{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","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":"2026-04-16T00:00:00.000Z","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":60336,"title":"Determine whether a property description closes","description":"The arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\r\n…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \r\nThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, N60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\r\nAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \r\nWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable tf with the result as well as the distance d of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \r\n*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things.  ","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: 382.35px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 191.175px; transform-origin: 407px 191.175px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; 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: 374.658px 7.79167px; transform-origin: 374.658px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9px; 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 21.45px; text-align: left; transform-origin: 384px 21.45px; white-space-collapse: preserve; 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: 369.6px 7.79167px; transform-origin: 369.6px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 369.6px 8.25px; transform-origin: 369.6px 8.25px; \"\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; 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: 381.992px 7.79167px; transform-origin: 381.992px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \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: 157.608px 7.79167px; transform-origin: 157.608px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; 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 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; 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: 374.458px 7.79167px; transform-origin: 374.458px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \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: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 7.7px 8.25px; transform-origin: 7.7px 8.25px; \"\u003etf\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: 119.408px 7.79167px; transform-origin: 119.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the result as well as the distance \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: 3.85px 7.79167px; transform-origin: 3.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.25px; transform-origin: 3.85px 8.25px; \"\u003ed\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: 7.96667px 7.79167px; transform-origin: 7.96667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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: 382.4px 7.79167px; transform-origin: 382.4px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,d] = isPropertyClosed(s)\r\n  tf = sum(str2num(s))==0;\r\nend","test_suite":"%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.32 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 8.800129070465346e-04;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.1 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.220001760044587;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N52°17ʹ31ʺE 46.13 m' 'S52°17ʹ31ʺE 23.67 m' 'S52°17ʹ31ʺW 46.13 m' 'N52°17ʹ31ʺW 23.67 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 1.913194867290181e-14;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n    \r\n%%\r\nc = {'N52°17ʹ31ʺE 46.14 m' 'S52°17ʹ31ʺE 23.66 m' 'S52°17ʹ31ʺW 46.12 m' 'N52°17ʹ31ʺW 23.68 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.024465531079178;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°52ʹ34ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.018626452840054;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.007209083851337;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°32ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.142364438065814;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.64 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.002087577619808;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.4 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.238926560421110;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nn = randi(10);\r\nm = n+randi(10);\r\nA = m^2-n^2; B = 2*m*n; C = m^2+n^2;\r\nth = acosd(A/C);\r\ndeg = floor(th);\r\nmnt = floor(60*(th-deg));\r\nscd = floor(3600*(th-deg-mnt/60));\r\nc = {['N0°0ʹ0ʺW ' num2str(A,5) ' m'],['S' num2str(deg,2) '°' num2str(mnt,2) 'ʹ' num2str(scd,2) 'ʺE ' num2str(C,5)\t' m'],['N90°0ʹ0ʺW ' num2str(B,5) ' m']};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nassert(tf)\r\n\r\n%%\r\nfiletext = fileread('isPropertyClosed.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:37:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-19T01:52:51.000Z","updated_at":"2024-06-04T15:37:54.000Z","published_at":"2024-05-19T01:53:17.000Z","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\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \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 text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\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\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \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\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the result as well as the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \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*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60336,"title":"Determine whether a property description closes","description":"The arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\r\n…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \r\nThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, N60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\r\nAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \r\nWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable tf with the result as well as the distance d of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \r\n*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things.  ","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: 382.35px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 191.175px; transform-origin: 407px 191.175px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; 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: 374.658px 7.79167px; transform-origin: 374.658px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9px; 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 21.45px; text-align: left; transform-origin: 384px 21.45px; white-space-collapse: preserve; 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: 369.6px 7.79167px; transform-origin: 369.6px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 369.6px 8.25px; transform-origin: 369.6px 8.25px; \"\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; 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: 381.992px 7.79167px; transform-origin: 381.992px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \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: 157.608px 7.79167px; transform-origin: 157.608px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; 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 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; 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: 374.458px 7.79167px; transform-origin: 374.458px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \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: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 7.7px 8.25px; transform-origin: 7.7px 8.25px; \"\u003etf\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: 119.408px 7.79167px; transform-origin: 119.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the result as well as the distance \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: 3.85px 7.79167px; transform-origin: 3.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.25px; transform-origin: 3.85px 8.25px; \"\u003ed\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: 7.96667px 7.79167px; transform-origin: 7.96667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; 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: 382.4px 7.79167px; transform-origin: 382.4px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,d] = isPropertyClosed(s)\r\n  tf = sum(str2num(s))==0;\r\nend","test_suite":"%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.32 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 8.800129070465346e-04;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.1 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.220001760044587;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N52°17ʹ31ʺE 46.13 m' 'S52°17ʹ31ʺE 23.67 m' 'S52°17ʹ31ʺW 46.13 m' 'N52°17ʹ31ʺW 23.67 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 1.913194867290181e-14;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n    \r\n%%\r\nc = {'N52°17ʹ31ʺE 46.14 m' 'S52°17ʹ31ʺE 23.66 m' 'S52°17ʹ31ʺW 46.12 m' 'N52°17ʹ31ʺW 23.68 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.024465531079178;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°52ʹ34ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.018626452840054;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.007209083851337;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°32ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.142364438065814;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.64 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.002087577619808;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.4 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.238926560421110;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nn = randi(10);\r\nm = n+randi(10);\r\nA = m^2-n^2; B = 2*m*n; C = m^2+n^2;\r\nth = acosd(A/C);\r\ndeg = floor(th);\r\nmnt = floor(60*(th-deg));\r\nscd = floor(3600*(th-deg-mnt/60));\r\nc = {['N0°0ʹ0ʺW ' num2str(A,5) ' m'],['S' num2str(deg,2) '°' num2str(mnt,2) 'ʹ' num2str(scd,2) 'ʺE ' num2str(C,5)\t' m'],['N90°0ʹ0ʺW ' num2str(B,5) ' m']};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nassert(tf)\r\n\r\n%%\r\nfiletext = fileread('isPropertyClosed.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:37:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-19T01:52:51.000Z","updated_at":"2024-06-04T15:37:54.000Z","published_at":"2024-05-19T01:53:17.000Z","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\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \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 text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\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\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \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\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the result as well as the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the end point from the point of beginning. 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