{"id":12143,"date":"2021-03-10T18:29:00","date_gmt":"2021-03-10T12:59:00","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=12143"},"modified":"2021-10-23T08:04:51","modified_gmt":"2021-10-23T02:34:51","slug":"04-04-00-2","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/pure-mathematics\/04-calculus\/04-04-practical-uses-of-differentiation\/04-04-00-2\/","title":{"rendered":"04.04.00 -\u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1 \u0dc0\u0dbd \u0db7\u0dcf\u0dc0\u0dd2\u0dad"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/uc?id=175TauDVmsD0r3r3-lPPqycieRhUx7wH_&amp;export=download\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<p><strong>\u0dc3\u0d82\u200d\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I (\u0dc1\u0dd4\u0daf\u0dca\u0db0 \u0d9c\u0dab\u0dd2\u0dad\u0dba) \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda <strong>A \u0d9a\u0ddc\u0da7\u0dc3\u0dda<\/strong><\/strong> <strong>\u0d9c\u0dd0\u0da7<strong>\u0dbd\u0dd4<\/strong>\u0dc0\u0d9a<\/strong> <strong>\u0dc4\u0dcf B \u0d9a\u0ddc\u0da7\u0dc3\u0dda 14 \u0dc0\u0dd0\u0db1\u0dd2 \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0\u0dd9\u0dc4\u0dd2 \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dd9\u0dc4\u0dd2 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0dc0\u0dda.<\/strong><\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf: (22.)&nbsp;&nbsp;&nbsp; \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1\u0dca\u0db1\u0dda \u0d86\u0db7\u0dbb\u0dab \u0dc3\u0dd4\u0dbb\u0dd0\u0d9a\u0dd4\u0db8\u0dca \u0db4\u0dd9\u0da7\u0dca\u0da7\u0dd2\u0dba\u0d9a \u0d85\u0db1\u0dd4\u0dbb\u0dd4\u0dc0\u0d9a\u0dd2. \u0d91\u0dba \u0d8b\u0dc3 h \u0dc0\u0dd6 \u0dc3\u0dd2\u0dbd\u0dd2\u0db1\u0dca\u0da9\u0dbb\u0dba\u0d9a\u0dca \u0dc4\u0dcf \u0d91\u0dc4\u0dd2&nbsp;&nbsp; \u0daf\u0dd9\u0d9a\u0dd9\u0dc5\u0dc0\u0dbb\u0da7 \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0 \u0d9a\u0dbb\u0db1 \u0dbd\u0daf \u0d85\u0dbb\u0dba r \u0dc0\u0dd6 \u0d9a\u0dd4\u0dc4\u0dbb \u0d85\u0dbb\u0dca\u0db0 \u0d9c\u0ddd\u0dbd \u0daf\u0dd9\u0d9a\u0d9a\u0dd2\u0db1\u0dca \u0dc3\u0db8\u0db1\u0dca\u0dc0\u0dd2\u0dad\u0dba.<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"i\"><li>\u0db4\u0dd9\u0da7\u0dca\u0da7\u0dd2\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 V \u0dc3\u0dc4 \u0db6\u0dcf\u0dc4\u0dd2\u0dbb \u0db4\u0dd8\u0dc2\u0dca\u0da8 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba S \u0dc3\u0db3\u0dc4\u0dcf \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1 h \u0dc4\u0dcf r \u0d87\u0dc3\u0dd4\u0dbb\u0dd2\u0db1\u0dca \u0dbd\u0db6\u0dcf\u0d9c\u0db1\u0dca\u0db1.<\/li><li>V = 36\u03c0 \u0db1\u0db8\u0dca s = 72\u03c0\/r + 4\u03c0r<sup>2<\/sup>\/3 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/li><li>S \u0dc4\u0dd2 \u0d85\u0dc0\u0db8 \u0d85\u0d9c\u0dba 36\u03c0 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"245\" height=\"389\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture.png\" alt=\"\" class=\"wp-image-14253\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture.png 245w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-189x300.png 189w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-150x238.png 150w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" type=\"i\"><li>V=4\u03c0r<sup>3<\/sup>\/3 + \u03c0r<sup>2<\/sup>h<\/li><\/ol>\n\n\n\n<p>S= 2\u03c0rh &nbsp;+ 4\u03c0r<sup>2<\/sup><\/p>\n\n\n\n<p>ii.&nbsp;V=36\u03c0<\/p>\n\n\n\n<p>&nbsp;4\u03c0r<sup>3<\/sup>\/3 + \u03c0r<sup>2<\/sup>h = 36\u03c0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u03c0r<sup>2<\/sup>h = 36\u03c0 \u2013 4\u03c0r<sup>3<\/sup>\/3<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; h =<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\left[3\\left(36\\mathrm\\pi\\right)-4\\mathrm{\u03c0r}^3\\right]}{3\\mathrm{\u03c0r}}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; h = (108-4r<sup>3<\/sup>)\/3r<sup>2<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; h = 36\/r<sup>2<\/sup> \u2013 4r\/3<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; S = 2\u03c0rh+4\u03c0r<sup>2<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; S = 2\u03c0r (36\/r<sup>2<\/sup> \u2013 4r\/3) + 4\u03c0r<sup>2<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; S = 72\u03c0\/r \u2013 8\u03c0r<sup>2<\/sup>\/3 + 4\u03c0r<sup>2<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; S = 72\u03c0\/r + 4\u03c0r<sup>2<\/sup>\/3<\/p>\n\n\n\n<p>iii.S, r \u0dc0\u0dd2\u0dc1\u0dba\u0dd9\u0db1\u0dca \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dd2\u0db8,<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dr}\\end{array}<\/span>= {r(0)-72\u03c0(1)}\/r<sup>2<\/sup> + {3(4\u03c0)(2r)-4\u03c0r<sup>2<\/sup>(0)}\/9<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dr}\\end{array}<\/span> = -72\u03c0\/r<sup>2 <\/sup>+ 24\u03c0r\/9<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dr}\\end{array}<\/span>= 24\u03c0 (-3\/r<sup>2<\/sup> + r\/9)<\/p>\n\n\n\n<p>\u0dc3\u0dca\u0dad\u0dcf\u0dc0\u0dbb \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc3\u0db3\u0dc4\u0dcf,<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac{ds}{dr}\\end{array}<\/span>= 0 \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\"> \\begin{array}{rcl}&amp;&amp;\\frac{ds}{dr}\\end{array}<\/span>= 0<\/p>\n\n\n\n<p>24\u03c0 (-3\/r<sup>2<\/sup> + r\/9) = 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r\/ 9 = 3\/r<sup>2<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;r<sup>3 <\/sup>= 27<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; r = 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"685\" height=\"326\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-1.png\" alt=\"\" class=\"wp-image-14263\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-1.png 685w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-1-300x143.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-1-150x71.png 150w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; &nbsp;S = 72\u03c0\/r + 4\u03c0r<sup>2<\/sup>\/3<\/p>\n\n\n\n<p>&nbsp; &nbsp;&nbsp;&nbsp;S&nbsp;= 72\u03c0\/3 + 4\u03c0 (9)\/3<\/p>\n\n\n\n<p>&nbsp;&nbsp; &nbsp;&nbsp;S= 36\u03c0<\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf: (23.)&nbsp; &nbsp;&nbsp;\u0db8\u0dd2\u0db1\u0dd2\u0dc3\u0dd9\u0d9a\u0dca \u0d9c\u0d9f\u0d9a \u0dc3\u0dd8\u0da2\u0dd4 \u0d89\u0dc0\u0dd4\u0dbb\u0da7 3 km \u0daf\u0dd4\u0dbb\u0dd2\u0db1\u0dca \u0db1\u0dd2\u0dc1\u0dca\u0da0\u0dbd \u0da2\u0dbd\u0dba\u0dda \u0dad\u0dd2\u0db6\u0dd9\u0db1 \u0db6\u0ddd\u0da7\u0dca\u0da7\u0dd4\u0dc0\u0d9a \u0dc3\u0dd2\u0da7\u0dd2\u0dba\u0dd2. \u0d94\u0dc4\u0dd4 \u0dc3\u0dd2\u0da7\u0dd2\u0db1 \u0d91\u0db8 \u0dc3\u0dca\u0dad\u0dcf\u0db1\u0dba\u0dda \u0dc3\u0dd2\u0da7 15 km \u0daf\u0dd4\u0dbb\u0dd2\u0db1\u0dca \u0d9c\u0d82 \u0d89\u0dc0\u0dd4\u0dbb\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2 \u0db6\u0dbd\u0dc0\u0dda\u0d9c \u0db8\u0db0\u0dca\u200d\u0dba\u0dc3\u0dca\u0dad\u0dcf\u0db1\u0dba\u0d9a\u0da7 \u0dba\u0dcf\u0db8\u0da7 \u0d94\u0dc4\u0dd4\u0da7 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dc0 \u0d87\u0dad. \u0d94\u0dc4\u0dd4\u0da7&nbsp; \u0db6\u0ddd\u0da7\u0dca\u0da7\u0dd4\u0dc0 \u0db4\u0dd0\u0daf\u0dd3\u0db8 2 kmh<sup>-1<\/sup> \u0dc0\u0dda\u0d9c\u0dba\u0d9a\u0dd2\u0db1\u0dca\u0daf \u0d9c\u0d82 \u0d89\u0dc0\u0dd4\u0dbb \u0daf\u0dd2\u0d9c\u0dda \u0db4\u0dcf \u0d9c\u0db8\u0db1\u0dd2\u0db1\u0dca \u0dba\u0dcf\u0db8 4 kmh<sup>-1<\/sup> \u0dc0\u0dda\u0d9c\u0dba\u0d9a\u0dd2\u0db1\u0dca\u0daf \u0d9a\u0dc5 \u0dc4\u0dd0\u0d9a\u0dd2 \u0db1\u0db8\u0dca&nbsp; \u0db6\u0dbd\u0dc0\u0dda\u0d9c \u0db8\u0db0\u0dca\u200d\u0dba\u0dc3\u0dca\u0dad\u0dcf\u0db1\u0dba\u0da7 \u0dc4\u0dd0\u0d9a\u0dd2 \u0d89\u0d9a\u0dca\u0db8\u0dab\u0dd2\u0db1\u0dca \u0dbd\u0d9f\u0dcf \u0dc0\u0dd3\u0db8 \u0db4\u0dd2\u0dab\u0dd2\u0dc3 \u0d94\u0dc4\u0dd4 \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca \u0d89\u0dc0\u0dd4\u0dbb\u0dda \u0d9a\u0dd2\u0db1\u0db8\u0dca \u0dc3\u0dca\u0dad\u0dcf\u0db1\u0dba\u0d9a\u0da7 \u0db6\u0ddd\u0da7\u0dca\u0da7\u0dd4\u0dc0\u0dd9\u0db1\u0dca &nbsp;&nbsp;&nbsp;\u0db4\u0dd0\u0db8\u0dd2\u0dab\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4 \u0dc0\u0dda\u0daf?<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u0dc0\u0dda\u0d9c\u0dba = \u0daf\u0dd4\u0dbb\/\u0d9a\u0dcf\u0dbd\u0dba<\/p>\n\n\n\n<p>\u0d9a\u0dcf\u0dbd\u0dba = \u0daf\u0dd4\u0dbb\/\u0dc0\u0dda\u0d9c\u0dba<\/p>\r\n<p>\u0db8\u0dd4\u0dbd\u0dd4 \u0d9c\u0db8\u0db1\u0da7 \u0d9c\u0dad \u0dc0\u0db1 \u0d9a\u0dcf\u0dbd\u0dba T \u0db1\u0db8\u0dca,<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\sqrt{\\left(3^2+x^2\\right)}}2+\\frac{\\sqrt{\\left(15^2-3^2\\right)}{\\displaystyle-}{\\displaystyle x}}4<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\left(2\\sqrt{\\left(3^2+x^2\\right)}+\\sqrt{\\left(15^2-3^2\\right)}-x\\right)}4<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"996\" height=\"428\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2.png\" alt=\"\" class=\"wp-image-14265\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2.png 996w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2-300x129.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2-768x330.png 768w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2-150x64.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2-696x299.png 696w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-2-977x420.png 977w\" sizes=\"(max-width: 996px) 100vw, 996px\" \/><\/figure>\n\n\n\n<p>&nbsp;<\/p>\r\n<p>T, x \u0dc0\u0dd2\u0dc1\u0dba\u0dd9\u0db1\u0dca \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba ,<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dT}{dx}\\end{array}<\/span>= <span class=\"wp-katex-eq\" data-display=\"false\">\\frac12\\left(\\frac{\\displaystyle(2x)}{2\\sqrt{\\left(9+x^2\\right)}}\\;\\right)+\\frac{\\left(0-1\\right)}4<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dT}{dx}\\end{array}<\/span> = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\sqrt{\\left(9+x^2\\right)}(2x)}4\\;+\\frac{\\left(0-1\\right)}4<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dT}{dx}\\end{array}<\/span> =<span class=\"wp-katex-eq\" data-display=\"false\">\\frac14\\left(\\frac{\\displaystyle(2x)}{\\sqrt{\\left(9+x^2\\right)}}\\;-1\\right)<\/span><\/p>\n\n\n\n<p>\u0dc3\u0dca\u0dad\u0dcf\u0dc0\u0dbb \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc3\u0db3\u0dc4\u0dcf,<\/p>\n\n\n\n<p>&nbsp;<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dT}{dx}\\end{array}<\/span>= 0<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\frac14\\left(\\frac{\\displaystyle(2x)}{\\sqrt{\\left(9+x^2\\right)}}\\;-1\\right)<\/span> = 0<\/p>\n\n\n\n<p>2x = <span class=\"wp-katex-eq\" data-display=\"false\">2x=\\sqrt{9+x^2}<\/span><\/p>\n\n\n\n<p>4x<sup>2 <\/sup>= 9+x<sup>2<\/sup><\/p>\n\n\n\n<p>x <sup>2 &nbsp;<\/sup>= &nbsp;3<\/p>\n\n\n\n<p>&nbsp; x = \u00b1\u221a3<\/p>\n\n\n\n<p>x &nbsp;&gt; 0 \u0db1\u0dd2\u0dc3\u0dcf &nbsp;x = \u221a3<\/p>\n\n\n\n<p>\u0db6\u0ddd\u0da7\u0dca\u0da7\u0dd4\u0dc0 \u0d9c\u0d82 \u0d89\u0dc0\u0dd4\u0dbb\u0da7 \u0d87\u0db3\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0dba\u0dda \u0d85\u0da9\u0dd2\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u221a3 km \u0d9a \u0daf\u0dd4\u0dbb\u0d9a\u0daf\u0dd3 \u0d9c\u0d82 \u0d89\u0dc0\u0dd4\u0dbb\u0da7 \u0dbd\u0d9f\u0dcf \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf: (24.)&nbsp; &nbsp;&nbsp;\u0d85\u0dbb\u0dba r \u0dc0\u0db1 \u0d9c\u0ddd\u0dbd\u0dba\u0d9a\u0dca \u0dad\u0dd4\u0dc5 \u0dc3\u0dd8\u0da2\u0dd4 \u0dc0\u0dd8\u0dad\u0dca\u0dad \u0d9a\u0dda\u0dad\u0dd4\u0dc0\u0d9a\u0dca \u0d85\u0db1\u0dca\u0dad\u0dbb\u0dca\u0d9c\u0dad \u0d9a\u0dbb\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda. \u0d9c\u0ddd\u0dbd\u0dba\u0dda \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dda,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u0d9a\u0dda\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dad\u0dd4\u0dbd \u0db8\u0dca\u0d9f\u0dd2\u0db1\u0dca \u0d86\u0db4\u0dcf\u0dad\u0dd2\u0dad \u0d85\u0da9 \u0dc3\u0dd2\u0dbb\u0dc3\u0dca \u0d9a\u0ddd\u0dab\u0dba 2\u03b8 \u0db1\u0db8\u0dca \u0d9a\u0dda\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 V = V<sub>0<\/sub>[sin<sup>2<\/sup>2\u03b8(1+cos2\u03b8)\/4] \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1. \u0db8\u0dd9\u0dc4\u0dd2 V<sub>0 <\/sub>\u0dba\u0db1\u0dd4 \u0d9c\u0ddd\u0dbd\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0dba\u0dd2. \u0d92 \u0db1\u0dba\u0dd2\u0db1\u0dca \u0d9a\u0dda\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0d8b\u0db4\u0dbb\u0dd2\u0db8\u0dba\u0d9a\u0dca \u0db1\u0db8\u0dca \u0d91\u0dba \u0d9c\u0ddd\u0dbd\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0dd9\u0db1\u0dca 8\/27 \u0d9a\u0dca \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"809\" height=\"426\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3.png\" alt=\"\" class=\"wp-image-14272\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3.png 809w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3-300x158.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3-768x404.png 768w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3-150x79.png 150w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3-696x366.png 696w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-3-798x420.png 798w\" sizes=\"(max-width: 809px) 100vw, 809px\" \/><\/figure>\n\n\n\n<p>&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V = 1\/3\u03c0a<sup>2<\/sup>h<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V = 1\/3\u03c0 (r<sup>2<\/sup>sin<sup>2<\/sup>2\u03b8) (r+rcos2\u03b8)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V= (4\/3\u03c0r<sup>3<\/sup>) {sin<sup>2<\/sup>2\u03b8 (1+cos2\u03b8)\/4}<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V = V<sub>0 <\/sub>[sin<sup>2 <\/sup>2\u03b8(1+cos2\u03b8)\/4]<\/p>\n\n\n\n<p>&nbsp;<\/p>\r\n<p>\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{d\\theta}\\end{array}<\/span>= (V<sub>0<\/sub>\/4) {(sin<sup>2<\/sup>2\u03b8 )(-sin2\u03b8)(2) + (1+cos2\u03b8)(2sin2\u03b8cos2\u03b8)(2)}<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{d\\theta}\\end{array}<\/span> = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{v_o}4<\/span>{-2sin<sup>3<\/sup>2\u03b8 + 4(1+cos2\u03b8) (sin2\u03b8cos2\u03b8)}<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{d\\theta}\\end{array}<\/span>= <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{v_o}2<\/span>{2(1+cos2\u03b8) (sin2\u03b8cos2\u03b8) \u2013sin<sup>3<\/sup>2\u03b8}<\/p>\n\n\n\n<p>&nbsp;<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{d\\theta}\\end{array}<\/span>= 0<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{v_o}2<\/span>{2(1+cos2\u03b8) (sin2\u03b8cos2\u03b8) \u2013 sin<sup>3<\/sup>2\u03b8} = 0<\/p>\n\n\n\n<p>2(1+cos2\u03b8) (sin2\u03b8cos2\u03b8) = sin<sup>3<\/sup>2\u03b8<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2cos2\u03b8+2cos<sup>2<\/sup>2\u03b8 = sin<sup>2<\/sup>2\u03b8<\/p>\n\n\n\n<p>&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2cos2\u03b8+2cos<sup>2<\/sup>2\u03b8 = 1-cos<sup>2<\/sup>2\u03b8<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3cos<sup>2<\/sup>2\u03b8+2cos2\u03b8-1 = 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3cos2\u03b8-1)(cos2\u03b8+1) = 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; cos2\u03b8 = 1\/3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; cos2\u03b8 = -1&nbsp; &nbsp;(\u03b8&lt;0 \u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0dba \u0d9c\u0dad \u0db1\u0ddc\u0dc4\u0dd0\u0d9a.)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; cos2\u03b8 = 1\/3<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"653\" height=\"349\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-4.png\" alt=\"\" class=\"wp-image-14279\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-4.png 653w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-4-300x160.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-4-150x80.png 150w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><\/figure>\n\n\n\n<p>V max = V<sub>0<\/sub>\/4{(1-cos<sup>2<\/sup>2\u03b8) (1+cos2\u03b8)}<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V max = V<sub>0<\/sub>\/4{(1- 1\/9) (1+ 1\/3)}<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V max&nbsp;= V<sub>0<\/sub>\/4(8\/9) (4\/3)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; V max = V<sub>0 <\/sub>(8\/27)<\/p>\n\n\n\n<div class=\"wp-block-cover has-background-dim\" style=\"background-color:#fba96e\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#7b3605;font-size:20px\"><strong>\u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba (0,0) \u0dc0\u0db1 <span class=\"wp-katex-eq\" data-display=\"false\">y=e^{-x^2}\\;\u0dc4\u0dcf\\;y=-e^{-x^2}<\/span> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d85\u0dad\u0dbb \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0db1 \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/10\/04.04_img-01.jpg\" alt=\"\" class=\"wp-image-33673\" width=\"558\" height=\"209\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/learnsteer.sasnaka.org\/science\/?p=33674\" style=\"border-radius:10px;background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(123,54,5) 3%)\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<p>\u0d8b\u0daf\u0dcf: (25.)&nbsp; &nbsp;&nbsp;\u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1\u0dca\u0db1\u0dda \u0d85\u0dbb\u0dca\u0db0 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dcf\u0d9a\u0dcf\u0dbb \u0dc4\u0dcf \u0d91\u0dc4\u0dd2 \u0dc0\u0dd2\u0dc2\u0dca\u200d\u0d9a\u0db8\u0dca\u0db7\u0dba \u0db4\u0dcf\u0daf\u0dba\u0d9a\u0dca \u0dc0\u0dd6 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dc3\u0d82\u200d\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0dc0\u0dd6 \u0dbb\u0dd6\u0db4 \u0dc3\u0da7\u0dc4\u0db1\u0d9a\u0dd2. \u0db8\u0dd9\u0dc4\u0dd2 \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba 20m \u0dc0\u0dda. \u0db8\u0dd9\u0dc4\u0dd2 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0d8b\u0db4\u0dbb\u0dd2\u0db8 \u0dc0\u0dd3\u0db8\u0da7 \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dba\u0da7 \u0d9c\u0dad \u0dc4\u0dd0\u0d9a\u0dd2 \u0daf\u0dd2\u0d9c \u0dc4\u0dcf \u0db4\u0dc5\u0dbd \u0db4\u0dd2\u0dc5\u0dd2\u0dc0\u0dd9\u0dbd\u0dd2\u0db1\u0dca y\u0dc4\u0dcf x \u0db1\u0db8\u0dca, x = 40\/(\u03c0+4) , y = 20\/(\u03c0+4) \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"280\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-5.png\" alt=\"\" class=\"wp-image-14294\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-5.png 230w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-5-150x183.png 150w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"235\" height=\"364\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-6.png\" alt=\"\" class=\"wp-image-14297\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-6.png 235w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-6-194x300.png 194w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-6-150x232.png 150w\" sizes=\"(max-width: 235px) 100vw, 235px\" \/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba = 2y+2x+ 2\u03c0x\/2<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 20 = 2y+2x+\u03c0 x<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2y = 20- x (2+\u03c0)<\/p>\n\n\n\n<p>\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba A = 2xy+ \u03c0x<sup>2<\/sup>\/2<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A= x {20-x (2+\u03c0)} + \u03c0x<sup>2<\/sup>\/2<\/p>\n\n\n\n<p>&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A = 20x-(2+\u03c0). X<sup>2<\/sup>+ \u03c0x<sup>2<\/sup>\/2<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dA}{dx}\\end{array}<\/span>= 20-2x (2+\u03c0) + \u03c0 x<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dA}{dx}\\end{array}<\/span>= 20-4x-\u03c0x<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dA}{dx}\\end{array}<\/span>= 0<\/p>\n\n\n\n<p>20-4x-\u03c0x = 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;20 = x (4+\u03c0)<\/p>\n\n\n\n<p>x = 20\/ (4 +\u03c0)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"396\" height=\"208\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-7.png\" alt=\"\" class=\"wp-image-14298\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-7.png 396w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-7-300x158.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-7-150x79.png 150w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2x = 40\/ (4+\u03c0)<\/p>\n\n\n\n<p>2y (4+\u03c0) = 20(4+\u03c0)-(\u03c0+2)20<\/p>\n\n\n\n<p>2y (4+\u03c0) = 80+20\u03c0-20\u03c0-40<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y = 20\/ (4+\u03c0)<\/p>\n\n\n\n<p><strong>\u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0d87\u0dc3\u0dd4\u0dbb\u0dd2\u0db1\u0dca \u0dc1\u0dd3\u0d9d\u0dca\u200d\u0dbb\u0dad\u0dcf\u0dc0\u0dba \u0dbd\u0db6\u0dcf\u0d9c\u0dd0\u0db1\u0dd3\u0db8<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>x \u0da7 \u0dc3\u0dcf\u0db4\u0dda\u0d9a\u0dca\u0dc2\u0dc0 y \u0dc0\u0dd9\u0db1\u0dc3\u0dca \u0dc0\u0dd3\u0db8\u0dda \u0dc1\u0dd3\u0d9d\u0dca\u200d\u0dbb\u0dad\u0dcf\u0dc0\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\u00a0\\begin{array}{rcl}&amp;&amp;\\frac{dy}{dx}\\end{array}<\/span>&nbsp;\u0dbd\u0dd9\u0dc3 \u0d85\u0dbb\u0dca\u0dad \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda.<\/li><li>s \u0dc0\u0dd2\u0dc3\u0dca\u0dad\u0dcf\u0db4\u0db1\u0dba\u0d9a\u0dca\u0daf t \u0d9a\u0dcf\u0dbd\u0dba\u0d9a\u0dca\u0daf \u0dc0\u0dd2\u0da7,<\/li><\/ul>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}<\/span>= v (\u0db4\u0dca\u200d\u0dbb\u0dc0\u0dda\u0d9c\u0dba) = \u1e61<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{dt}\\end{array}<\/span>= a (\u0dad\u0dca\u0dc0\u0dbb\u0dab\u0dba) =v<\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf:(26.)&nbsp; \u0dad\u0dd2\u0dbb\u0dc3\u0dca \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0da0\u0dbd\u0db1\u0dba \u0dc0\u0db1 \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0d9a t \u0d9a\u0dcf\u0dbd\u0dba\u0d9a\u0daf\u0dd3 \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dc5 \u0daf\u0dd4\u0dbb s \u0db1\u0db8\u0dca, s=t<sup>3<\/sup>-9t<sup>2<\/sup>+24t &nbsp;\u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0dd9\u0db1\u0dca \u0daf\u0dd9\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\n\n\n\n<p>i.\u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dd9\u0dc4\u0dd2 \u0d86\u0dbb\u0db8\u0dca\u0db7\u0d9a \u0db4\u0dca\u200d\u0dbb\u0dc0\u0dda\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n<p>ii. s \u00a0\u0dc0\u0dd0\u0da9\u0dd2\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0dc4\u0dcf \u0d85\u0da9\u0dd4\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dca\u0db1\u0dcf \u0dc0\u0dd6 \u0d85\u0dc0\u0dc3\u0dca\u0dad\u0dcf \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n<p>i.s=t<sup>3<\/sup>-9t<sup>2<\/sup>+24t<\/p>\n\n\n\n<p>&nbsp;<\/p>\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}<\/span>= 3t<sup>2<\/sup>-18t+24 = v<\/p>\n\n\n\n<p>a=<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dv}{dt}\\end{array}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a =6t-18<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t=0 \u0dc0\u0dd2\u0da7,<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v=3(0)-18(0) +24<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v=24 ms<sup>-1<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0dba\u0db8\u0dca \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dd0\u0da9\u0dd2\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dy}{dx}\\end{array}<\/span>&gt; 0 \u0dc0\u0dda.<\/li><\/ul>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \u0dba\u0db8\u0dca \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0d85\u0da9\u0dd4\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0dc0\u0dd2\u0da7&nbsp;&nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dy}{dx}\\end{array}<\/span>&lt; 0 \u0dc0\u0dda.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}<\/span>= 3(t2-6t+8)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\"> \\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}<\/span>= 3(t-4) (t-2)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"565\" height=\"292\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-8.png\" alt=\"\" class=\"wp-image-14328\" srcset=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-8.png 565w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-8-300x155.png 300w, https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/05\/Capture-8-150x78.png 150w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/figure>\n\n\n\n<p>&nbsp;s \u0dc0\u0dd0\u0da9\u0dd2\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0dc0\u0dd2\u0da7,&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\"> \\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}<\/span>&gt; 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0 &lt; x &lt; 2<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4 &lt; x &lt; \u221e<\/p>\n\n\n\n<p>&nbsp;s \u0d85\u0da9\u0dd4\u0dc0\u0dd9\u0db8\u0dd2\u0db1\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0dc0\u0dd2\u0da7,&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{ds}{dt}\\end{array}\u00a0<\/span>&lt; 0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 &lt; x &lt; 4<\/p>\n\n\n\n<p>\u0d8b\u0daf\u0dcf: (27.)&nbsp; &nbsp;&nbsp;\u0d9c\u0ddd\u0dbd\u0dba\u0d9a \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba 4\u03c0 cm<sup>2<\/sup>s<sup>-1<\/sup> \u0d9a\u0dd2\u0db1\u0dca \u0dc0\u0dd0\u0da9\u0dd2 \u0dc0\u0dda. r = 2 cm \u0dc0\u0db1 \u0dc0\u0dd2\u0da7,<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"i\"><li>\u0d91\u0dc4\u0dd2 \u0d85\u0dbb\u0dba \u0dc0\u0dd0\u0da9\u0dd2\u0dc0\u0dd3\u0db8\u0dda \u0dc1\u0dd3\u0d9d\u0dca\u200d\u0dbb\u0dad\u0dcf\u0dc0\u0dba<\/li><li>\u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0dc0\u0dd0\u0da9\u0dd2\u0dc0\u0dd3\u0db8\u0dda \u0dc1\u0dd3\u0d9d\u0dca\u200d\u0dbb\u0dad\u0dcf\u0dc0\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/li><\/ol>\n\n\n\n<ol class=\"wp-block-list\" type=\"i\"><li>A = 4\u03c0r<sup>2<\/sup><\/li><\/ol>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;\u0daf\u0dd9\u0db4\u0dc3\u0db8 t \u0dc0\u0dd2\u0dc2\u0dba\u0dd9\u0db1\u0dca \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba\u0dd9\u0db1\u0dca,<\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\frac{dA}{dt}\\end{array}<\/span>= (4\u03c0) (2r) <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dr}{dt}\\right)\\end{array}<\/span><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 4\u03c0 = (4\u03c0) (2r) <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dr}{dt}\\right)\\end{array}<\/span><\/p>\n\n\n\n<p>&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dr}{dt}\\right)\\end{array}<\/span>= 1\/2r<\/p>\n\n\n\n<p>r = 2 \u0dc0\u0dd2\u0da7,&nbsp;&nbsp; <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dr}{dt}\\right)\\end{array}<\/span>= (1\/4) cms<sup>-1<\/sup><\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"i\"><li>&nbsp;V = (4\/3)\u03c0r<sup>3<\/sup><\/li><\/ol>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dv}{dt}\\right)\\end{array}<\/span>= (4\/3) (\u03c0) (3r<sup>2<\/sup>)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dr}{dt}\\right)\\end{array}<\/span><\/p>\n\n\n\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dv}{dt}\\right)\\end{array}<\/span>=(4\/3) (3\u03c0r<sup>2<\/sup>)(1\/2r)<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dv}{dt}\\right)\\end{array}<\/span>= 2\u03c0r&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>r = 2 \u0dc0\u0dd2\u0da7, <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\left(\\frac{dv}{dt}\\right)\\end{array}<\/span>= 4\u03c0 cm<sup>3<\/sup>s<sup>-1<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color: #272062;text-align: center\"><span style=\"font-size: 18pt;color: #ffffff\"><em><strong><span style=\"font-family: 'book antiqua', palatino, serif\">\u201cHe who sees things grow from the beginning will have the best view of them.\u201d<\/span><\/strong><\/em><\/span><br \/><span style=\"font-family: tahoma, arial, helvetica, sans-serif;font-size: 10pt;color: #808080\">&#8211; Aristotle &#8211;<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0dc0\u0dd0\u0da9\u0dd2\u0daf\u0dd4\u0dbb<sup>&nbsp; <\/sup>\u0dc0\u0dd2\u0dc3\u0dca\u0dad\u0dbb\u0dc3\u0db3\u0dc4\u0dcf,<\/strong><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_19573\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/kBsM5vML6mw?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_75747\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/aCaFI_hT_ks?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_54635\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/ZqLlXjW2HL8?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_31455\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/LLpqPw_9zh0?enablejsapi=1&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-embed-handler wp-block-embed-embed-handler wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_75374\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/?enablejsapi=1&#038;list=PLcUOoycaDS-mDbLZ3uKs0t_0BP5nU6JfX&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-embed-handler wp-block-embed-embed-handler wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"epyt-video-wrapper\"><iframe loading=\"lazy\"  id=\"_ytid_43399\"  width=\"696\" height=\"392\"  data-origwidth=\"696\" data-origheight=\"392\"  data-relstop=\"1\" src=\"https:\/\/www.youtube.com\/embed\/?enablejsapi=1&#038;list=PLcUOoycaDS-lD63Z_OIBmDI-htXbxFq2G&#038;autoplay=0&#038;cc_load_policy=0&#038;cc_lang_pref=&#038;iv_load_policy=1&#038;loop=0&#038;rel=0&#038;fs=1&#038;playsinline=0&#038;autohide=2&#038;theme=dark&#038;color=red&#038;controls=1&#038;\" class=\"__youtube_prefs__  epyt-is-override  no-lazyload\" title=\"YouTube player\"  allow=\"fullscreen; accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen data-no-lazy=\"1\" data-skipgform_ajax_framebjll=\"\"><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=175TauDVmsD0r3r3-lPPqycieRhUx7wH_&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" href=\"https:\/\/drive.google.com\/drive\/folders\/1cmG8C2feQUAMvv2JKenwbgG1EOhK5nbu?usp=sharing\" style=\"border-radius:15px\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\n\n\n\n<p>&nbsp;<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda\u0daf\u0dd3, \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda\u0daf\u0dd3 \u0dc3\u0dca\u0db4\u0dbb\u0dca\u0dc1\u0d9a\u0dba\u0dda \u0db6\u0dd1\u0dc0\u0dd4\u0db8, \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1\u0dba\u0dda \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0dc4\u0dcf \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1\u0dba \u0dc0\u0dd9\u0db1\u0dc3\u0dca \u0dc0\u0dd3\u0db8\u0dda \u0dc1\u0dd3\u0d9d\u0dca\u200d\u0dbb\u0dad\u0dcf\u0dc0 \u0d85\u0db0\u0dca\u200d\u0dba\u0db1\u0dca\u200d\u0dba\u0dba \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\n","protected":false},"author":56,"featured_media":16557,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3670,3635,42,3630,3629],"tags":[3758,4050,4051,3721,3788,4087,3762,3760,3759,3794,3795,3738,4048,4049],"class_list":{"0":"post-12143","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-04-04-practical-uses-of-differentiation","8":"category-04-calculus","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-awakalanaya","13":"tag-awakalanaya-wyuthpanna","14":"tag-awkalna-wyuthpannawala-bawitha","15":"tag-com-maths","16":"tag-combined-mathematics","17":"tag-differentation-uses","18":"tag-differentiation","19":"tag-mathematics","20":"tag-maths","21":"tag-pure-mathematics","22":"tag-pure-maths","23":"tag-3738","24":"tag-4048","25":"tag-4049"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12143"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=12143"}],"version-history":[{"count":61,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12143\/revisions"}],"predecessor-version":[{"id":33703,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/12143\/revisions\/33703"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16557"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=12143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=12143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=12143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}