{"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":50631,"title":"Cosine effect in solar power towers","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: 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\"\u003eheliostats\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) do not aim at the sun (vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA4CAYAAACYCio/AAABD0lEQVRYhe2XYQ2DMBBGn4c6mAEMoAAFOMABDrCABiTgAQvVgAX243qhafgDg5Zk95Imo8nWx7XpvgPDMAzDMH7CA01pCYAa2HiJTMuLZDpEprv6A/VNow8iGzABn7Mi24NjOCMy3zT8gcTpqtxBEwQ8slVFcMCCVMb9tQTA+AYJkHujuIRhGMYVNH/oJVaR+UIbkH/XBQlBPnzecopoJvXRnAvP/vAbDzGzVyN++yHMZWNkT15x6KmQamVDexetSpEIqEyRzEjhJBYH5L6UCMiZUJGVjFWZDhaLD26WFtOFxapkPj64WdoGXTDt1rR/WXNIpAvqFnzYr/W0Uo/RIgm9RqqirWWxVtIwDON1fAHnd3ACjCJApQAAAABJRU5ErkJggg==\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe solar irradiance that bounces off the mirror is reduced by an amount proportional to reflectivity (assume 100% for this problem) and to the cosine of the angle between the normal vector to the heliostat and the other vector (sun or tower).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 60px; 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; perspective-origin: 384px 30px; text-align: left; transform-origin: 384px 30px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.5px 8px; transform-origin: 236.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe aim of this problem is to calculate the value of the cosine of the angle (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"cos(theta)\" style=\"width: 33.5px; height: 18px;\" width=\"33.5\" height=\"18\"\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: 35.5px 8px; transform-origin: 35.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) given 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: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enormalized\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: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vectors \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA4CAYAAACYCio/AAABD0lEQVRYhe2XYQ2DMBBGn4c6mAEMoAAFOMABDrCABiTgAQvVgAX243qhafgDg5Zk95Imo8nWx7XpvgPDMAzDMH7CA01pCYAa2HiJTMuLZDpEprv6A/VNow8iGzABn7Mi24NjOCMy3zT8gcTpqtxBEwQ8slVFcMCCVMb9tQTA+AYJkHujuIRhGMYVNH/oJVaR+UIbkH/XBQlBPnzecopoJvXRnAvP/vAbDzGzVyN++yHMZWNkT15x6KmQamVDexetSpEIqEyRzEjhJBYH5L6UCMiZUJGVjFWZDhaLD26WFtOFxapkPj64WdoGXTDt1rR/WXNIpAvqFnzYr/W0Uo/RIgm9RqqirWWxVtIwDON1fAHnd3ACjCJApQAAAABJRU5ErkJggg==\" alt=\"S\" style=\"width: 17px; height: 28px;\" width=\"17\" height=\"28\"\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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA8CAYAAAADm2gpAAABBElEQVRoge2XUQ2DMBBAn4c6wAAGUIACHMwBDrAwDUjAQy2gYRa6j/bSbh/LYMB1yb3kQvgovLTHcQeGYRiGYfzEACyA0xaBKFKFjAM8FcmsRKFmzwMaoDsoViAAD2LubGJMi8+IFWi/FZGsPyJKCc+OXTkKnyQmFJN2SBK9lkA1Ei3xK1GVEBF1CcMwjL/HATMVtIV34v9FDZckQrqq0JN70kBsMaVXvYyR2AqWIjI+qLSD0pd6jZeXyG5MmhJ9IXJpXrwzFSKqyKiwaEo48m7cNEVkXAhsGCHPQKqpalmHXMjmdD+iUMga8rEMKeaPK06i47Wsryj9/qX3WIhHYhiGYQhPGKFtN+aS55YAAAAASUVORK5CYII=\" alt=\"T\" style=\"width: 17px; height: 30px;\" width=\"17\" height=\"30\"\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: 163.5px 8px; transform-origin: 163.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that are known for every heliostat at every moment.\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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eHints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 98px 8px; transform-origin: 98px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eVectors are 3×1, with norm = 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eMake use of scalar product to calculate cosines, taking advantage of the normalized vectors.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function costheta = cosine_effect(s,t)\r\n    costheta = s'*t;\r\nend","test_suite":"%%\r\ns = [0.131;0.9064;0.4015];\r\nt = [0.606;0.5595;0.5654];\r\ny_correct = 0.952225;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.464;0.3063;0.8312];\r\nt = [0.4748;0.0111;0.88];\r\ny_correct = 0.988723;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.2723;0.9419;0.1967];\r\nt = [0.5048;0.3619;0.7837];\r\ny_correct = 0.90346;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6188;0.6217;0.4803];\r\nt = [0.3197;0.901;0.2932];\r\ny_correct = 0.974384;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0558;0.9708;0.2335];\r\nt = [0.7516;0.1574;0.6406];\r\ny_correct = 0.819875;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6055;0.4877;0.6289];\r\nt = [0.0481;0.6866;0.7255];\r\ny_correct = 0.954014;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.543;0.3969;0.74];\r\nt = [0.3393;0.1861;0.9221];\r\ny_correct = 0.985002;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6818;0.719;0.1346];\r\nt = [0.807;0.2223;0.5471];\r\ny_correct = 0.944363;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.49;0.2646;0.8306];\r\nt = [0.6066;0.736;0.3007];\r\ny_correct = 0.933216;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4027;0.5963;0.6945];\r\nt = [0.4281;0.6023;0.6738];\r\ny_correct = 0.999889;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.7066;0.2176;0.6733];\r\nt = [0.1189;0.7977;0.5912];\r\ny_correct = 0.909841;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3783;0.8162;0.4367];\r\nt = [0.6835;0.5943;0.4239];\r\ny_correct = 0.982034;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6461;0.3837;0.6597];\r\nt = [0.2987;0.6588;0.6905];\r\ny_correct = 0.974999;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.5069;0.3904;0.7685];\r\nt = [0.3379;0.0217;0.9409];\r\ny_correct = 0.975392;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0829;0.9172;0.3897];\r\nt = [0.0039;0.9956;0.0936];\r\ny_correct = 0.98741;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.9503;0.1126;0.2904];\r\nt = [0.1529;0.6544;0.7406];\r\ny_correct = 0.846803;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3519;0.3553;0.866];\r\nt = [0.6345;0.6394;0.4343];\r\ny_correct = 0.955666;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.8303;0.557;0.019];\r\nt = [0.605;0.4145;0.6799];\r\ny_correct = 0.934393;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.2458;0.4361;0.8657];\r\nt = [0.1713;0.8422;0.5112];\r\ny_correct = 0.962273;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.5596;0.6441;0.5216];\r\nt = [0.4502;0.8849;0.1193];\r\ny_correct = 0.970604;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4017;0.6335;0.6613];\r\nt = [0.4941;0.5698;0.6567];\r\ny_correct = 0.998438;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6328;0.1213;0.7647];\r\nt = [0.4235;0.6907;0.5862];\r\ny_correct = 0.948689;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6637;0.2984;0.6859];\r\nt = [0.1894;0.9587;0.2123];\r\ny_correct = 0.882446;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0484;0.841;0.5388];\r\nt = [0.2956;0.8876;0.3533];\r\ny_correct = 0.987704;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.792;0.3042;0.5293];\r\nt = [0.8189;0.5368;0.2029];\r\ny_correct = 0.979591;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.8298;0.1;0.5491];\r\nt = [0.7965;0.0613;0.6015];\r\ny_correct = 0.999344;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.1416;0.3261;0.9347];\r\nt = [0.4045;0.4427;0.8002];\r\ny_correct = 0.987314;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3135;0.5325;0.7862];\r\nt = [0.1271;0.7016;0.7012];\r\ny_correct = 0.991147;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4278;0.8839;0.1888];\r\nt = [0.0361;0.8996;0.4352];\r\ny_correct = 0.972812;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6453;0.6641;0.3776];\r\nt = [0.9671;0.2513;0.0398];\r\ny_correct = 0.950265;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-02T15:31:20.000Z","updated_at":"2025-10-15T01:28:33.000Z","published_at":"2021-03-02T15:33:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Solar thermal power plants with central receiver (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Solar_power_tower\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Solar_power_tower\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) the mirrors (called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Heliostat\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eheliostats\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) do not aim at the sun (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) or the tower (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), but the bisector of these two directions (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"265\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"464\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe solar irradiance that bounces off the mirror is reduced by an amount proportional to reflectivity (assume 100% for this problem) and to the cosine of the angle between the normal vector to the heliostat and the other vector (sun or tower).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim of this problem is to calculate the value of the cosine of the angle (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"cos(theta)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\cos\\\\theta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) given the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormalized\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are known for every heliostat at every moment.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\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\u003eVectors are 3×1, with norm = 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMake use of scalar product to calculate cosines, taking advantage of the normalized vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is the car sale and the cars are arranged according to the pascal's Traingle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 50.7042px; transform-origin: 420.1px 50.7042px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     2     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     3     3     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     4     6     4     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePattern like this so the car number is given like \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     n=10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo,you have to create a pascal's traingle and add the numbers and you have to add like this:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 111.549px; transform-origin: 420.1px 111.549px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     2     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     3     3     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     4     6     4     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%You have to add the numbers on the traingle except the 0 and you will get a matrix like:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     2     3     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     4     6     7     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     8    11    14    15     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    16    20    26    30    31\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo the number of the vehicle is given accoring to only positive numbers not 0 (Don't recognize zero when counting the vehical number!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing functions are not allowed!:-every function except eye,find,size\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou have to output the pascal's traingle number you summed up on that particular row and column like\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 50.7042px; transform-origin: 420.1px 50.7042px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%if I asked\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    n=10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%Output Should be:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    y=15;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWishing You luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = car_sale(n)\r\n  y = x;\r\nend\r\n","test_suite":"%%\r\nx = 10;\r\ny_correct = 15;\r\nassert(isequal(car_sale(x),y_correct))\r\n%%\r\nx=15\r\ny=31;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=78\r\ny=4095\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=108;\r\ny= 16489\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=45;\r\ny=511;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=21;\r\ny=63;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=8;\r\ny=11;\r\nassert(isequal(car_sale(x),y));\r\n\r\n%%\r\nfile=fileread('car_sale.m');\r\nassert(isempty(strfind(file,'regexp')));\r\nassert(isempty(strfind(file,'regex')));\r\nassert(isempty(strfind(file,'cumsum')));\r\nassert(isempty(strfind(file,'pascal')));\r\nassert(isempty(strfind(file,'abs')));\r\nassert(isempty(strfind(file,'celi')));\r\nassert(isempty(strfind(file,'ans')));\r\nassert(isempty(strfind(file,'!')));\r\nassert(isempty(strfind(file,'conv')));\r\nassert(isempty(strfind(file,'sum')));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":517513,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-02-14T02:11:38.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-01-17T09:17:21.000Z","updated_at":"2024-11-18T02:44:16.000Z","published_at":"2021-01-18T01:53:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"172\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the car sale and the cars are arranged according to the pascal's Traingle.\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[     1     0     0     0     0\\n     1     1     0     0     0\\n     1     2     1     0     0\\n     1     3     3     1     0\\n     1     4     6     4     1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePattern like this so the car number is given like \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[     n=10;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo,you have to create a pascal's traingle and add the numbers and you have to add like this:-\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[     1     0     0     0     0\\n     1     1     0     0     0\\n     1     2     1     0     0\\n     1     3     3     1     0\\n     1     4     6     4     1\\n    %You have to add the numbers on the traingle except the 0 and you will get a matrix like:-\\n     1     0     0     0     0\\n     2     3     0     0     0\\n     4     6     7     0     0\\n     8    11    14    15     0\\n    16    20    26    30    31]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo the number of the vehicle is given accoring to only positive numbers not 0 (Don't recognize zero when counting the vehical number!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing functions are not allowed!:-every function except eye,find,size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have to output the pascal's traingle number you summed up on that particular row and column like\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[    %if I asked\\n    %input\\n    n=10;\\n    %Output Should be:-\\n    y=15;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWishing You luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.7\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.7\",\"contentType\":\"image/7\",\"content\":\"https://th.bing.com/th/id/OIP.c5GCWa3fpE_MA4A9JhhR4wHaDp?w=328\u0026h=172\u0026c=7\u0026o=5\u0026pid=1.7\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":50631,"title":"Cosine effect in solar power towers","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 562.367px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 281.183px; transform-origin: 407px 281.183px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 52px; 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; perspective-origin: 384px 26px; text-align: left; transform-origin: 384px 26px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn Solar thermal power plants with central receiver (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Solar_power_tower\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Solar_power_tower\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) the mirrors (called \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Heliostat\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 30px 8px; transform-origin: 30px 8px; \"\u003eheliostats\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97px 8px; transform-origin: 97px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) do not aim at the sun (vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA4CAYAAACYCio/AAABD0lEQVRYhe2XYQ2DMBBGn4c6mAEMoAAFOMABDrCABiTgAQvVgAX243qhafgDg5Zk95Imo8nWx7XpvgPDMAzDMH7CA01pCYAa2HiJTMuLZDpEprv6A/VNow8iGzABn7Mi24NjOCMy3zT8gcTpqtxBEwQ8slVFcMCCVMb9tQTA+AYJkHujuIRhGMYVNH/oJVaR+UIbkH/XBQlBPnzecopoJvXRnAvP/vAbDzGzVyN++yHMZWNkT15x6KmQamVDexetSpEIqEyRzEjhJBYH5L6UCMiZUJGVjFWZDhaLD26WFtOFxapkPj64WdoGXTDt1rR/WXNIpAvqFnzYr/W0Uo/RIgm9RqqirWWxVtIwDON1fAHnd3ACjCJApQAAAABJRU5ErkJggg==\" alt=\"S\" style=\"width: 17px; height: 28px;\" width=\"17\" height=\"28\"\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: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) or the tower (vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA8CAYAAAADm2gpAAABBElEQVRoge2XUQ2DMBBAn4c6wAAGUIACHMwBDrAwDUjAQy2gYRa6j/bSbh/LYMB1yb3kQvgovLTHcQeGYRiGYfzEACyA0xaBKFKFjAM8FcmsRKFmzwMaoDsoViAAD2LubGJMi8+IFWi/FZGsPyJKCc+OXTkKnyQmFJN2SBK9lkA1Ei3xK1GVEBF1CcMwjL/HATMVtIV34v9FDZckQrqq0JN70kBsMaVXvYyR2AqWIjI+qLSD0pd6jZeXyG5MmhJ9IXJpXrwzFSKqyKiwaEo48m7cNEVkXAhsGCHPQKqpalmHXMjmdD+iUMga8rEMKeaPK06i47Wsryj9/qX3WIhHYhiGYQhPGKFtN+aS55YAAAAASUVORK5CYII=\" alt=\"T\" style=\"width: 17px; height: 30px;\" width=\"17\" height=\"30\"\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: 154px 8px; transform-origin: 154px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), but the bisector of these two directions (vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA4CAYAAACYCio/AAABK0lEQVRYhe2XbQ2DMBBAnwcczAAGpmAKcICDOcACGioBD1hAwyx0P9oLB2PL2LjAsntJ/9CEe+314wqO4ziO43zFAFz2lgA4A5GDyFQcSKYmydSf/uC8UbtmkQgE4LRWJBq2Zo1It1EbFiRWz8oWXLLAQErVLhRAT5qZ4q8lANojSEA6N3aXcBzHWcP8Iivyt9IyaEkqdALj9R6UQMP0yq+sRGS0YRZMLrjAeO3H/M0UPXJyQF2TSl9rLdIzpqWZBSyViGn1XqhAUgpqKqazZYYOFHmsP2X9dNYiLa+r8RtfvmPeRQLdFvr0+jA/R17Nhjym5utmc/SrbWnEsptkF9UYpajj+YhPTLdthdGBprftUlp02vosa1I8l4zPyGcLscn9VysJx3Gcn+AOM9qMINg1yfYAAAAASUVORK5CYII=\" alt=\"N\" style=\"width: 17px; height: 28px;\" width=\"17\" height=\"28\"\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: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 270.5px; 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; perspective-origin: 384px 135.25px; text-align: left; transform-origin: 384px 135.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe solar irradiance that bounces off the mirror is reduced by an amount proportional to reflectivity (assume 100% for this problem) and to the cosine of the angle between the normal vector to the heliostat and the other vector (sun or tower).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 60px; 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; perspective-origin: 384px 30px; text-align: left; transform-origin: 384px 30px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.5px 8px; transform-origin: 236.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe aim of this problem is to calculate the value of the cosine of the angle (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"cos(theta)\" style=\"width: 33.5px; height: 18px;\" width=\"33.5\" height=\"18\"\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: 35.5px 8px; transform-origin: 35.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) given 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: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enormalized\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: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vectors \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA4CAYAAACYCio/AAABD0lEQVRYhe2XYQ2DMBBGn4c6mAEMoAAFOMABDrCABiTgAQvVgAX243qhafgDg5Zk95Imo8nWx7XpvgPDMAzDMH7CA01pCYAa2HiJTMuLZDpEprv6A/VNow8iGzABn7Mi24NjOCMy3zT8gcTpqtxBEwQ8slVFcMCCVMb9tQTA+AYJkHujuIRhGMYVNH/oJVaR+UIbkH/XBQlBPnzecopoJvXRnAvP/vAbDzGzVyN++yHMZWNkT15x6KmQamVDexetSpEIqEyRzEjhJBYH5L6UCMiZUJGVjFWZDhaLD26WFtOFxapkPj64WdoGXTDt1rR/WXNIpAvqFnzYr/W0Uo/RIgm9RqqirWWxVtIwDON1fAHnd3ACjCJApQAAAABJRU5ErkJggg==\" alt=\"S\" style=\"width: 17px; height: 28px;\" width=\"17\" height=\"28\"\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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAA8CAYAAAADm2gpAAABBElEQVRoge2XUQ2DMBBAn4c6wAAGUIACHMwBDrAwDUjAQy2gYRa6j/bSbh/LYMB1yb3kQvgovLTHcQeGYRiGYfzEACyA0xaBKFKFjAM8FcmsRKFmzwMaoDsoViAAD2LubGJMi8+IFWi/FZGsPyJKCc+OXTkKnyQmFJN2SBK9lkA1Ei3xK1GVEBF1CcMwjL/HATMVtIV34v9FDZckQrqq0JN70kBsMaVXvYyR2AqWIjI+qLSD0pd6jZeXyG5MmhJ9IXJpXrwzFSKqyKiwaEo48m7cNEVkXAhsGCHPQKqpalmHXMjmdD+iUMga8rEMKeaPK06i47Wsryj9/qX3WIhHYhiGYQhPGKFtN+aS55YAAAAASUVORK5CYII=\" alt=\"T\" style=\"width: 17px; height: 30px;\" width=\"17\" height=\"30\"\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: 163.5px 8px; transform-origin: 163.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that are known for every heliostat at every moment.\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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eHints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 98px 8px; transform-origin: 98px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eVectors are 3×1, with norm = 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; 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 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eMake use of scalar product to calculate cosines, taking advantage of the normalized vectors.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function costheta = cosine_effect(s,t)\r\n    costheta = s'*t;\r\nend","test_suite":"%%\r\ns = [0.131;0.9064;0.4015];\r\nt = [0.606;0.5595;0.5654];\r\ny_correct = 0.952225;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.464;0.3063;0.8312];\r\nt = [0.4748;0.0111;0.88];\r\ny_correct = 0.988723;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.2723;0.9419;0.1967];\r\nt = [0.5048;0.3619;0.7837];\r\ny_correct = 0.90346;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6188;0.6217;0.4803];\r\nt = [0.3197;0.901;0.2932];\r\ny_correct = 0.974384;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0558;0.9708;0.2335];\r\nt = [0.7516;0.1574;0.6406];\r\ny_correct = 0.819875;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6055;0.4877;0.6289];\r\nt = [0.0481;0.6866;0.7255];\r\ny_correct = 0.954014;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.543;0.3969;0.74];\r\nt = [0.3393;0.1861;0.9221];\r\ny_correct = 0.985002;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6818;0.719;0.1346];\r\nt = [0.807;0.2223;0.5471];\r\ny_correct = 0.944363;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.49;0.2646;0.8306];\r\nt = [0.6066;0.736;0.3007];\r\ny_correct = 0.933216;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4027;0.5963;0.6945];\r\nt = [0.4281;0.6023;0.6738];\r\ny_correct = 0.999889;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.7066;0.2176;0.6733];\r\nt = [0.1189;0.7977;0.5912];\r\ny_correct = 0.909841;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3783;0.8162;0.4367];\r\nt = [0.6835;0.5943;0.4239];\r\ny_correct = 0.982034;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6461;0.3837;0.6597];\r\nt = [0.2987;0.6588;0.6905];\r\ny_correct = 0.974999;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.5069;0.3904;0.7685];\r\nt = [0.3379;0.0217;0.9409];\r\ny_correct = 0.975392;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0829;0.9172;0.3897];\r\nt = [0.0039;0.9956;0.0936];\r\ny_correct = 0.98741;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.9503;0.1126;0.2904];\r\nt = [0.1529;0.6544;0.7406];\r\ny_correct = 0.846803;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3519;0.3553;0.866];\r\nt = [0.6345;0.6394;0.4343];\r\ny_correct = 0.955666;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.8303;0.557;0.019];\r\nt = [0.605;0.4145;0.6799];\r\ny_correct = 0.934393;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.2458;0.4361;0.8657];\r\nt = [0.1713;0.8422;0.5112];\r\ny_correct = 0.962273;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.5596;0.6441;0.5216];\r\nt = [0.4502;0.8849;0.1193];\r\ny_correct = 0.970604;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4017;0.6335;0.6613];\r\nt = [0.4941;0.5698;0.6567];\r\ny_correct = 0.998438;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6328;0.1213;0.7647];\r\nt = [0.4235;0.6907;0.5862];\r\ny_correct = 0.948689;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6637;0.2984;0.6859];\r\nt = [0.1894;0.9587;0.2123];\r\ny_correct = 0.882446;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.0484;0.841;0.5388];\r\nt = [0.2956;0.8876;0.3533];\r\ny_correct = 0.987704;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.792;0.3042;0.5293];\r\nt = [0.8189;0.5368;0.2029];\r\ny_correct = 0.979591;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.8298;0.1;0.5491];\r\nt = [0.7965;0.0613;0.6015];\r\ny_correct = 0.999344;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.1416;0.3261;0.9347];\r\nt = [0.4045;0.4427;0.8002];\r\ny_correct = 0.987314;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.3135;0.5325;0.7862];\r\nt = [0.1271;0.7016;0.7012];\r\ny_correct = 0.991147;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.4278;0.8839;0.1888];\r\nt = [0.0361;0.8996;0.4352];\r\ny_correct = 0.972812;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)\r\n\r\n%%\r\ns = [0.6453;0.6641;0.3776];\r\nt = [0.9671;0.2513;0.0398];\r\ny_correct = 0.950265;\r\nassert(abs(cosine_effect(s,t)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":12767,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-02T15:31:20.000Z","updated_at":"2025-10-15T01:28:33.000Z","published_at":"2021-03-02T15:33:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Solar thermal power plants with central receiver (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Solar_power_tower\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Solar_power_tower\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) the mirrors (called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Heliostat\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eheliostats\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e) do not aim at the sun (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) or the tower (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), but the bisector of these two directions (vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"265\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"464\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe solar irradiance that bounces off the mirror is reduced by an amount proportional to reflectivity (assume 100% for this problem) and to the cosine of the angle between the normal vector to the heliostat and the other vector (sun or tower).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim of this problem is to calculate the value of the cosine of the angle (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"cos(theta)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\cos\\\\theta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) given the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enormalized\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{s}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\vec{t}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are known for every heliostat at every moment.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\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\u003eVectors are 3×1, with norm = 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMake use of scalar product to calculate cosines, taking advantage of the normalized vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is the car sale and the cars are arranged according to the pascal's Traingle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 50.7042px; transform-origin: 420.1px 50.7042px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     2     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     3     3     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     4     6     4     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePattern like this so the car number is given like \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     n=10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo,you have to create a pascal's traingle and add the numbers and you have to add like this:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 111.549px; transform-origin: 420.1px 111.549px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     1     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     2     1     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     3     3     1     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     4     6     4     1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%You have to add the numbers on the traingle except the 0 and you will get a matrix like:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     1     0     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     2     3     0     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     4     6     7     0     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e     8    11    14    15     0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    16    20    26    30    31\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo the number of the vehicle is given accoring to only positive numbers not 0 (Don't recognize zero when counting the vehical number!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing functions are not allowed!:-every function except eye,find,size\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 20.2817px; transform-origin: 246.004px 20.2817px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou have to output the pascal's traingle number you summed up on that particular row and column like\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 420.094px 50.7042px; transform-origin: 420.1px 50.7042px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%if I asked\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%input\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    n=10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); color: rgb(2, 128, 9); margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration: none; text-decoration-color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); \"\u003e%Output Should be:-\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.997653px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.997653px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; perspective-origin: 420.094px 10.1408px; transform-origin: 420.1px 10.1408px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; white-space: pre; perspective-origin: 0px 0px; transform-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e    y=15;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; white-space: pre-wrap; perspective-origin: 245.998px 10.1408px; transform-origin: 246.004px 10.1408px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWishing You luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = car_sale(n)\r\n  y = x;\r\nend\r\n","test_suite":"%%\r\nx = 10;\r\ny_correct = 15;\r\nassert(isequal(car_sale(x),y_correct))\r\n%%\r\nx=15\r\ny=31;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=78\r\ny=4095\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=108;\r\ny= 16489\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=45;\r\ny=511;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=21;\r\ny=63;\r\nassert(isequal(car_sale(x),y));\r\n%%\r\nx=8;\r\ny=11;\r\nassert(isequal(car_sale(x),y));\r\n\r\n%%\r\nfile=fileread('car_sale.m');\r\nassert(isempty(strfind(file,'regexp')));\r\nassert(isempty(strfind(file,'regex')));\r\nassert(isempty(strfind(file,'cumsum')));\r\nassert(isempty(strfind(file,'pascal')));\r\nassert(isempty(strfind(file,'abs')));\r\nassert(isempty(strfind(file,'celi')));\r\nassert(isempty(strfind(file,'ans')));\r\nassert(isempty(strfind(file,'!')));\r\nassert(isempty(strfind(file,'conv')));\r\nassert(isempty(strfind(file,'sum')));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":517513,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2021-02-14T02:11:38.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-01-17T09:17:21.000Z","updated_at":"2024-11-18T02:44:16.000Z","published_at":"2021-01-18T01:53:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"172\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the car sale and the cars are arranged according to the pascal's Traingle.\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[     1     0     0     0     0\\n     1     1     0     0     0\\n     1     2     1     0     0\\n     1     3     3     1     0\\n     1     4     6     4     1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePattern like this so the car number is given like \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[     n=10;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo,you have to create a pascal's traingle and add the numbers and you have to add like this:-\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[     1     0     0     0     0\\n     1     1     0     0     0\\n     1     2     1     0     0\\n     1     3     3     1     0\\n     1     4     6     4     1\\n    %You have to add the numbers on the traingle except the 0 and you will get a matrix like:-\\n     1     0     0     0     0\\n     2     3     0     0     0\\n     4     6     7     0     0\\n     8    11    14    15     0\\n    16    20    26    30    31]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo the number of the vehicle is given accoring to only positive numbers not 0 (Don't recognize zero when counting the vehical number!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing functions are not allowed!:-every function except eye,find,size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have to output the pascal's traingle number you summed up on that particular row and column like\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[    %if I asked\\n    %input\\n    n=10;\\n    %Output Should be:-\\n    y=15;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWishing You 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