{"id":2565,"date":"2023-02-17T22:13:21","date_gmt":"2023-02-17T21:13:21","guid":{"rendered":"http:\/\/matma.com.pl\/?p=2565"},"modified":"2023-02-19T15:18:34","modified_gmt":"2023-02-19T14:18:34","slug":"zadanie-68-0-4-zbior-podstawa","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=2565","title":{"rendered":"zadanie 68 (0-4) zbi\u00f3r podstawa"},"content":{"rendered":"<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone  wp-image-2566\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2023\/02\/Zrzut-ekranu-2023-02-17-215606-300x238.jpg\" alt=\"\" width=\"405\" height=\"321\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2023\/02\/Zrzut-ekranu-2023-02-17-215606-300x238.jpg 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2023\/02\/Zrzut-ekranu-2023-02-17-215606.jpg 472w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/td>\n<td style=\"width: 50%;\">Z podobie\u0144stwa tr\u00f3jk\u0105t\u00f3w mo\u017cemy napisa\u0107, \u017ce<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}=\\frac{x}{4-y}\" alt=\"\\frac{3}{4}=\\frac{x}{4-y}\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3\\left&amp;space;(&amp;space;4-y&amp;space;\\right&amp;space;)=4x\" alt=\"3\\left ( 4-y \\right )=4x\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?12-3y=4x\" alt=\"12-3y=4x\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?-3y=4x-12\\;&amp;space;\\;&amp;space;\/:\\left&amp;space;(&amp;space;-3&amp;space;\\right&amp;space;)\" alt=\"-3y=4x-12\\; \\; \/:\\left ( -3 \\right )\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?y=-\\frac{4}{3}x+4\" alt=\"y=-\\frac{4}{3}x+4\" align=\"absmiddle\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Obliczmy pole prostok\u0105ta<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P=x\\cdot&amp;space;y\" alt=\"P=x\\cdot y\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;x&amp;space;\\right&amp;space;)=x\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{4}{3}x+4&amp;space;\\right&amp;space;)\" alt=\"P\\left ( x \\right )=x\\cdot \\left ( -\\frac{4}{3}x+4 \\right )\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P(x)=-\\frac{4}{3}x^2+4x\" alt=\"P(x)=-\\frac{4}{3}x^2+4x\" align=\"absmiddle\" \/><\/p>\n<p>Okre\u015blmy dziedzin\u0119 naszej funkcji:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x&lt;&amp;space;\\;&amp;space;\\wedge&amp;space;\\;&amp;space;x&lt;&amp;space;4\" alt=\"x&lt; \\; \\wedge \\; x&lt; 4\" align=\"absmiddle\" \/> oraz <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x&gt;&amp;space;0\" alt=\"x&gt; 0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?D:x\\in&amp;space;\\left&amp;space;(&amp;space;0,3&amp;space;\\right&amp;space;)\" alt=\"D:x\\in \\left ( 0,3 \\right )\" align=\"absmiddle\" \/><\/p>\n<p>Funkcja <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P\" alt=\"P\" align=\"absmiddle\" \/> opisuj\u0105ca pole kwadratu jest parabol\u0105 z ramionami skierowanymi do do\u0142u. Musimy obliczy\u0107 wsp\u00f3\u0142rz\u0119dne jej wierzcho\u0142ka <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?W=(p,q)\" alt=\"W=(p,q)\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?p=\\frac{-4}{2\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{4}{3}&amp;space;\\right&amp;space;)}=-4\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{3}{8}&amp;space;\\right&amp;space;)=\\frac{3}{2}\" alt=\"p=\\frac{-4}{2\\cdot \\left ( -\\frac{4}{3} \\right )}=-4\\cdot \\left ( -\\frac{3}{8} \\right )=\\frac{3}{2}\" align=\"absmiddle\" \/><\/p>\n<p>Sprawdzamy, \u017ce <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?p\\in&amp;space;D\" alt=\"p\\in D\" align=\"absmiddle\" \/>. Zatem pozostaje nam obliczy\u0107 najwi\u0119ksz\u0105 warto\u015b\u0107 naszej funkcji kwadratowej<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?q=P(p)=-\\frac{4}{3}\\cdot&amp;space;\\left&amp;space;(&amp;space;\\frac{3}{2}&amp;space;\\right&amp;space;)^2+4\\cdot&amp;space;\\frac{3}{2}=-\\frac{4}{3}\\cdot&amp;space;\\frac{9}{4}+6=-3+6=3\" alt=\"q=P(p)=-\\frac{4}{3}\\cdot \\left ( \\frac{3}{2} \\right )^2+4\\cdot \\frac{3}{2}=-\\frac{4}{3}\\cdot \\frac{9}{4}+6=-3+6=3\" align=\"absmiddle\" \/><\/p>\n<p>Zatem najwi\u0119ksze pole naszego prostok\u0105ta b\u0119dzie r\u00f3wne <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3\" alt=\"3\" align=\"absmiddle\" \/>, dla <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=\\frac{3}{2}\" alt=\"x=\\frac{3}{2}\" align=\"absmiddle\" \/> oraz<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?y=-\\frac{4}{3}\\cdot&amp;space;\\frac{3}{2}+4=-2+4=2\" alt=\"y=-\\frac{4}{3}\\cdot \\frac{3}{2}+4=-2+4=2\" align=\"absmiddle\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Z podobie\u0144stwa tr\u00f3jk\u0105t\u00f3w mo\u017cemy napisa\u0107, \u017ce Obliczmy pole prostok\u0105ta Okre\u015blmy dziedzin\u0119 naszej funkcji: oraz Funkcja opisuj\u0105ca pole kwadratu jest parabol\u0105 z ramionami skierowanymi do do\u0142u. Musimy obliczy\u0107 wsp\u00f3\u0142rz\u0119dne jej wierzcho\u0142ka Sprawdzamy, \u017ce . Zatem pozostaje nam obliczy\u0107 najwi\u0119ksz\u0105 warto\u015b\u0107 naszej funkcji kwadratowej Zatem najwi\u0119ksze pole naszego prostok\u0105ta b\u0119dzie r\u00f3wne , dla oraz<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"class_list":["post-2565","post","type-post","status-publish","format-standard","hentry","category-matura"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>zadanie 68 (0-4) zbi\u00f3r podstawa - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=2565\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"zadanie 68 (0-4) zbi\u00f3r podstawa - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Z podobie\u0144stwa tr\u00f3jk\u0105t\u00f3w mo\u017cemy napisa\u0107, \u017ce Obliczmy pole prostok\u0105ta Okre\u015blmy dziedzin\u0119 naszej funkcji: oraz Funkcja opisuj\u0105ca pole kwadratu jest parabol\u0105 z ramionami skierowanymi do do\u0142u. 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