/+vZs4qlpev37t6+tLp9PpdPq+ffvwDkf5tLS0hIeHMxiMvXv3SiQSrPHWrVs2NjYcDufvv//GNzziq6mpmTZtmo2Nzd27d7GWsrIyJycnW1vbwsJCfGNTOoWFhba2ttiC11jL69evV69eTafTd+zYgW9sSu3atWtDhw6l0+njxo2rrKzEOxwlg91lhg4dmpKS0tLSgqLo27dv16xZQ6fTjx07hnd0Sqa8vNzBwUH2D2ZNTc2sWbOYTOatW7ekh6laTeXUqVNZWVkeHh54B6KsqqureTyeubn59OnT1dXVscavvvpqypQpfD6/sLAQ3/CI7/79+48ePXJ1dbWyssJajIyMAgICqqurr1y5gm9sSiczM1MgEMybN49Op2MtFAplwYIFurq6ubm5IpEI3/CUlEAgiIiIsLS0/N///od3LErp9u3bPB6Py+VOmTIFWzadTCZ7eXnRaLR79+7JdVuA9lVXV9fU1IwdO1b6B1NbW9vBwUEkEuXn50sPU6lMpaCgYOfOnZ6enp+yaTNoU3V1tZqamrm5udwWSwMGDMArJOWSl5fX1NRkZ2cnu/ODhYXFgAEDbt269ebNGxxjUzoVFRW6urqWlpayjVpaWr1798YrJGUnkUiioqIEAsGaNWtoNBre4Sil/Px8dXV1V1dX2WucyWTeu3cvMjJS+gUPfAp1dXUNDY2amhqxWCxtxL6EyN50VCdTEQqFkZGRAwYM+OGHH2A1206ztLS8dOnS7t27NTTe7bQgFAozMjJoNNrAgQNxjE0pVFRU0Gg0Y2Nj2cZ+/fpRKJSXL1/KXo3go3788cfc3FwWiyXbePv27fLyciMjIy0tLbwCU16XLl06deqUn5/fsGHD8I5FKaEoWlxcPGDAgIEDByYkJHA4HBhR+znMzc0nTZqUmZm5d+9ekUjU3NyclpZ29OjRIUOG2NraSg8j3L4/nYOi6PHjx2/dunXgwAFDQ8NHjx7hHZHqwN7b/Pz8yZMnW1hY4B0OoTU0NLQ5k6JPnz4GBgb//PMP1FQ+E5/P37Vrl5aW1vTp02G/0o7i8/nbt2/ncDhz586FTorOaWhoqKioaGpq2rBhQ05ODovFYrPZWVlZBw4cePjwYXR0NFSqOoRMJq9fv37AgAEHDhyIjo7GGidOnLh+/XpDQ0PpYSqSqdy7dy82NpbL5XI4HLxjUSkoiiYnJ2/fvp3BYKxevRqKVe1DUVQikbT5kJqa6tQv8SIQCEJCQoqLi1etWiX7fQt8iqampujo6Pr6+uXLl1MoFBjl8zmqqqqam5tPnDhhbW2NIEhjY+PGjRsTExMPHTq0bNkyvKNTJs3NzSdPnoyPj9fU1LS3t+/du3dWVtalS5doNFpoaCiVSsUOU4W/nkKh8Oeff9bT01u8eDF8zepCzc3NsbGxa9asMTIy2rt3r5GREd4RER2JRJLtNZPV0tKi4GBUTElJibe3d15enr+///z58+FK76i0tLRTp04FBAQMGTIEXuQr8wAABnBJREFU71hUgb+/P5amIAhCoVAWL15sYGDA4/Hq6urwDUy5XLx4cfPmzdbW1jweb/fu3b/88ktGRsbMmTOTk5MPHDiA/reyg5JlKvv372fIsLKyun//fkxMzKNHj0JDQ/X09PAOUJm0fjMfPHggfVQkEq1evXrLli3Dhw8/evSoubk5jqEqCy0trS+++KJ1++vXr//55x8dHR0YCto52dnZXC63uLg4NDQ0MDAQansdha0yNWHChJkzZ+Idi3LDvo2QyWQGgyHbrqOjY2JiUlNTAz28n04ikaSmpqqrqwcEBEjncFAolODg4CFDhly+fLm2thZrVPreH7FYfPv2bZFI5OXlJfdQZGRkZGTkypUrFy1ahEtsyksgEPj7++fm5rq4uGzatEluHhBoh6mpqVAorKysZDKZ0sa6urrGxsYBAwZoamriGJsywvof161b17t37z179owfPx6qKZ1QVFRUXl5eXl6empoq9xCbzR40aFBSUlKbSTaQo6WlZWRkJJFIWi8uCnXTjhKLxTU1NWQyWe4PI4VC0dHR4fP50s50JctUFi1aJJd2vHnzxtHR0dTUVLaRz+dnZmZaWVlZWloOHTpUoSEqj9ZvJkYoFIaEhOTl5S1cuHDFihXw/bVDrK2tyWRyVlaW7D314cOH1dXVNjY2UFPpqLS0tHXr1n3xxRd79+4dPnw43uEoK319fS6XK9vS1NR07dq1xsZGJyengQMHQg796ezs7BITE3k8noODg/Qa5/P5RUVF5ubmffr0wTc8JaKpqamjo4PlK7LtjY2NNTU1Ghoa776WKHpFOoW4dOkSrFHbOdhii3Jr1IJPV1VV5eLiYmNjI11gEdao7bS7d+/a2NjIrlELuopQKPTy8oI1ajuhrKxs/PjxNjY2mZmZWAu2dDKDwYA1ajsqJSWFwWDMnTu3pqYGa3n79u2OHTsYDEZ4eDi2BDCKokpWUwHd7f79+2fPnkUQ5MiRI8ePH5d7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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n  a = x;\r\n  b = x;\r\n  k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe shifting constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 1. An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomial has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b, k]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61151,"title":"Scaling vertically functions","description":"Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by the scale factor k (see figure below). Return\r\ny_scaled, which is the 1×n vector that stands for the outputs of the scaled function;\r\ns = 'strech' or 'compress', if the graph will be away from or towards the x-axis, respectively, becoming narrower or wider relative to the original function's graph. Return s = '', if there is no change in size;\r\nr = 'flip' or 'flat' if the graph will be reflected over the x-axis or collapses the entire graph onto the x-axis, respectively. Return r = '', if the orientation is preserved.\r\ninput: (x, y, k)\r\noutput: [y_scaled, s, r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 489.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 244.988px; transform-origin: 408px 244.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function by the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of inputs and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below). Return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_scaled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the scaled function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if there is no change in size;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis or collapses the entire graph onto the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if the orientation is preserved.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_scaled, s, r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"369\" height=\"250\" style=\"vertical-align: baseline;width: 369px;height: 250px\" 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\" alt=\"Scaling function's graph\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_scaled, s, r] = scaling(x,y,k)\r\n  y_scaled = x;\r\n  s = x;\r\n  r = x;\r\nend","test_suite":"%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 2.62; \r\ny_correct = [10.48  12.052  11.528  8.908  8.122  4.716  3.668  5.24];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = sin(x).*cos(x);\r\nk = 2;\r\ny_correct = sin(2*x);\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = 1 - cos(2*x);\r\nk = 0.5;\r\ny_correct = (sin(x)).^2;\r\ns_correct = 'compress';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = (cos(x)).^2 -1;\r\ns_correct = '';\r\nr_correct = 'flip';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 0;\r\ny_correct = 0.*x;\r\ns_correct = 'compress';\r\nr_correct = 'flat';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nfiletext = fileread('scaling.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -2:0.5:2;\r\ny = polyval([1/3 0 -1 0], x);\r\nk = 3;\r\ny_correct = [-2 9/8 2 11/8 0 -11/8 -2 -9/8 2];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(isequal(s, s_correct))\r\nassert(isequal(r, r_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-11T13:38:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-06T11:12:26.000Z","updated_at":"2026-03-28T12:45:32.000Z","published_at":"2026-01-11T13:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" 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Return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_scaled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the scaled function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if there is no change in size;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis or collapses the entire graph onto the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if the orientation is preserved.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61157,"title":"Scaling vertically parabola by evaluating its area over an interval","description":"Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a\u003e0) will be equal to the area under the original parabola (see figure below).\r\ninput: (p, a)\r\noutput: k\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 447.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 223.9px; transform-origin: 408px 223.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that scales the shifted parabola such that its area over the interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[-a; a] (a\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be equal to the area under the original parabola (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, a)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"250\" style=\"vertical-align: baseline;width: 326px;height: 250px\" 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\" alt=\"Scale parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = scale_parabola(p, a)\r\n  k = x;\r\nend","test_suite":"%%\r\np = [1 0 1];\r\na = 2;\r\nk_correct = 7/4;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [1 0 -1];\r\na = 2;\r\nk_correct = 0.25;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [5 0 0];\r\na = 0.5;\r\nk_correct = 1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\nfiletext = fileread('scale_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-3 0 1];\r\na = 1;\r\nk_correct = 0;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 1;\r\nk_correct = -1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 3;\r\nk_correct = 7/9;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-16T14:57:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-01-16T14:57:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-10T14:36:03.000Z","updated_at":"2026-03-29T13:27:42.000Z","published_at":"2026-01-15T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that scales the shifted parabola such that its area over the interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-a; a] (a\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be equal to the area under the original parabola (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61164,"title":"Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k,  that vertically transforms the polynomial p by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\r\nV0, the m0×2 matrix that represents the vertex of the original polynomial p;\r\nV1, the m1×2 matrix that represents the scaled vertex for case 1:\r\nV2, the m2×2 matrix that represents the scaled vertex for case 2;\r\nwhere 1 \u003c= m0, m1, m2 \u003c n and n stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing x-values (in ascending order), while the y-value of the vertex in the second column. \r\nHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at m, multiple distinct, x-values.\r\ninput: (p, k)\r\noutput: [V0, V1, V2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 611.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 305.55px; transform-origin: 469px 305.556px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the scale factor, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  that vertically transforms the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 452px 30.65px; transform-origin: 452px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV0,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the vertex of the original polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 1:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix that represents the scaled vertex for case 2;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values (in ascending order), while the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of the vertex in the second column. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, multiple distinct, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, 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alt=\"Comparing scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [V0, V1, V2] = vertices(p,k)\r\n  V0 = x;\r\n  V1 = x;\r\n  V2 = x;\r\nend","test_suite":"%%\r\np = [1 -4 -3];\r\nk = 5;\r\nV0_correct = [2 -7];\r\nV1_correct = [2 -35];\r\nV2_correct = [0.4 -3.8];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.25 -1 -2 0 0];\r\nk = 4;\r\nV0_correct = [4 -32];\r\nV1_correct = [4 -128];\r\nV2_correct = [(3+sqrt(73))/8 -(827+73*sqrt(73))/2^9];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(isequal(V1,V1_correct))\r\ntolerance = 1e-13;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.5 2.4 -3 -22 4.5 54 30.4];\r\nk = 5;\r\nV0_correct = [-1 -2];\r\nV1_correct = [-1 -10];\r\nV2_correct = [-0.901803848596367 -0.57405744023312];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\ntolerance = 1e-13;\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('vertices.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 0 0 0 1];\r\nk = 1/3;\r\nV0_correct = [0 1];\r\nV1_correct = [0 1/3];\r\nV2_correct = [0 1];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(isequal(V0,V0_correct))\r\nassert(all(isapprox(V1,V1_correct), 'all'))\r\nassert(isequal(V2,V2_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nk = 10;\r\nV0_correct = [-2 0];\r\nV1_correct = [-2 0];\r\nV2_correct = [-0.590924701770178 1.75514977256519];\r\n[V0, V1, V2] = vertices(p,k);\r\ntolerance = 1e-13;\r\nassert(all(abs(V0 - V0_correct) \u003c tolerance))\r\nassert(all(abs(V1 - V1_correct) \u003c tolerance))\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\nk = 0.2;\r\nV0_correct = [-1 -6.25; 5 -6.25]; \r\nV1_correct = [-1 -1.25; 5 -1.25];\r\nV2_correct = [29.43264376174156 -11878.00773655344];\r\n[V0, V1, V2] = vertices(p,k);\r\nassert(all(isapprox(V0,V0_correct), 'all'))\r\nassert(all(isapprox(V0(1,:), V0_correct(1,:)), 'all'))\r\ntolerance1 = 1e-13;\r\nassert(all(abs(V1(2,:) - V1_correct(2,:)) \u003c tolerance1))\r\ntolerance = 1e-11;\r\nassert(all(abs(V2 - V2_correct) \u003c tolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-04-02T17:08:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2026-04-02T17:08:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-14T14:02:53.000Z","updated_at":"2026-04-03T19:14:06.000Z","published_at":"2026-01-19T17:28:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the scale factor, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,  that vertically transforms the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV0,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the vertex of the original polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix that represents the scaled vertex for case 2;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1 \u0026lt;= m0, m1, m2 \u0026lt; n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values (in ascending order), while the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of the vertex in the second column. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, multiple distinct, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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the plane region bounded by two polynomials","description":"Let p and q be n-degree and m-degree polynomials with n \u003e= m \u003e= 1. Consider clockwise rotate the plane region bounded by these two polynomials until its axis of rotation will be parallel to the x-axis (see figure below). Here, the axis of rotation is the straight line, r, that passes through the two points of intersection, A and B, of the polynomials, p and q, such that are located at the lowest and highest x-values, respectively, and the center of rotation is located at the y-axis.\r\nFind two 2×2 matrices, M = [A, B] and Mrotated, where\r\nA and B are the 2×1 vectors corresponding to the endpoints;\r\nMrotated stands for the rotated endpoints A and B. \r\ninput: (p, q)\r\noutput: [M, Mrotated]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 455.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 227.837px; transform-origin: 469px 227.837px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 42px; text-align: left; transform-origin: 445px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eq \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003em\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomials with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en \u0026gt;= m \u0026gt;= 1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Consider clockwise rotate the plane region bounded by these two polynomials until its axis of rotation will be parallel to the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis (see figure below). Here, the axis of rotation is the straight line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that passes through the two points of intersection, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the polynomials, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eq\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, such that are located at the lowest and highest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values, respectively, and the center of rotation is located at the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind two \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrices, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A, B]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eMrotated\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 452px 20.4375px; transform-origin: 452px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vectors corresponding to the endpoints;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 424px 10.2125px; text-align: left; transform-origin: 424px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eMrotated\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the rotated endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, q)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[M, Mrotated]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 210.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 105.4px; text-align: left; transform-origin: 445px 105.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"257\" height=\"205\" style=\"vertical-align: baseline;width: 257px;height: 205px\" 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\" alt=\"Rotate plane region\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [M, Mrotated] = rotating(p,q)\r\n  M = x;\r\n  Mrotated = x;\r\nend","test_suite":"%%\r\np = [1 0 0 1];\r\nq = [-1 1 2];\r\nM_correct = [-1 1; 0 2];\r\nMrotated_correct = [-sqrt(2) sqrt(2); 1 1];\r\n[M, Mrotated] = rotating(p,q);\r\ntolerance = 1e-6;\r\nassert(all(abs(M - M_correct) \u003c tolerance, 'all'))\r\nassert(all(abs(Mrotated - Mrotated_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [-1 0 1];\r\nq = [-1 -1];\r\nM_correct = [-1 2; 0 -3]; \r\nMrotated_correct = [sqrt(2) -2*sqrt(2); -1 -1];\r\n[M, Mrotated] = rotating(p,q);\r\nassert(isequal(M, M_correct))\r\nassert(all(isapprox(Mrotated, Mrotated_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('rotating.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 0]; \r\nq = [-1 120 -108];\r\nM_correct = [2 6; 128 576];\r\nMrotated_correct = [sqrt(50180) sqrt(451620); -96 -96];\r\n[M, Mrotated] = rotating(p,q);\r\ntolerance = 1e-11;\r\nassert(all(abs(M - M_correct) \u003c tolerance, 'all'))\r\nassert(all(abs(Mrotated - Mrotated_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [3 -24 18 120 60];\r\nq = [-1 4 -10];\r\nM_correct = [-1 5; -15 -15];\r\nMrotated_correct = [-1 5; -15 -15];\r\n[M, Mrotated] = rotating(p,q);\r\ntolerance = 1e-11;\r\nassert(all(abs(M - M_correct) \u003c tolerance, 'all'))\r\nassert(all(abs(Mrotated - Mrotated_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [1 0 -31/3 0];\r\nq = [1 -50/3 -181/3 0];\r\nM_correct = [-3 0; 4 0];\r\nMrotated_correct = [5 0; 0 0];\r\n[M, Mrotated] = rotating(p,q);\r\ntolerance = 1e-11;\r\nassert(all(abs(M - M_correct) \u003c tolerance, 'all'))\r\nassert(all(abs(Mrotated - Mrotated_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [1 1 -1 -1];\r\nq = [-1 -1 1 1];\r\nM_correct = [-1 1; 0 0];\r\nMrotated_correct = [-1 1; 0 0];\r\n[M, Mrotated] = rotating(p,q);\r\ntolerance = 1e-7;\r\nassert(all(abs(M - M_correct) \u003c tolerance, 'all'))\r\nassert(all(abs(Mrotated - Mrotated_correct) \u003c tolerance, 'all'))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-02-03T14:32:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-17T15:22:06.000Z","updated_at":"2026-04-02T17:28:11.000Z","published_at":"2026-02-03T14:32:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eq \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomials with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en \u0026gt;= m \u0026gt;= 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Consider clockwise rotate the plane region bounded by these two polynomials until its axis of rotation will be parallel to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis (see figure below). Here, the axis of rotation is the straight line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that passes through the two points of intersection, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the polynomials, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that are located at the lowest and highest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values, respectively, and the center of rotation is located at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind two \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrices, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A, B]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMrotated\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vectors corresponding to the endpoints;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc 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2d curve around a vertical axis","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the Oxz plane, around the vertical axis that passes through the vertex by an angle θ (see figures below).\r\nGiven the x-value of a point P, xP, belonging to the 2d curve, find R being the rotated point P.\r\nHint. Find critical points for their identification and behavior.\r\ninput: (p, xP, theta)\r\noutput: R\r\n              ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 443.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 221.9px; transform-origin: 469px 221.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxz\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eθ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figures below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of a point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003exP,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e belonging to the 2d curve, find \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e being the rotated point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Find critical points for their identification and behavior.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, xP, theta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 251.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 125.9px; text-align: left; transform-origin: 445px 125.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"106\" style=\"vertical-align: baseline;width: 326px;height: 106px\" 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\" alt=\"Rotating 3d\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = rotate3d(p, xP, theta)\r\n  R = x;\r\nend","test_suite":"%%\r\np = [3 -20 12 96 -39];\r\nxP = 4;\r\ntheta = pi/2;\r\nR_correct = [-1 5 25];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 1;\r\ntheta = pi/3;\r\nR_correct = [0 sqrt(3) 52];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 0;\r\ntheta = pi;\r\nR_correct = [-2 0 -39];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [2 0 0 0 0 0 -16];\r\nxP = sqrt(2);\r\ntheta = 3*pi/4;\r\nR_correct = [-1 1 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\nfiletext = fileread('rotate3d.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np =  [-11/4 7 11/4 -7 0];\r\nxP = 0;\r\ntheta = 2*pi/3;\r\nR_correct = [3 -sqrt(3) 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np =  [-1 28/11 1 -28/11 0];\r\nxP = -1;\r\ntheta = pi/2;\r\nR_correct = [2 -3 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-02-14T16:56:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-01T12:37:27.000Z","updated_at":"2026-04-01T09:52:04.000Z","published_at":"2026-02-14T16:56:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxz\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eθ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figures below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of a point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exP,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e belonging to the 2d curve, find \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e being the rotated point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Find critical points for their identification and behavior.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, xP, theta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61165,"title":"Breaking straight lines","description":"Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\r\nBreak the given line by building a piecewise linear function constituted by two branches:\r\none branch stands for the parent polynomial p;\r\nand another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).\r\nGiven (P, p), find\r\nR, the breaking point;\r\nr, the 1×2 array that represents the perpendicular line. 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margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a point in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane and let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone branch stands for the parent polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand another branch stands for the perpendicular line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that passes by the point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the breaking point;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array that represents the perpendicular line. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e violates the definition of a function, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(R, r)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 213.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 106.9px; text-align: left; transform-origin: 384px 106.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"251\" height=\"208\" style=\"vertical-align: baseline;width: 251px;height: 208px\" 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alt=\"Break line\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [R, r] = breaking(P,p)\r\n  R = x;\r\n  r = x;\r\nend","test_suite":"%%\r\nP = [1 1];\r\np = [2 1];\r\nR_correct = [0.2 1.4];\r\nr_correct = [-0.5 1.5];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1];\r\nR_correct = [0.8 0.6];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1.5];\r\nR_correct = [1 1];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [1 -1];\r\nR_correct = [1.5 0.5];\r\nr_correct = [-1 2];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nfiletext = fileread('breaking.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nP = [1 1];\r\np = [0 2];\r\nR_correct = [1 2];\r\nr_correct = '';\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.2 2];  \r\nR_correct = [15/13 23/13];\r\nr_correct = [5 -4];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-29T17:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2026-01-29T17:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-15T15:30:33.000Z","updated_at":"2026-03-31T17:02:16.000Z","published_at":"2026-01-26T14:18:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a point in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane and let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eone branch stands for the parent polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand another branch stands for the perpendicular line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that passes by the point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the breaking point;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array that represents the perpendicular line. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e violates the definition of a function, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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