{"id":11554,"date":"2013-02-19T23:24:29","date_gmt":"2013-02-19T23:24:29","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11554"},"modified":"2022-01-20T17:15:59","modified_gmt":"2022-01-20T17:15:59","slug":"um-galinheiro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11554","title":{"rendered":"Um galinheiro"},"content":{"rendered":"<p><ul id='GTTabs_ul_11554' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11554' class='GTTabs_curr'><a  id=\"11554_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11554' ><a  id=\"11554_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_11554'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11556\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11556\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro.jpg\" data-orig-size=\"463,209\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Galinheiro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro.jpg\" class=\"alignright  wp-image-11556\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro.jpg\" alt=\"Galinheiro\" width=\"278\" height=\"125\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro.jpg 463w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro-300x135.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro-150x67.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/galinheiro-400x180.jpg 400w\" sizes=\"auto, (max-width: 278px) 100vw, 278px\" \/><\/a>Um agricultor comprou $6$ metros de rede para fazer um galinheiro retangular, como ilustra a figura.<\/p>\n<ol>\n<li>Complete a seguinte tabela:\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11557\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11557\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela.jpg\" data-orig-size=\"608,224\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela.jpg\" class=\"alignnone  wp-image-11557\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela.jpg\" alt=\"tabela\" width=\"426\" height=\"157\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela.jpg 608w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela-300x110.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela-150x55.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/tabela-400x147.jpg 400w\" sizes=\"auto, (max-width: 426px) 100vw, 426px\" \/><\/a><\/p>\n<\/li>\n<li>Num referencial cartesiano, marque os pontos $\\left( {c,l} \\right)$ que obteve na al\u00ednea anterior.<\/li>\n<li>Explique como se pode obter os valores de $l$ \u00e0 custa de $c$. Exprima $l$ em fun\u00e7\u00e3o de $c$.<\/li>\n<li>Determine o valor de c, e o correspondente valor de $l$, para o qual a \u00e1rea \u00e9 m\u00e1xima.<\/li>\n<li>Qual \u00e9 a forma do galinheiro de \u00e1rea m\u00e1xima.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11554' onClick='GTTabs_show(1,11554)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11554'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Apresenta-se seguidamente a tabela completa:<br>\u00ad<br>\n<table class=\"aligncenter\" style=\"width: 60%;\" border=\"1\" cellspacing=\"2\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #ffe4c4;\">$c$<br>comprimento (m)<\/td>\n<td style=\"text-align: center; background-color: #ffe4c4;\">$l$<br>largura (m)<\/td>\n<td style=\"text-align: center; background-color: #ffe4c4;\">\u00c1rea do galinheiro (m<sup>2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$0,5$<\/td>\n<td style=\"text-align: center;\">$2,5$<\/td>\n<td style=\"text-align: center;\">$1,25$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$1$<\/td>\n<td style=\"text-align: center;\">$2$<\/td>\n<td style=\"text-align: center;\">$2$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$1,5$<\/td>\n<td style=\"text-align: center;\">$1,5$<\/td>\n<td style=\"text-align: center;\">$2,25$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$2$<\/td>\n<td style=\"text-align: center;\">$1$<\/td>\n<td style=\"text-align: center;\">$2$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$2,5$<\/td>\n<td style=\"text-align: center;\">$0,5$<\/td>\n<td style=\"text-align: center;\">$1,25$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11577\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11577\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b.png\" data-orig-size=\"764,700\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"10-pag29-3V2b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b.png\" class=\"wp-image-11577 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b.png\" alt=\"10-pag29-3V2b\" width=\"458\" height=\"420\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b.png 764w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b-300x274.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b-150x137.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag29-3V2b-400x366.png 400w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/a><br>\u00ad<\/li>\n<li>Pode-se obter os valores de $l$ \u00e0 custa de $c$ tendo em considera\u00e7\u00e3o que o semiper\u00edmetro do galinheiro \u00e9 $3$ m, isto \u00e9, que $c + l = 3$.<br>Portanto, $l = 3 &#8211; c$.<br>\u00ad<\/li>\n<li>A \u00e1rea pode ser expressa por:<br>$\\begin{array}{*{20}{l}}<br>A&amp; = &amp;{c\\left( {3 &#8211; c} \\right)} \\\\<br>{}&amp; = &amp;{3c &#8211; {c^2}}<br>\\end{array}$<br>De acordo com o resultado fornecido pela calculadora gr\u00e1fica, a \u00e1rea \u00e9 m\u00e1xima para $c = l = 1,5$:<br>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11571\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11571\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"janela2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2.png\" class=\"aligncenter size-full wp-image-11571\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2.png\" alt=\"janela2\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/janela2-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11570\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11570\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"graf2a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a.png\" class=\"alignnone size-full wp-image-11570\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a.png\" alt=\"graf2a\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/graf2a-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00ad<\/p><\/li>\n<li>Para que o galinheiro tenha \u00e1rea m\u00e1xima, este deve ter&nbsp;a forma de um quadrado.<\/li>\n<\/ol>\n\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11554' onClick='GTTabs_show(0,11554)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um agricultor comprou $6$ metros de rede para fazer um galinheiro retangular, como ilustra a figura. Complete a seguinte tabela: Num referencial cartesiano, marque os pontos $\\left( {c,l} \\right)$ que obteve&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20748,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,343],"tags":[429,128,344],"series":[],"class_list":["post-11554","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-funcoes-e-graficos","tag-10-o-ano","tag-funcoes-2","tag-grafico"],"views":2814,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10V2Pag029-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11554","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11554"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11554\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20748"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11554"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11554"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}