{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2509,"title":"Wind Chill Computation","description":"On a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \"wind chill,\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\r\n\r\n  windChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16\r\n\r\nComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.","description_html":"\u003cp\u003eOn a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \"wind chill,\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ewindChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16\r\n\u003c/pre\u003e\u003cp\u003eComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.\u003c/p\u003e","function_template":"function windChill = ComputeWindChill(T, W)\r\n  windChill = ... ;\r\nend","test_suite":"%%\r\nwc_correct1 = 23.1871;\r\nwc_result1  = ComputeWindChill(32, 10);\r\nassert(abs(wc_result1 - wc_correct1) \u003c 0.0001)\r\n%%\r\nwc_correct2 = -9.0101;\r\nwc_result2  = ComputeWindChill(10, 20);\r\nassert(abs(wc_result2 - wc_correct2) \u003c 0.0001)\r\n%%\r\nwc_correct3 = 17.4215;\r\nwc_result3  = ComputeWindChill(20, 2);\r\nassert(abs(wc_result3 - wc_correct3) \u003c 0.0001)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-14T22:08:29.000Z","updated_at":"2026-02-17T08:49:29.000Z","published_at":"2014-08-14T22:37:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \\\"wind chill,\\\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[windChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2510,"title":"Solving Quadratic Equations (Version 1)","description":"Quadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2.  The quadratic formula can be used to find the roots:\r\n\r\n\u003c\u003chttps://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\u003e\u003e\r\n\r\nThe formula can be translated into the computation of two roots x1 and x2:\r\n\r\n  x1 = -b + ...\r\n  x2 = -b - ...\r\n\r\nComplete the function to solve the quadratic equation denoted by a, b, and c.  Assume the _discriminant_ --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real. ","description_html":"\u003cp\u003eQuadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2.  The quadratic formula can be used to find the roots:\u003c/p\u003e\u003cimg src = \"https://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\"\u003e\u003cp\u003eThe formula can be translated into the computation of two roots x1 and x2:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex1 = -b + ...\r\nx2 = -b - ...\r\n\u003c/pre\u003e\u003cp\u003eComplete the function to solve the quadratic equation denoted by a, b, and c.  Assume the \u003ci\u003ediscriminant\u003c/i\u003e --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real.\u003c/p\u003e","function_template":"function [x1, x2] = SolveQuadraticEquation(a, b, c)\r\n  x1 = -b + ... ;\r\n  x2 = -b - ... ;\r\nend\r\n","test_suite":"%%\r\nqe_correct1_1 = -1;\r\nqe_correct1_2 = -2;\r\n[qe_result1_1, qe_result1_2] = SolveQuadraticEquation(1, 3, 2);\r\nassert( (abs(qe_result1_1 - qe_correct1_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_2) \u003c 0.0001) || ...\r\n        (abs(qe_result1_1 - qe_correct1_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_1) \u003c 0.0001) );\r\n%%\r\nqe_correct2_1 = 0.224745;\r\nqe_correct2_2 = -2.22474;\r\n[qe_result2_1, qe_result2_2] = SolveQuadraticEquation(2, 4, -1);\r\nassert( (abs(qe_result2_1 - qe_correct2_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_2) \u003c 0.0001) || ...\r\n        (abs(qe_result2_1 - qe_correct2_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_1) \u003c 0.0001) );\r\n%%\r\nqe_correct3_1 = -1;\r\nqe_correct3_2 = -1;\r\n[qe_result3_1, qe_result3_2] = SolveQuadraticEquation(2, 4, 2);\r\nassert( (abs(qe_result3_1 - qe_correct3_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_2) \u003c 0.0001) || ...\r\n        (abs(qe_result3_1 - qe_correct3_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_1) \u003c 0.0001) );\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":505,"test_suite_updated_at":"2014-08-15T09:50:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-14T23:08:09.000Z","updated_at":"2026-03-31T12:44:20.000Z","published_at":"2014-08-15T09:50:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eQuadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2. The quadratic formula can be used to find the roots:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe formula can be translated into the computation of two roots x1 and x2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x1 = -b + ...\\nx2 = -b - ...]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function to solve the quadratic equation denoted by a, b, and c. Assume the\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\u003ediscriminant\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAMAAABEpIrGAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAAC1QTFRFeHh4k5OT9vb2gYGBnJycwMDAt7e3ioqK0tLS7e3t29vb5OTkycnJ////b29vvCMpXwAAAKZJREFUeNq8k0sWwyAIAEXzh3D/41ZrahASklXZ6cxTEAz8EOGFsDvxTyECM0RHgJIwOEIt6VFYX19BAd0kKe8vTpn0vY9uheXoQjGYrICtf9mg3Qgo+kt12fE4sxQwaGFQXCdJmmshaV4EnKYxmgMO/pvJVJ92NrwNbSpnrJafUz1kYbRcjP121ii4EKDVIPnVx+n4hdBzKyhuBM21YLgSLOePAAMAW0UziCh1I3kAAAAASUVORK5CYII=\"}]}"},{"id":2609,"title":"If-then-else","description":"Complete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y.  Otherwise 7 is assigned to y.\r\n  ","description_html":"\u003cp\u003eComplete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y.  Otherwise 7 is assigned to y.\u003c/p\u003e","function_template":"function y = if_then_else(x)\r\n  ???\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 14;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 12;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 13;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 0;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = -2;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":391,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-09-29T06:00:18.000Z","updated_at":"2026-02-18T14:51:46.000Z","published_at":"2014-09-29T06:00:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y. Otherwise 7 is assigned to y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"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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3SMiIvr27Ttr1qwzZ840y8nXr1/flKsGNvHuzchoNE6ePHnIkCFXrlyRu5Za0UILAPAoBoNh1qxZWVlZHTt2HDNmjK+v76lTp/bu3fv555//+c9/HjFihNwFogGIKQAAj5KZmfmvf/1r7ty5v/3tby3XHTx16lRCQsKaNWv69+8fEhIib4VwHJM+AACPcvDgQY1GM2TIEEtGEUL07NlzwoQJly5dys/Pl7E2NBQxBQDgUbp06VJeXq7X622Oz58///jx43369JF+LCsr27Jly+DBgyMiIiIjI6dNm2ZpXqmsrNyzZ8/IkSMjIyMjIiKioqISExNzc3PtPlxFRcU777xjOc/MmTOtk5DZbD548OATTzzRtWvXqKiol19+ubS0tI7ijUbjihUr7r///oiIiOHDh3/++eeTJk2aPHmy0WiUWknmzZu3efPmyMjIqKioTz/9VAhx5syZxMTEvn37RkREdO/e/Yknnti7d6+0wf+VK1eGDBkyb9683bt3R0dHR0REREdHv/POO5brJEtOnz49adKk7t2716xfdkz6AACESE+Xu4LGiokRWq31gUceeSQtLW3u3Lk7duyIi4t76KGH2rdvb3NV5IqKipdffnn79u2DBw+eP39+Xl5eenr6M888k5aW1qtXr82bN7/++usDBw5MTU1t1arV/v379+3bV1BQsHXrVunywtbnSU5O/uCDD6KiombOnHn16tX09PT4+Pj09PSwsDAhxGeffTZnzpz27du/9NJLQojNmzcXFhb6+fnZ/asYjcbf//73Bw8eHD169MMPP/zVV1/NnDnTbDb379/fcpv9+/cfP378pZdeunz5clRUVE5OTkJCwl133ZWYmNilS5ecnJwdO3bMmTMnODg4OjracpesrKxRo0b17t17586dKSkpZ86cSUlJkX6bl5eXmJg4cuTIZ5555sCBAzt37rx06VJ6enpAQEDTnpjmQUwBAAiRkCB3BY2VkiKSk60P3HfffR988MEf/vCHAwcOZGdnCyFat24dGxubkJDQp08fKa8cPHhw586dv/vd7+bOnSsd+cUvfjFjxoyMjIywsLCsrKyHH374r3/9q7+/vxBizJgxqampu3btysvLs4kp0nnGjx//pz/9qWXLlkKIwYMHJyYmvvbaa2+88UZZWdmmTZs6d+5sSS1Dhw6Nj4+vbWVNRkbG119/vWDBgsTERJVKNWbMmN69e6emplrfpry8/MUXXxwyZIj04+rVq319fTds2NCjRw8hxMiRI6Ojo6dPn3706FFLTPnxxx+XL18u9Q6PHDly8eLFn3766dixY6W7CCH+9Kc/jRs3Tgjxy1/+0s/Pb9euXXq9Xt5LQFsw6QMA8DTh4eE7duzQ6XQrV6584oknhBB///vfJ0yYsGTJEmm+IzMzMzAwcPTo0ZZRlr59+x44cGDmzJnBwcHbtm37f//v/0kZRQihUqlCQ0PtPtBnn33m4+Pz1FNPSRlFCNG7d++YmJhvvvnm0qVLFy5cOHv27JgxY6SMIoQICwsbM2aM3VOZTKZ9+/aFhYWNGjVKqkqlUo0YMaJ79+7WNwsNDe3Zs6flx9mzZx84cMASOIQQbdu2tRmtiY6OjomJkf7csmXLp556ymQyHT16VDrSsWNHS6BRqVSDBg0yGAyXL1+u/b+uSzGaAgDwTCEhIePGjRs3bpzZbP7uu+8WLVr0/vvvDxo0aNSoUQaDwd/fPzAwsLb7VlZWFhYWnjp16sKFC9nZ2UeOHGnRwvaLfWlpaX5+fuvWrc+fP289QFJZWWkwGIqKiq5evWo0GiMjI63vZfOjRXl5+Y0bNzp06GA92+Lv79+2bVvrm3Xo0OGuu+6yuW9JScnJkycvXrx46NAhnU5nMBisf9uuXTtL5BJCBAUFaTSaU6dOST+2aNFCrb4TBix5SyGIKQAAIX76tu1+unSx/knqJ33ooYeWLVtmOahSqXr27PnKK69MmTJF6tKo43xms/nLL79ctGjRjRs3hBCBgYFRUVF2N2Qzm80mk+n69euLFy+ueZ6rV682/i9VO5u0lJeXN2/evMOHDwshfH19u3bt2q9fv3/+85/1nkdpcaQ2LoopUltQSEjIypUrbX515syZ1157LTs7+9atW4GBgcOGDZs5c6ZlfAwA4AoZGXJX0DzatWvXunXrI0eOXL161WZ/FD8/v1atWkkfzwEBAWVlZcXFxffcc4/02+Li4ueffz48PDwhIeGPf/xjt27dli1bdu+990qrmtevX18zpmg0mi5dunz//ffbt2/v2LFjzWJOnDgREBBw9OjRoUOHWg6eO3fObuV+fn5t27b99ttvDQaDRqORDt66devmzZtBQUF271JWVrZ06dILFy5s2LDh4YcfbtWqlfSgX331lfXNbt68+eOPP0q/FUJcvny5uLi4W7duds+pNK7oTamsrNy6davUx2Rj7969o0ePzsrK6tev31NPPdW2bdsPP/wwPj5eUauhAADuom3btqNHjz5z5syyZctKSkosx8vKyjZv3lxcXPx///d/QoiYmJji4uL9+/dLC3eFEP/6179ycnLuv//+goKCq1evDh48ODw8XMooRUVFmZmZ5eXlxcXFNg/30EMPXb58+e9//7vlPAaD4bnnnnv00Udzc3O1Wm23bt327t2bl5cn/baoqGjfvn12K1er1cOGDcvPz9+9e7flbAcOHDh//nxtf1mDwXD69OmuXbtGR0dLKaSysjIrK8umueTw4cMnT56U/lxRUfG3v/2tTZs2gwcPdvA/qbycPppSVla2atWqzZs3W/6jW1y9enXt2rUBAQHr169/4IEHhBCVlZUbNmxYuXKl1CNtPVsGAIAjnnnmmZycnE8++eQf//jHgAEDOnfufP369YMHD/7www9PP/20NLDx0EMPjR8/fuXKlTqdbuzYsceOHfvoo4969uw5YsSI8vLysLCwjRs3lpSU9O7dOycnZ9euXUVFRRUVFeXl5TaPNXz48K+//nrFihUHDhwYO3ZsSUnJBx98cPr06YULF2q1WpVKtWTJksTExIkTJ06fPl3UtyA5Njb2wQcffP3110+fPi0tSN6/f39tNxZCtG3btk+fPn//+9//8Ic/PP744yUlJTt37vzuu+9UKpV1e4rBYIiPj3/++ee7dOmyZcuW48ePL1y48L777qt7BxeFcG4OOHPmzMKFC48fP96zZ88LFy7Y/DYnJ+f06dPPPvtsv379pCM+Pj4TJ07cvXv30aNHb9y4YRmLAwDAQQEBAWvWrBk5cuTGjRsPHz584MABX1/f3r17//rXv7ZsTduyZcslS5b06NFj48aNc+fObd269ejRo+fPny+tN163bl1qampaWtrt27fvvffeOXPmRERETJs2LScnx3r6xvo86enp8+bNa9GiRffu3f/yl78MHz5cWq3Tp0+fd99996WXXnrllVd8fHwee+yx6dOnv/baa3Yr12g0a9euXb169Y4dOz755JMePXq88cYbmzZtqu1vqlarU1JSNBrNp59++tlnnwUGBo4ZM2b16tV//OMfc3NzLUll4MCBcXFxq1evvnr1ateuXa3LUz5VzUGO5mI0GqdPn3748OGkpKQHH3zw+eeff+yxx6x7U959992VK1cmJyfHxcVZ32vatGkFBQU7duywG1PWrFkjhEhKSmq2QtVqYTI129m8TEFBQUBAgGUaFfL6/vvvO3TowDCkEphMpoKCgs6dO8tdiB3N/y4Kp7ly5cqTTz45YMCAmp2djt89LCxsw4YNTnqjbsQ/pwbdxbm9Kb169dqzZ8+MGTN8fX1r/vaZZ545cuSIdUYRQpw+ffrkyZNhYWE1F1w1v8xMoVKJykqhUonwcJGZ6fRHBACgFhs3bhw+fPjZs2ctRw4dOlRYWOgu7a7O4MRvXRqNxu4arToYDIY1a9aUlpZOmDDB6V/Q9XphvbWfXi9iY0V8vEhLc+7jAgBgz4MPPrhhw4Zp06Y9//zz7dq1++abbz766KPw8PDRo0fLXZpsFDQ4bDQak5OTs7OzJ02aVPeidp1OV/PgsGHDatsl0C6/zz7zqzl8kp4uMjNFfPxNhkMdU1JSUllZaWLWTBmKi4v9/f2Z9FECk8lUXFyskKui2CgvL6+jKxMy6tWr11tvvbVy5cply5ZJm3Q8+eSTs2fPbtOmjdyl1aW8vPzmzZt2f1VYWFhzZZNOp7Pse1svpbydFRUVzZ49+6uvvoqLi1u8eHEjtp1pUEYRer361Vdr+5VISdFs2mRcu9aN9zuCV1KpnNhthgYxm83u0qIIRRkwYMD27dub62z33HNPVlZWc52tERr20WyPImLK2bNnZ86cefbs2WnTpi1YsKDejBIdHd3U5q+jR8VPq9iFECI+3ubqoOq8vKCxY2te0Qo2ysrKaKFVDoPBEBwczGiKEphMpvLy8tp25ZIXQyloXn5+fnX8U2/i57X8b2fZ2dlz5swxGAwvvvjic889Jy0Vcy69vtq1QGNiRFqaSE4WW7aIny5sXSUlRaSni/h4wgoAT2J36hxohAbN4DSCzFdIPnr06Jw5c27duvXWW28lJCS4IqMIUa1zVqutiiDSH3JzhVZb7cZ6vUhJEbGxQq93RW0A4GSDBg1y6ueKAplMJqPRKHcVnik6OnrQoEHOO7+coyn5+fkLFiwQQmzevFnahdYV9Ppq8zsxMdUaULRakZsrUlNth1UyM0V4OHNAADxAdHS0t8UUo9FoMBg6dOggdyFoMDljyo4dO86fP+/r6zt79mybXrOOHTuuXbvW5qpRzcN6uscylGIjOVlMnSoSEmx3UpHmgNLSaK0FAMAFZIspRqPx3//+txDi1q1bNS806KwFC5mZ1ZJHTIztFI+FVisyMkRmpkhIqDbdI22vIrWz1HZfAADQHFwUU6Kioo4dO2Z9RKPRvPfee6559DtsulLq3cktJoY5IAAA5CJzC61L2QylOJ4wpNbamhM9KSlssQ8AgPN4TUyx2RpfqxXx8Q24uzQHVHP0RZoDsu53AQAAzcRrYorNUErjLtwTHy9yc20ngIQQ6ekiPLxaDAIAAE3mHTGl5lBKo5fqWLZXsTmDtL0Kc0AAADQf74gpmZnVVus0/RrI0hxQzWEVaQ6IYRUAAJqDF8SUmlvjN9euJ9KwSs2wIg2rAACApvGCmGJ3a/zmIp0wI8POFvskFQAAmsbTY0rdW+M3F2l7FZthFZIKAABN4+kxxZGt8ZtLzdZaqVUFAAA0ikfHFMe3xm8u0s621kklM5OkAgBA43h0TGno1vjNouYDkVQAAGgUz40pjd4av+m0WpGba1sMSQUAgAby0JjSxK3xm46kAgBAk3loTGmWrfGbiKQCAEDTeGJMacat8ZuIpAIAQBN4Ykxp9q3xm4KkAgBAY3lcTHHe1viNRlIBAKBRPC6mOHVr/EaTLlVojaQCAEB9PCumuGZr/MaJiSGpAADQIJ4VU1y5NX4jkFQAAGgID4oprt8avxFIKgAAOMyDYoosW+M3AkkFAADHeEpMkXFr/Eawm1SsZ6wAAICHxBTZt8ZvhJpJJT2dpAIAgDWPiCnuNZRiQVIBAKBO7h9T3HEoxYKkAgBA7dw/pihqa/xGIKkAAFALN48pCtwavxFIKgAA2OPmMUWZW+M3gt2kYr2jLgAA3sedY4qSt8ZvhJpJJSGBpAIA8GbuHFMUvjV+I8TE2PbWkFQAAF7MbWOKXu8GW+M3Qnw8SQUAAInbxhSboRS3W+BTB5IKAABCCHeNKW66n5vjSCoAALhpTBn02Wd3fnCv/dwcZzepWIczAAA8nVvGlOjy8js/eN5QikXNpBIbS1IBAHgPt4wpd3jqUIpFfLxISal2hKQCAPAabh5TPKlztjbJybZRjKQCAPAO7hxT3H0/N8elpZFUAABeyC1jim74cA/Zz81xJBUAgPdxy5hyaPhwkZvrLUMpFiQVAICXccuY4r1IKgAAb0JMcTckFQCA1yCmuKG0NNsJL5IKAMATEVPcU0YGSQUA4PGIKW6LpAIA8HQuiilGo3Hq1Knz58+v+av8/PyZM2dGRkZGREQMHjz4nXfeqaiocE1Vbo+kAgDwaK6IKZWVlVu3bs3Ozq75q5MnT44bN+6zzz7r16/fuHHjTCZTSkpKcnIyScVRJBUAgOdyekwpKytbvnz5ypUrzWazza8qKirWrVtXXFz8l7/85b332wK1yAAAIABJREFU3lu5cuUXX3wxePDgjz/+WKfTObswz1EzqXAtZQCAR3BuTDlz5szkyZM3b97cs2dPPz8/m99euHBBp9NFR0fH/PQpGxAQkJSU5Ovr++mnn9aMNaiVTVLR60kqAAAP4MSYYjQaU1JScnJy5syZk5qa2rJlS5sbnDp16vr16/379/f397ccDA8P79Sp07fffltUVOS82jwQSQUA4HGcO5rSq1evPXv2zJgxw9fXt+ZvCwsLhRCRkZHWB319fYOCgoqLi41Go1Nr80AkFQCAZ3FiTNFoNIsXL77vvvtqu8HFixdrHmzdunVoaKjRaCwuLnZebR6LpAIA8CBqGR/b7nIelUrVokU94clug+2wYcNCQ0ObpzK3tmuX34gRfpb/RHq9SEgoX7euPDraGY9WUlJSWVlpMpmccXI0VHFxsb+/v1ot5+saEpPJVFxcHBAQIHchEEIIo9FYWlpq3WAA1ygsLNy3b5/NQakt1cEzyLm9W81uFSGE2Wy+fft2I85GRrEo37vXZkxFnZgoWzVwIZVKRe+5QpjNZpVKJXcVgMya/tEs57euLl261DxYWlpaWFio0WgCAwNru2N0dHRSUpIzS3N/GRnWG6io8/KC+vYVubnN/jhlZWUBAQEajabZz4xGMBgMwcHBjKYogclkKi8vDwoKkrsQCCGEWq328fHh6ZBFEz+v5RxNkWLKuXPnrA/eunXr5s2bgYGBfPI1Vc0+lfBw2YoBAKDh5Iwp3bp1a9eunU6nKysrsxw8f/68Xq//+c9/HhwcLGNtHsLmWsokFQCAW5EzpnTq1KlPnz46nW7//v3ShLrBYFi7du3t27dHjx7NtG4z0GpJKgAA9yXnHLa/v//vfve7I0eOzJ079/333+/YsWN2dvaVK1cmTZrkeA8w6iElFetlyVJScUKfCgAAzUvO0RQhRJ8+fT788MMhQ4b897///fjjj9VqdUpKit0ta9F4jKkAANyTi0ZToqKijh07ZvdX4eHhmzZtck0Z3svumEpsrMjIkLMqAADqJPNoClyn5phKZqaIjZWtHgAA6kNM8SZSUrFGUgEAKBgxxctotbbNsyQVAIBSEVO8D0kFAOAmiCleiaQCAHAHxBRvRVIBACgeMcWLkVQAAMpGTPFuJBUAgIIRU7yeVmu7yRtJBQCgDMQUCBETQ1IBACgQMQVCCJIKAECJiCn4CUkFAKAwxBRYsZtUEhJkqgYA4O2IKaiuZlJJTyepAABkQUxBDSQVAIAyEFNgD0kFAKAAxBTUgqQCAJAbMQW1I6kAAGRFTEGd7CaV1FSZqgEAeBdiCupTM6mkpIj0dHmKAQB4E2IKHFAzqSQkkFQAAM5GTIFjYmJEWlq1IyQVAICTEVPgsPj4mknFf/t2maoBAHg+YgoaokZSCZozx++DD+QqBwDg2dRyFwB3Ex8vhLBelqxOTBSvvnrnV0OGiJgY19cFAPA8xBQ0XI2kIvR6IYRISblzRKsVMTFCqyW1AAAajZiCRqmZVGzo9dUabLXaquAiGG4BADiKmILGio8X8fFCpXLoxnq90OtFZuadIwy3AADqQ0xBkxRcuhRw/brm2jWRlWUni9SB4RYAQH2IKWgyrVb06lUtWOj1YssWIYTIzGxAamG4BQBQHTEFTqDViuRkIUTV/0sRRBpuycys6retV23DLV263Bl3AQB4NGIKnM96Qkf8tCyoWYZbWAINAB6NmAKX02qFEPaHWxxPLdK9bJZAW4ZbpNkiAICbI6ZAASwJw5JaRJOHW6SYwnALALgzYgqUx+5wS2amuHixYalF1NhxTgpDpBYAcBPEFLgDSxuKzSSRYLgFADwZMQVuyLont3mHW1gCDQBKQkyBR2iu4RZ2nAMAJSGmwBM113ALO84BgKyIKfAOtQ23sME/ACgYMQVeyWbHOcEG/wCgRMQUQAhR5wb/1iModWODfwBoVsQUwB7r4Za0NDb4BwBZEFMABzTLjnOi9g3+SS0AYA8xBWiUmj25gg3+AaCZEVOA5uC8Df7pyQXgxeSPKWfOnHnttdeys7Nv3boVGhqakJAwZcoUf39/uesCmoYd5wCgyWSOKdnZ2b/97W/Ly8sHDBhw7733fv3118uWLfvqq6/efPPNgIAAeWsDmhM7zgFAw8kZU4xG41tvvVVRUfGXv/xlxIgRQoiysrIlS5bs2rUrMzNz1KhRMtYGOJ0Tdpzr0KmTz69/LV58sdmLBQBZtJDxsX/44Yf8/Pw+ffo8/PDD0hF/f//hw4ebzeaDBw/KWBggA2lcJDlZpKWJjAxhNovcXJGSIlJSHB8mUeflqZYsEeHhDVh8BAAKJudoikqlUqvVN2/eLCsr02g00kGj0SiEuPvuu2UsDFCEOnacy8ys6re1S68XsbEiI4NpIADuTs7RlHbt2k2cOPHs2bPLli0rKioym81HjhxZtWrV3XffPXz4cBkLA5TIerglN7fqf3UMt8TGitRUVxcJAM1K5tGUX/3qV4GBgcnJyZ988ol0sHfv3suXL+/Ro4eMhQFuwN4SaNOzz6qzs+/cJiVFZGaKjAwZygOA5iBnTDGbzRkZGa+//roQYujQoW3btj18+PCxY8deffXVN954IyQkpLY76nS6mgeHDRsWGhrqxHJhT0lJSWVlpclkkrsQCBEUlLduXaclS4J+Cv1CCJGZKcLDy9etK4+Olq8yb2QymYqLi1mxqBBGo7G0tJStLlyvsLBw3759Ngd1Ol20w+9Ick765OTkzJs3Lzg4eO/evRs2bFi+fPnnn3++YMGCAwcOLF26tKKiokFnI6MAKpWqYsMG08aN1Y7q9X4jRjTgAopoDmazWaVSyV0FILOmfzTLOZqyb98+g8GQmpoaHh4uHfHx8YmPjz906NChQ4f0en337t3t3jE6OjopKcmFlaJWZWVlAQEBlg5oyMtgMAQHB6unTRNDh4qfXlaSoDlzxLFjIi1Nrtq8jclkKi8vDwoKkrsQCCGEWq328fHh6ZBFEz+v5RxNKSwsFELYfML5+/u3a9fuxx9/LC8vl6kuwP1ptSI317a1Nj1dxMbKUw8ANIqcMUUaC7p06ZL1wbKysmvXrknJV6a6AI+g1YqMjGpXCBJVrSrsqgLAXcgZU2JjYzUazdatW3Nzc6UjZrN5z549Op3ugQceCK8+ZA2gMaQFzNakXVVoVQHgDuTsTenXr9/MmTNfe+21ESNGDBgwICws7L///e/58+fDwsJmzZpFSzbQPOLjRUyMiI2ttiNcQoLIyqJVBYDCyTmaolKppk2b9u677/bu3fvw4cMffvhhUVHRr371q08++aRXr14yFgZ4GmkCiFYVAO5G5iskq1SqgQMHbt++Xd4yAM8nJZXU1GrdKlKrSloa2+oDUCY5R1MAuFpysu2mtFKrCtvqA1AkYgrgZWJiRG5u1V77FikpIiFBnnoAoHbEFMD71NaqwvI6AApDTAG8kt1dVfR6dlUBoCjEFMCL0aoCQNmIKYB3k1pVbCaAUlJYqwxACYgpgNez26oirVW23hEOAFyOmAJACCHst6rExtKqAkBGxBQAP6FVBYDCEFMAWKFVBYCSEFMAVEerCgDFIKYAsIdWFQAKQEwBUAtaVQDIjZgCoHa0qgCQFTEFQJ3qaFVhAgiAkxFTADiAVhUAciCmAHBMzVYVIWhVAeBUVTGlrKzszJkzFRUV8lYDQNFoVQHgWlUxxWAwJCYm9uvXb8GCBUeOHKmsrJS3LAAKJbWqxMdXO0irCgDnqIopfn5+999/f0VFxc6dO8ePH9+3b9+lS5fm5uaazWZ56wOgRGlpIi2t2hFaVQA4QVVMadOmzdq1a0+cOLFly5ZHHnnk1q1b6enpjz766IMPPvjGG2/k5eWRVwBUEx9PqwoAZ6vWQtuyZcuHH35406ZNUl4ZOXLkzZs333zzzf/7v/8bOnToxo0br169KlehABSHVhUATmZ/pY+UV6TxlZ07dz799NNlZWXLli2Ljo5+/PHHP/roI6PR6OJCASgRrSoAnKmeBclXrlw5fPjwkSNHpHEUs9l87ty5P/zhDw8++ODGjRtZGQRACFpVADiLuuYhs9mcn5+/ffv2Xbt2Xbp0SQihUql69eo1derUxx57TAixb9++P//5z8uXLy8tLZ09e7arSwagQPHxQqu1ne6JjRXx8bYJBgAcdiemmM1mvV7/4Ycf7tq168qVK9LB8PDwSZMmTZgwITg42HLLCRMmdO7cOTEx8fPPPyemAKgitaokJFQbRElPF3q9nWZbAHBAVUy5evXq1KlTv/vuO+nHjh07Tp48ecyYMWFhYXbvFh4eHhwc/OOPP7qoTABuQWpVSU2ttrO+1KqSlmbbbAsA9amKKWazubS09O677x47duxzzz0XFhamUqnquFtFRcXTTz/dp08flxQJwK0kJ4suXURCwp0jUqtKWpptsy0A1KkqpgQEBLz77rsdOnTw8fFx5G5hYWG/+c1vnFkYAHcWHy9iYkR4eLWDCQkiK4tWFQCOq1rp4+/v36lTJwczCgDUT6u1s6tKejq7qgBwHFdIBuA0UquKdZ+KYFcVAA1ATAHgZMnJtit9pFaV9HR56gHgPogpAJxPWqus1VY7mJBQrc0WAGogpgBwCWkCqGarik2bLQBYIaYAcBW7rSp6Pa0qAGpDTAHgWrW1qqSmylQQAOUipgBwObutKikprFUGYIOYAkAOdltVpLXKer0sFQFQIGIKAJnU1qoSG0urCgAJMQWArGhVAVA7YgoAuUmtKjYTQLSqACCmAFAEWlUA2ENMAaAYtKoAqI6YAkBJaFUBYIWYAkBhaFUB8BNiCgDlqaNVhQkgwJvIH1NKSkpWrFgxYMCAiIiIqKioRYsW5efny10UAAWgVQXwejLHlEuXLk2dOvXtt99u06bNU089FRERsWPHjvj4eJIKACHstaoIQasK4D3kjClms3nTpk3Hjx9fsGDB559/vnz58k8++WThwoUXLlzYtGmTjIUBUBBaVQAvJmdMOXfu3N///veHH344Pj7ex8dHCKFSqUaNGnXvvfeePXu2pKRExtoAKIjUqhIfX+0grSqAF1DL+Njnzp27du1aXFycv7+/5WCHDh0yao7xAkBamhgyRCQk3DkitarUbLYF4CnkHE05f/68RqPp0qXL3r17H3/88a5du9JCC6Au8fG0qgBeRc6YotfrhRDr16+fPXt269atn3zyyXvuuefDDz+khRZArWhVAbyJnJM+Qgij0ZiVlbV69eoRI0YIISorKzds2LBy5crXXnvtjTfeUKvtl6fT6WoeHDZsWGhoqHPLRQ0lJSWVlZUmk0nuQiCEEMXFxf7+/rW9cDxHUJDYtUs9bZpm5847BzMzRXh4+bp15dHR8lV2h8lkKi4uDggIkLsQCCGE0WgsLS21bjCAaxQWFu7bt8/moE6ni3b4dSr/vimTJk0aPny49GcfH5/Jkyfff//933zzzaVLlxp0HjIKoFKpzGaz3FW4iGnTJtPGjdUO6fV+I0YopKnWbDarVCq5qwBk1vSPZjm/dbVs2VII0b17d+sXc2BgYNeuXS9cuFBcXFzbHaOjo5OSklxRIupTVlYWEBCg0WjkLgRCCGEwGIKDgz1/NMVi2jTRrZvNdE/Q2LEiJUUkJ8tVlMRkMpWXlwcFBclbBiRqtdrHx4enQxZN/LyWczSlW7duQojy8nLrg2az+fbt2zJVBMDd0KoCeDQ5Y8r999/v5+f31VdflZWVWQ5eu3bt5MmTbdu2bdeunYy1AXAb0q4qNtvqs6sK4BHkjCk9e/bs06ePTqfbs2ePNKFeWVn50UcfnT17NjY2ll4TAA2QnCzS0qodkXZVSU+Xpx4AzUHOmKLRaBYvXnzPPfcsXLgwLi5u0aJFjz/++Ouvv96zZ89p06bRfQagYeLjRW6u7cGEhGo7wgFwKzKv9OnVq9f777//5JNP/u9///vwww9LSkp+/etfv/feex07dpS3MABuSau106qSnk6rCuCm5F+QHBYWtnz58iNHjly4cOHw4cMLFy5s06aN3EUBcFu0qgAeRP6YAgDNLznZdlt9WlUAN0RMAeChpLXKWm21g7SqAG6FmALAc0kTQLSqAG6LmALAo9GqArgzYgoAL1Bbq0pqqkwFAXAIMQWAd7DbqpKSQqsKoGTEFABeo7ZWlfBwodfLUhGAuhFTAHgTu60q0gQQrSqA8hBTAHgfWlUAN0FMAeCVpFYVmwmglBTWKgOKQkwB4K3stqpIa5VpVQGUgZgCwLvRqgIoGDEFgNejVQVQKmIKANCqArhKA2dUiSkAIISgVQVwJr2+6nJa4eGdXnzR8fsRUwDAit1WFS4ABDSOXi8yM0VCgggPFwkJ0utovNHo+AmIKQBQXc1WFSFoVQEaRq8XqakiNlbExor09EafhpgCADXQqgI0jtXkjkhJsTthmqdWO36+BtwUALyI1KpiszJZalVJS7NNMICXkyZ3srLqGjjRakVMjBgyZGdxseMnZjQFAGrHripA3fT6O60ntWUUrVakpIjcXJGWJuLjG3R6RlMAoE7JyWLIENvpnthYkZIikpNlqgmQm14vtmwR6el1rYPTakV8vBgypCmjj8QUAKiP1Kry0zqFKikpIjPTTrMt4MGkyZ0tW+oaUJQmd6ZObZa5UWIKADhAalWxGdamVQVewpHWEyGq0kkDp3XqRkwBAIelpYkhQ0RCwp0jUqtKzX3hAM8gTe7YdGjZkCZ3pk4VWm2zPz4xBQAaIj5eaLW0qsDDSekkM9Nlkzu1IaYAQAPRqgJP5XjryZAhzTu5UxtiCgA0HK0q8DBSOqm79USa3HHtqCExBQAaq7ZWlbQ0MWWKfGUBDnPVuuJGI6YAQBPEx4uYGBEeXu1gQoI6K0ssXSpTTUB9XL6uuNGIKQDQNFqtnVaV9PSQ774TX38tW1VATQ3Z0t41rSf1IqYAQJNJrSqpqdbrNv10OqFSVQ2YC8E6IMjJ8XXFCvuHSkwBgGaSnCy6dKnWqiKE0OurPhtSUogscDUH1xXL13pSL2IKADQfqVUlNtZ+QyKRBa7hPq0n9SKmiJ/9TEycqNgcCcDdaLUiI8O0erV6zZq6bmYTWWJihFbrpH084S3k29Leebw3pljP01lm6/h6A6AZaLVi5crv583rXFlZ/5C7EEKvr/pcsY4sfHmC4xxfV+xuUdhLY0pmpkhIsPNs2v16w3sFgEbSakVyctX3Hke6BIRVZJHubll2wdsQalLMlvbO43UxxZFmZ8stea8A0GxqRhYh6nkz0uurhvEFb0Oworwt7Z3Hu2KKtD+kzSCK9Nqv9+uN5b1CKL0tGoDiSZFFCJGcTGRBA+j1IjVVgVvaO4+3xJTaBlFiYkRaWtU8nYMjssJqbkhYtbO423wfAGVoYmQRfHPyAorf0t55VGazWe4aGmbNmjVCiKSkJMfvotfb7g8p6oubDr5X2JC+4bhPA3UzKCgoCAgI0Gg0chcCIYT4/vvvO3TooFZ7y9cPJTOZTAUFBZ07d278KaQgcvFiPR9ONjz0s6qJjEajwWDo0KGD3IU0kAetK7bWoM9xz387q74tZBVpx8g6Bj9svt7o9SIry6HWN+kfVUJC1Rm8J68AaGbWKw8tkcWRtyGbwV4ii9txcEt77/ha7Mkxxe5ETyPm7CyzwNJ7hRCOdusnJIjUVHdc/wVAYWwii+PfnGwiS5cuHv+p5t4c39Leaz5XPHbSx+6S43oHURrK8bkhz2ppuoNJH0Vh0kc5mmHSxxGORxZr3rdDlNInfdx/S/sGadCkjwfGlNrCaEqKc1+SlkHZOiKL54VgYoqiEFOUw0UxxRqRpXYKjSke2npSL6+OKbUtOXbxSEZqqkOx2APeFogpikJMUQ4ZYooNx9cuWnjuwkVlxRQpUEord+rguR2OXhpTHFly7GKOTDKmpLj3GB4xRVGIKcohf0yx1rjI4kH7cCslpnjulvYN4q4rfSoqKhYvXvz5559v27YtKiqqQfdtxJJjF7DsOSmN6tnNzVKIkb1UAJ6MPfvl5QVb2juPgmLK7t27P/7440Z8L2/ckmNXiompWihUW4yW+vGlCwl56CAfAGVoXGRhA9xG8KYt7Z1HKTHlzJkzK1asaOgMVHMtOXYNy5tDHZNBLGMG4DpcZshJvG9Le+dRREwpKytbuXJlcHBweHj4qVOnHLyXa5YcO4P0zjB1qkODK/wzBuAK7NnfdF68pb3ztJC7ACGE2LZtW3Z29vz58zt16uTI7aWcWnNFT0qKyM1VekaxkN4TcnNFbm6tbwVSXgkPF6mpDdgsGwCaxDLKYjZXvUNJX5vqJr1hxcYKlarqbcvxjl23JvXxxMaK8HCRkmL/zVpKJxkZIjdXJCeTURwn/2jK0aNHN2zYMG7cuJiYmM8++8yRu/z1r+NNpmpH3HrUwfKGUNsyZgZXAMjGZpTFwcsMecOe/Wxp7xIyxxSDwbBq1aqQkJCkpCTHV1GaTNUGXWRccty8HOlckfKKuy9jBuCWmmvPfnd//2JLexeSM6aYzeb333//m2++efvtt0NCQhpxBrU6LzLyUFxc3t/+JoYNGxYaGtrsRbpeUJBIShJJSSI9XWRnq3futLP0yXoZc1LSTRdXaK2kpKSystJkM7oFmRQXF/v7+7NvihKYTKbi4uKAgAC5C3GaoCDRp4/o00ckJVmaVPwOHfLT6eq6V83IIsTNhlzxvnGMRmNpaam/v39TTqLOy/P74AP1gQN1xDJTp07lgwaZpky5k8NuyvkWLbvCwsJ9+/bZHNTpdNHR0Q6eQc63s6NHj7755puTJk0aPHhwg+7o56crL4/WasWMGYfU6jzpoGdkFGvx8SI+3pSSYty5U1Nnp21Qp06mefOMjClCpXK/DRs9ldlsVqlUclfhKj8t+SkXwpSXp87L8zt0yPFRlqCUFFOnTsbx44Vw4AJpriclsO3b60pgWq2IiTH94hfGCRNcWJkbaPpHs2xvakVFRc8//7wQYvPmzcHBwdLB+fPnf/HFF3Vv7ybtXhcYmORtn8r1jjLKMsTILrSKwi60yqGsXWhl1JQ9+5uvEa8xu9B6/Zb2zuMem+WfOHFiypQpBoPB7m8DAgJqCysN+ut5HsfXu7mm05aYoijEFOUgptjRlD37m/YNrGExhS3tncw9NssPDg4eP358eXm59UGdTpefnx8bG9uxY0fLEAusObhHXEqKSE/nRQRASZqyZ7+01tGplxny1usVK5yyZrIdn/Tx2tGUmuS9GjOjKYrCaIpyMJrSAI0bZWnIBrh1jaY4uK6YLe2bj3uMpqC5sIwZgHuTa89+trR3B8QUD2F5maen1/qtgKsxA1C6Ju7ZL01y1701C1vauxVlTfo4gkkfRzj4Mmx6fzqTPorCpI9yMOnTzByMLDZ+ShvG/v0NJ050OH2a1hMlcI+VPo1GTGkQZy9jJqYoCjFFOYgpTuT4nv0OYkt712rQ57giLj0I57Fc4LC2C4dZrm4oXSkMAJTOMnUtXbs1LU2kpDRy/EOrFSkpIiNDZGSQUZSJmOIVuBozAM9kiSzSxYczMhyKLDbXK2bbBgUjpngXBlcAeCyps6SOyCKlk7S0qjEYGlDcATHFGzk+uKJSVe3LAgDupHpkKd+7t+DSpap0wuSOWyGmeDUpr5jNdb1yU1JEbCyDKwDcllZrauAFbqEcxBQIIe6Mg9Y9GaRSifDwejZDAgCguRBTcIeDk0EJCXTaAgBcgZgCOxzvtB04MGT5cr/09KrLcRBcAADNiG2gUCtHrsacl6d+9VX797X8Qfqz9P9dutz5s+VXAADYRUxB/aS8MnVq/RvwW1hu48iNrXOMdXbp0oVAAwBejZgCRzkyuNI4UpQh0AAAbBBT0GDWV2POyyvZt+8utVotXaPU2RoaaIS9WSebrAMAUCxiChovPl4UFJTOnt3C+tKD1klCrxcXL945bjnoskAjGjhIQxsNACgKMQXNzPFRCuskIWOgEcw6AYBSEVMgG+t5mXrZBBcp09iM3Chw1olAAwBNQUyBe2joII1CZp2apY1GkGkAeCtiCjyNmwYa0YRBGksbzbVrfnFxzV0fAMiHmALv1eg2GmE162STdZytvgcKEULExFRdGhYA3B0xBaife7XRSBcukC50EB8vpk5lwgiAuyKmAM1MObNO0qWXLHllyBARE9P4swGA6xFTANm4LNBIeUV6rJiYqg36AED5iCmAG3Aw0Hz9dcGePSEtW6pru5SBXi/S04UQTAkBcA8t5C4AQLPp1MmUkiKSk4XZLHJzq7JIbaQhlvBwER4uUlNFZqbLygQARxFTAM8kzezk5lbllTq6UqS8EhtblVek4RYAUAJiCuDhpLySkVGVV+Lja72llFcSEoRKVRVZAEBexBTAW0h5JS1NmM0iI0PU1r8ikSKLJa8wJQRAFsQUwBtJ+7853sJimRIirwBwJWIK4NUa18ISG8uUEABXIKYAEKJ6C0vdU0J6fdUut5YpIRdcJQCAdyKmAKhG2gKOVc0AlICYAqBWjV7VzJQQgGZBTAFQP5tVzXVPCUk3YEoIQNMRUwA0gJRXrKeE6sCUEIAmIqYAaCQpsljyChvdAmh2xBQATWUzJVRvXpE2umVVM4B6EVMANBtLXnFko1tWNQOoFzEFgFOwqhlA0xFTADgXG90CaDRiCgAXadCqZqaEAAhiCgDXq7mqmSkhAHYRUwDIiY1uAdSBmAJAEWymhOLja71lzY1uAXgqYgoAZZHySlqaQ6uapchiyStMCQEehpgCQLkauqrZMiVEXgE8AzEFgBtoRAsLG90CHkD+mHLmzJlp06ZFRkZGRET07dt30aJF+fn5chcFQKGsW1jY6BbweDLHlL17944ePTorK6tfv35PPfVU27ZtP/zww/j4eJIKgLpptWx0C3g+OWPK1atX165dGxAQ8MEHH7z33nvLly///PPPFyxYcOHChddee80KjiP9AAATg0lEQVRkMslYGwA30rhVzQkJTAkBSidnTMnJyTl9+vTIkSP79esnHfHx8Zk4cWKPHj2OHj1648YNGWsD4I4atNFtejpTQoDSyRlTLl261KZNmz59+qhUKstBX1/fNm3ayFgVAA9Qc6PbOjAlBCiWnDHlmWeeOXLkSFxcnPXB06dPnzx5Miws7K677pKrMACeRIoslrzi+Ea36ekuqxGAfWq5C6jGYDCsWbOmtLR0woQJGo1G7nIAeBTLEIteL7ZsEZmZtQ6cSHlFCJGQIGJiqnp1ATSUNJcqvdCysoReL/R6UVg4aPnyQw6eQUExxWg0JicnZ2dnT5o0adSoUXXcUqfT1Tw4bNiw0NBQp1UH+0pKSiorK+l3Voji4mJ/f3+1WkGva2UKChJJSSIpSQhRFVbWrAmq7cbSDaSVRPHxYtCg8ujo8nofwmQyFRcXBwQENGPZaDSj0VhaWurv7y93IZ4sL08thNDp/IQQBw6opeuc1yJaCHeLKUVFRbNnz/7qq6/i4uIWL17csmXLhp6BjAKoVCqz2Sx3FW5GGixJSbmZl6feuVOTnl5rL+1PQyx+nTqpx483Snesjdlstu66AzyJNCgi/S8vT52fr5bSiTMoIqacPXt25syZZ8+enTZt2oIFC+rNKNHR0UnS9yDIraysLCAggBk6hTAYDMHBwYymNE5QkOjVy6Epobw89Zo1QWvWCK32zvYtNkwmU3l5eVBQrYM0cCW1Wu3j48PT0QiWOJKVVfWji3vM5X87y87OnjNnjsFgePHFF5977jkfHx+5KwLg1axbWDIzxcWLtS4Ukt6+raeEpk6ta5c5QMmcl0ikQK/ViiFDhBDiP//Z6fh9ZY4pR48enTNnzq1bt956661HHnlE3mIAwJqUPIS4M8RS75SQJa8MGaLu2tV1pQKOk/4NWxKJdZdrE0kZ3ZJIpB9rzo0WF+c5fk45Y0p+fv6CBQuEEJs3b37ggQdkrAQA6taIVUKdOnVQq+98jxRCdOlS7UfA2ewutGmWnQytI4iUSJz0D1vOmLJjx47z58/7+vrOnj3bptesY8eOa9euDQkJkas2ALDLJq9Iu9naJS18qO0jwfp7p3WIsRwEGsQDEoldssUUo9H473//Wwhx69atmhcaZMECAIWT8ooQIi1NZGaKrKx69rq1YRl4r+P8opYcU8cKI3gDT00kdskWUzQazXvvvSfXowNAM7JsAVfvlJDjGp1jZP9cQTOyRJCLF++0bDcLyz8VrbbqX44y46/8K30AwGNYpoTOnTMdPVpkNIZcvChE9X0mmosjOcYmtUjrLMgxyuSyhTaKTSR2EVMAoPlptaJVq/LOne38ynqdhXWIsf5Ds6j7bEwqyYhE4jhiCgC4lCUf1KaOHNOMO2sxqeQCsi/99QDEFABQlkbnGNdPKglyzE+c3dZqnUi86r8wMQUA3IwjOUb6gJTmFMRPH5+uzDEevOLaqxbayI6YAgCexvLZZpkFsL7qkMInlYSSJi9IJLIjpgCAd2FSqbZ6vHzprzIRUwAA1bhRjmncimsW2rgRYgoAoGHqzjEKXHHdvr26vNy/uJhE4n6IKQCA5qTIFdd+Qvg1+lTWiURp3TMej5gCAHAphUwq1VGYdy79VSZiCgBAWVyw4pqFNu6CmAIAcDMNXXF97pzJx6dCpfInkbgdYgoAwKPUHIwxGssNBkOHDv7yFIQmaCF3AQAAAPYRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgELJH1Py8/NnzpwZGRkZERExePDgd955p6KiQu6i4KjLly/LXQLu4OlQjsLCQrlLwB08He5L5phy8uTJcePGffbZZ/369Rs3bpzJZEpJSUlOTiapuIsVK1bs27dP7ipQZe7cubwdK8czzzwjdwmocuzYsblz58pdBRpDLeNjV1RUrFu3rri4+C9/+cuIESOEEAaD4fe///3HH388YsSIhx9+WMbaAACA7OQcTblw4YJOp4uOjo6JiZGOBAQEJCUl+fr6fvrpp2azWcbaAACA7OSMKadOnbp+/Xr//v39/f0tB8PDwzt16vTtt98WFRXJWBsAAJCdnDFFmkSPjIy0Pujr6xsUFFRcXGw0GmWqCwAAKIKcMeXixYs1D7Zu3To0NNRoNBYXF7u+JAAAoBwyt9DWPKhSqVq0qCc86XQ651SEBsvPz9fpdHl5eXIXAiGEyMvL27lzp9xVoEpeXt6aNWvkrgJCCKHT6fLz83k6FEJqS3XwxnLGlJYtW9Y8aDabb9++Xce9Bg0a5LSK0GDjx4+XuwTckZSUJHcJuIOnQzkc/1CEC0RHRzv+US5nTOnSpUvNg6WlpYWFhRqNJjAw0O69oqOj+QcHAIA3kLM3RYop586dsz5469atmzdvBgYGajQameoCAACKIGdM6datW7t27XQ6XVlZmeXg+fPn9Xr9z3/+8+DgYBlrAwAAspMzpnTq1KlPnz46nW7//v3SZm4Gg2Ht2rW3b98ePXq0SqWSsTYAACA7lbybvR49ejQxMfHmzZsDBgzo2LFjdnb2lStXJk2alJqaarfBFgAAeA+ZY4oQIjc399VXX83Ozr5161bHjh2nT5/+9NNPk1EAAID8MQUAAMAuOXtTAAAA6kBMAQAACkVMAQAACuVOMeXMmTOTJk3q3r17165dH3/88b1799JYI5ezZ88OHDgwoob169fLXZp3ycnJGTBgwP79+22OV1ZWfvrpp4MHD46IiIiMjJw2bVpubq4sFXqP2p6Ld999t+YrpXfv3idOnJClTs925syZadOmRUZGRkRE9O3bd9GiRfn5+dY34KXhSvU+HY68OuTcLL9B9u/fP2fOnIqKitjY2FatWmVlZc2YMWPhwoWJiYnssOJ6eXl5169fDwwMDAgIsD5u8yOcqqioaMWKFdevX7c5bjKZXnnlla1bt4aEhIwbN+7SpUtZWVnHjh3buHFjnz59ZCnV49X2XAghcnJyVCpVSEiIr6+v5WBAQIBa7TZvv+5i7969c+bMqaysHDBgwL333nv48OEPP/zwP//5T3p6elhYmOCl4Vr1Ph3CwVeH2R3cuHEjLi6uf//+R44ckY7k5eUNHTp04MCBp0+flrc277Rp06aIiIh//vOfchfivb7//vu4uLjw8PDw8PAvvvjC+lc6nS4qKurZZ58tKSmRjvzjH//o0aNHYmLiDz/8IEexHq6O58JoND777LOPPPLIlStX5CrPS1y5cmXEiBH9+/f/5ptvpCMmk+mtt96KiIiYNWtWRUWFmZeGCznydDj46nCPSZ/jx4+fPHly5MiRvXv3lo6EhYXNmjXr2rVr//znP+WtzTudOnUqKCioffv2chfijaRR67i4uHPnzv3sZz+z+a3ZbN67d++PP/74q1/9yjK49dhjjw0bNuzQoUM2l9BCE9X9XAghSktLL168GBYWdtddd7m+PK+Sk5Nz+vTpkSNH9uvXTzri4+MzceLEHj16HD169MaNG7w0XKnep0M4/Opwj5hy+PDhioqKQYMGWc/vREZG3n333d98882PP/4oY21eyGg05uXltW/fPjQ0VO5avNHJkyeXLFni4+Pz9ttv//KXv7T5bUlJybFjx+65557u3btbDqrV6oEDBxoMhuPHj7u2WA9X93MhhCgoKCgqKuratWvr1q1dX55XuXTpUps2bfr06WP9MeHr69umTRvpz7w0XKnep0M4/Opwj5hSWFgYEBDQqVMn64OBgYH+/v7Xr18vLy+XqzDvVFJSkp+fHxAQsHbt2gEDBkRERAwYMGDFihUlJSVyl+YVfHx8nnvuuS+++OKhhx6q+dsff/zxxo0bnTt3tn47EEJIQ18FBQUuqtI71P1cCCEuXbpkNBpv374tNRJK7f979uyprKx0cake75lnnjly5EhcXJz1wdOnT588eVL6vs5Lw5XqfTqEw68ON+jhKi0tvXLlSs3jd911V4cOHQoKChhNcbH8/Pzr16/n5+dfuHAhOjq6VatW2dnZb7/9dlZW1saNGy29UXCSn/3sZ3bnFyTXrl0zGo01j4eEhGg0msLCQmeW5nXqfi6EEN9++60QYtu2bV27do2Li7tx48a//vWvWbNmPf3008nJyVwVxKkMBsOaNWtKS0snTJig0Wj+97//8dKQkc3TIRx+dbhBTJFab+z+qkUL9xgN8jDFxcWtWrUaM2bMSy+95O/vL4QoKytbunTp9u3b//rXv7788sssYZBRZWWl3ddLixYtWBPnYpWVlSUlJRqN5tVXX/3lL38p/ffPzc2dPn36jh07fvGLX4wYMULuGj2W0WhMTk7Ozs6eNGnSqFGjBC8NWdl9Ohx8dbjBx7xKpartY+/27dsuLgZCiKFDhx45cmTZsmVSRhFC+Pv7/+53vwsLC5OucS1veV7Ox8fH7uvl9u3bZvYZci0fH5+lS5ceP3581KhRlg/C8PDwWbNmmUwmaU2QvBV6qqKiot///veffPJJXFzc4sWLpe/lvDTkUtvT4eCrww1iSuvWre+5556ax3/44YeCgoK2bdu2atXK9VXBRnBwcOfOnUtKSuxuHQGXadeunTSgauPq1atGo5GuZyXQarXSLENpaanctXigs2fPPv3009nZ2dOmTVuxYoXl5cBLQxa1PR21qfnqcIOYIoTQarUGg+Hy5cvWB4uLi8vKyu6++24/Pz+5CvNaBoOhoqLi/7d3PyFN/3Ecxz/f9v162iSq7yE9SH2jjCB2cNRBHIiaAw9qQWYQFRlkDlqgO+Ql8CAWSYxpiAjdVg0LozpkhDQQHP3xkEYRxugrguKoacFcrcNgiL/fr98Osc/X9nwcP6fX+PBmr+37+X6//1xXVdVms+U/D7IyZ7ZM0/z27dv69cz47Ny5U1KuAvXjx48vX7786491VVW51vDHRSKR1tbWT58+dXd3+/3+9ad/GI38+812iJynY3PUFKfTqWlaJBJZ/3nevn27tLRUUVHBvyn5lEqlOjo6nE7nxMTE+nXTND98+MBdytLZ7fb9+/cvLCzMzs5mF1Op1OTkpMPhOHjwoMRshSYWi1VVVTU2Nm44nvn69etEIsFdyn/cmzdvfD5fMpkcGBg4c+bMhp9MjEae/X47cp+OzVFT9u3bZxjGo0ePXr16lVkxTTMYDOq6Xl1dLTdboVFV9ciRI0KI27dvx+PxzGI8Hu/p6VleXm5qatq2bZvUgBDV1dWKogwPD2c36OnTp+Pj44cOHdqzZ4/cbAWlpKSkoqIiFos9ePAge4/ly5cvA4HA9u3bjx49KjfeX8Y0zc7OTiHEyMjIf30vMBp587/bkft0bI47MnRd93q9Pp/v5MmTVVVVmXf6rK6u+v3+9Q/qQX7U19cfP348FAq53W632y2EmJiYWFlZaWxsPHHihOx0EIcPH25ubg6FQh6Pp7Kycn5+PhqNbt26tb29PXvqGXmgqmpXV9fMzMy1a9fC4bDL5YrFYtFo1Gaz9fT0HDhwQHbAv8q9e/c+fvxYVFR06dKlDVfTSkpKAoGAruuMRt7ksh05TsfmqClCCI/Hs2PHjr6+vufPn//8+dMwDJ/PV19fz8Xd/NM07erVqy6Xa3Bw8PHjx0IIwzAuXLjQ0NDAcyCsILNB5eXlQ0NDo6OjRUVFbrf7ypUru3btkh2t4JSWlt65c+fWrVv379+/e/duZi+8Xm/2vR/4I1ZWVqampoQQyWRywzt4hRCKomQODDAa+ZHjduQ4HQo3YgEAAGvaHGdTAABAAaKmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAJAskUi0tLTs3r27u7s7lUpl10dHRw3DqK2tNU1TYjwAElFTAEjmcDj8fr/D4QiHw5OTk5nFz58/B4NBTdMuX75cWloqNyEAWagpAORzOp2nTp1KJpPBYDCRSKytrd28eXNubq65ubmmpkZ2OgDSqLIDAIBQFOXs2bORSCQajY6NjRUXF4+NjRmGcfHiRU3TZKcDII2STqdlZwAAIYR48eJFW1ub3W7fsmXL169f+/v7PR6P7FAAZOKiDwCrqKysbG1tXV5eXlpaOnbsWG1trexEACSjpgCwCkVRXC6XpmmKopSVlakqV6WBQkdNAWAVi4uLgUAglUrZbLbh4eH379/LTgRAMmoKAEtIp9ODg4Pv3r1ramo6ffr04uLi9evXv3//LjsXAJmoKQAsYWpqKhwO67p+/vz5tra28vLyZ8+ePXnyRHYuADJRUwDIF4/He3t7V1dXz507t3fvXl3XvV6vqqo3btyYm5uTnQ6ANNQUAJKl0+lQKDQ9Pe1yuVpaWjKLNTU1dXV18/PzAwMDa2trchMCkIWaAkCy6enpkZERu93u8/kcDkdmUdM0r9er6/rDhw/Hx8flJgQgC493AwAAFsW/KQAAwKJ+ASB+OXeEZTplAAAAAElFTkSuQmCC\" 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":2529,"title":"Solving Quadratic Equations (Version 2)","description":"Before attempting this problem, solve version 1:  \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003e.\r\n\r\nIn this version, the discriminant can have any value.  Complete the function so if the discriminant is negative, the function returns values of NaN --- \"Not a Number\" --- for x1 and x2.  Otherwise, the function computes x1 and x2 as before using the formula\r\n\r\n\u003c\u003chttps://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\u003e\u003e\r\n","description_html":"\u003cp\u003eBefore attempting this problem, solve version 1:  \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eIn this version, the discriminant can have any value.  Complete the function so if the discriminant is negative, the function returns values of NaN --- \"Not a Number\" --- for x1 and x2.  Otherwise, the function computes x1 and x2 as before using the formula\u003c/p\u003e\u003cimg src = \"https://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\"\u003e","function_template":"function [x1, x2] = SolveQuadraticEquation(a, b, c)\r\n\r\nend","test_suite":"%%\r\nqe_correct1_1 = -1;\r\nqe_correct1_2 = -2;\r\n[qe_result1_1, qe_result1_2] = SolveQuadraticEquation(1, 3, 2);\r\nassert( (abs(qe_result1_1 - qe_correct1_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_2) \u003c 0.0001) || ...\r\n        (abs(qe_result1_1 - qe_correct1_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_1) \u003c 0.0001) );\r\n%%\r\nqe_correct2_1 = 0.224745;\r\nqe_correct2_2 = -2.22474;\r\n[qe_result2_1, qe_result2_2] = SolveQuadraticEquation(2, 4, -1);\r\nassert( (abs(qe_result2_1 - qe_correct2_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_2) \u003c 0.0001) || ...\r\n        (abs(qe_result2_1 - qe_correct2_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_1) \u003c 0.0001) );\r\n%%\r\nqe_correct3_1 = -1;\r\nqe_correct3_2 = -1;\r\n[qe_result3_1, qe_result3_2] = SolveQuadraticEquation(2, 4, 2);\r\nassert( (abs(qe_result3_1 - qe_correct3_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_2) \u003c 0.0001) || ...\r\n        (abs(qe_result3_1 - qe_correct3_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_1) \u003c 0.0001) );\r\n%%\r\n[qe_result4_1, qe_result4_2] = SolveQuadraticEquation(4, 4, 4);\r\nassert( isnan(qe_result4_1) \u0026\u0026 isnan(qe_result4_2) );\r\n%%\r\n[qe_result5_1, qe_result5_2] = SolveQuadraticEquation(9.1, 12, 4.1);\r\nassert( isnan(qe_result5_1) \u0026\u0026 isnan(qe_result5_2) );\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":90,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-25T23:26:04.000Z","updated_at":"2026-03-16T12:13:52.000Z","published_at":"2014-08-25T23:42:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBefore attempting this problem, solve version 1: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this version, the discriminant can have any value. Complete the function so if the discriminant is negative, the function returns values of NaN --- \\\"Not a Number\\\" --- for x1 and x2. Otherwise, the function computes x1 and x2 as before using the formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAMAAABEpIrGAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAAC1QTFRFeHh4k5OT9vb2gYGBnJycwMDAt7e3ioqK0tLS7e3t29vb5OTkycnJ////b29vvCMpXwAAAKZJREFUeNq8k0sWwyAIAEXzh3D/41ZrahASklXZ6cxTEAz8EOGFsDvxTyECM0RHgJIwOEIt6VFYX19BAd0kKe8vTpn0vY9uheXoQjGYrICtf9mg3Qgo+kt12fE4sxQwaGFQXCdJmmshaV4EnKYxmgMO/pvJVJ92NrwNbSpnrJafUz1kYbRcjP121ii4EKDVIPnVx+n4hdBzKyhuBM21YLgSLOePAAMAW0UziCh1I3kAAAAASUVORK5CYII=\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2509,"title":"Wind Chill Computation","description":"On a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \"wind chill,\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\r\n\r\n  windChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16\r\n\r\nComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.","description_html":"\u003cp\u003eOn a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \"wind chill,\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ewindChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16\r\n\u003c/pre\u003e\u003cp\u003eComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.\u003c/p\u003e","function_template":"function windChill = ComputeWindChill(T, W)\r\n  windChill = ... ;\r\nend","test_suite":"%%\r\nwc_correct1 = 23.1871;\r\nwc_result1  = ComputeWindChill(32, 10);\r\nassert(abs(wc_result1 - wc_correct1) \u003c 0.0001)\r\n%%\r\nwc_correct2 = -9.0101;\r\nwc_result2  = ComputeWindChill(10, 20);\r\nassert(abs(wc_result2 - wc_correct2) \u003c 0.0001)\r\n%%\r\nwc_correct3 = 17.4215;\r\nwc_result3  = ComputeWindChill(20, 2);\r\nassert(abs(wc_result3 - wc_correct3) \u003c 0.0001)\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-14T22:08:29.000Z","updated_at":"2026-02-17T08:49:29.000Z","published_at":"2014-08-14T22:37:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the \\\"wind chill,\\\" indicating the temperature that is felt based on the actual temperature (T, in Fahrenheit) and wind speed (W, in miles per hour):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[windChill = 35.7 + 0.6T - 35.7W^0.16 + 0.43TW^0.16]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function to compute wind chill. Note: While math notation uses abutment for multiplication, as in 5y, MATLAB requires use of * when multiplying items, as in 5*y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2510,"title":"Solving Quadratic Equations (Version 1)","description":"Quadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2.  The quadratic formula can be used to find the roots:\r\n\r\n\u003c\u003chttps://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\u003e\u003e\r\n\r\nThe formula can be translated into the computation of two roots x1 and x2:\r\n\r\n  x1 = -b + ...\r\n  x2 = -b - ...\r\n\r\nComplete the function to solve the quadratic equation denoted by a, b, and c.  Assume the _discriminant_ --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real. ","description_html":"\u003cp\u003eQuadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2.  The quadratic formula can be used to find the roots:\u003c/p\u003e\u003cimg src = \"https://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\"\u003e\u003cp\u003eThe formula can be translated into the computation of two roots x1 and x2:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex1 = -b + ...\r\nx2 = -b - ...\r\n\u003c/pre\u003e\u003cp\u003eComplete the function to solve the quadratic equation denoted by a, b, and c.  Assume the \u003ci\u003ediscriminant\u003c/i\u003e --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real.\u003c/p\u003e","function_template":"function [x1, x2] = SolveQuadraticEquation(a, b, c)\r\n  x1 = -b + ... ;\r\n  x2 = -b - ... ;\r\nend\r\n","test_suite":"%%\r\nqe_correct1_1 = -1;\r\nqe_correct1_2 = -2;\r\n[qe_result1_1, qe_result1_2] = SolveQuadraticEquation(1, 3, 2);\r\nassert( (abs(qe_result1_1 - qe_correct1_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_2) \u003c 0.0001) || ...\r\n        (abs(qe_result1_1 - qe_correct1_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_1) \u003c 0.0001) );\r\n%%\r\nqe_correct2_1 = 0.224745;\r\nqe_correct2_2 = -2.22474;\r\n[qe_result2_1, qe_result2_2] = SolveQuadraticEquation(2, 4, -1);\r\nassert( (abs(qe_result2_1 - qe_correct2_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_2) \u003c 0.0001) || ...\r\n        (abs(qe_result2_1 - qe_correct2_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_1) \u003c 0.0001) );\r\n%%\r\nqe_correct3_1 = -1;\r\nqe_correct3_2 = -1;\r\n[qe_result3_1, qe_result3_2] = SolveQuadraticEquation(2, 4, 2);\r\nassert( (abs(qe_result3_1 - qe_correct3_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_2) \u003c 0.0001) || ...\r\n        (abs(qe_result3_1 - qe_correct3_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_1) \u003c 0.0001) );\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":505,"test_suite_updated_at":"2014-08-15T09:50:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-14T23:08:09.000Z","updated_at":"2026-03-31T12:44:20.000Z","published_at":"2014-08-15T09:50:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eQuadratic equations have the form: ax^2 + bx + c = 0. Example: x^2 + 3x + 2 = 0, where a = 1, b = 3, and c = 2. The equation has 2 real solutions (roots): x = -1 and x = -2. The quadratic formula can be used to find the roots:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe formula can be translated into the computation of two roots x1 and x2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x1 = -b + ...\\nx2 = -b - ...]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function to solve the quadratic equation denoted by a, b, and c. Assume the\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\u003ediscriminant\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e --- b^2 - 4ac --- is not negative, ensuring that x1 and x2 are real.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAMAAABEpIrGAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAAC1QTFRFeHh4k5OT9vb2gYGBnJycwMDAt7e3ioqK0tLS7e3t29vb5OTkycnJ////b29vvCMpXwAAAKZJREFUeNq8k0sWwyAIAEXzh3D/41ZrahASklXZ6cxTEAz8EOGFsDvxTyECM0RHgJIwOEIt6VFYX19BAd0kKe8vTpn0vY9uheXoQjGYrICtf9mg3Qgo+kt12fE4sxQwaGFQXCdJmmshaV4EnKYxmgMO/pvJVJ92NrwNbSpnrJafUz1kYbRcjP121ii4EKDVIPnVx+n4hdBzKyhuBM21YLgSLOePAAMAW0UziCh1I3kAAAAASUVORK5CYII=\"}]}"},{"id":2609,"title":"If-then-else","description":"Complete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y.  Otherwise 7 is assigned to y.\r\n  ","description_html":"\u003cp\u003eComplete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y.  Otherwise 7 is assigned to y.\u003c/p\u003e","function_template":"function y = if_then_else(x)\r\n  ???\r\nend","test_suite":"%%\r\nx = 10;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 14;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 12;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 13;\r\ny_correct = 18;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 0;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n%%\r\nx = -2;\r\ny_correct = 7;\r\nassert(isequal(if_then_else(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":391,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-09-29T06:00:18.000Z","updated_at":"2026-02-18T14:51:46.000Z","published_at":"2014-09-29T06:00:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eComplete the function below such that if the value of x is in the range 10 to 14, inclusive, the value 18 is assigned to y. Otherwise 7 is assigned to y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"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":2529,"title":"Solving Quadratic Equations (Version 2)","description":"Before attempting this problem, solve version 1:  \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003e.\r\n\r\nIn this version, the discriminant can have any value.  Complete the function so if the discriminant is negative, the function returns values of NaN --- \"Not a Number\" --- for x1 and x2.  Otherwise, the function computes x1 and x2 as before using the formula\r\n\r\n\u003c\u003chttps://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\u003e\u003e\r\n","description_html":"\u003cp\u003eBefore attempting this problem, solve version 1:  \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eIn this version, the discriminant can have any value.  Complete the function so if the discriminant is negative, the function returns values of NaN --- \"Not a Number\" --- for x1 and x2.  Otherwise, the function computes x1 and x2 as before using the formula\u003c/p\u003e\u003cimg src = \"https://dl.dropboxusercontent.com/u/57773343/__IMAGES/QuadraticSolution1.gif\"\u003e","function_template":"function [x1, x2] = SolveQuadraticEquation(a, b, c)\r\n\r\nend","test_suite":"%%\r\nqe_correct1_1 = -1;\r\nqe_correct1_2 = -2;\r\n[qe_result1_1, qe_result1_2] = SolveQuadraticEquation(1, 3, 2);\r\nassert( (abs(qe_result1_1 - qe_correct1_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_2) \u003c 0.0001) || ...\r\n        (abs(qe_result1_1 - qe_correct1_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result1_2 - qe_correct1_1) \u003c 0.0001) );\r\n%%\r\nqe_correct2_1 = 0.224745;\r\nqe_correct2_2 = -2.22474;\r\n[qe_result2_1, qe_result2_2] = SolveQuadraticEquation(2, 4, -1);\r\nassert( (abs(qe_result2_1 - qe_correct2_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_2) \u003c 0.0001) || ...\r\n        (abs(qe_result2_1 - qe_correct2_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result2_2 - qe_correct2_1) \u003c 0.0001) );\r\n%%\r\nqe_correct3_1 = -1;\r\nqe_correct3_2 = -1;\r\n[qe_result3_1, qe_result3_2] = SolveQuadraticEquation(2, 4, 2);\r\nassert( (abs(qe_result3_1 - qe_correct3_1) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_2) \u003c 0.0001) || ...\r\n        (abs(qe_result3_1 - qe_correct3_2) \u003c 0.0001  \u0026\u0026 ...\r\n         abs(qe_result3_2 - qe_correct3_1) \u003c 0.0001) );\r\n%%\r\n[qe_result4_1, qe_result4_2] = SolveQuadraticEquation(4, 4, 4);\r\nassert( isnan(qe_result4_1) \u0026\u0026 isnan(qe_result4_2) );\r\n%%\r\n[qe_result5_1, qe_result5_2] = SolveQuadraticEquation(9.1, 12, 4.1);\r\nassert( isnan(qe_result5_1) \u0026\u0026 isnan(qe_result5_2) );\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":24594,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":90,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-25T23:26:04.000Z","updated_at":"2026-03-16T12:13:52.000Z","published_at":"2014-08-25T23:42:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBefore attempting this problem, solve version 1: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/2510-solving-quadratic-equations-version-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this version, the discriminant can have any value. 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