{"id":6636,"date":"2011-03-21T23:35:10","date_gmt":"2011-03-21T23:35:10","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6636"},"modified":"2022-01-24T23:44:06","modified_gmt":"2022-01-24T23:44:06","slug":"uma-folha-rectangular-de-metal","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6636","title":{"rendered":"Uma folha retangular de metal"},"content":{"rendered":"<p><ul id='GTTabs_ul_6636' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6636' class='GTTabs_curr'><a  id=\"6636_0\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<li id='GTTabs_li_1_6636' ><a  id=\"6636_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_6636'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6637\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6637\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\" data-orig-size=\"234,427\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Caleira\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\" class=\"alignright size-medium wp-image-6637\" title=\"Caleira\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-164x300.jpg\" alt=\"\" width=\"131\" height=\"240\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-164x300.jpg 164w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-82x150.jpg 82w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg 234w\" sizes=\"auto, (max-width: 131px) 100vw, 131px\" \/><\/a>Uma folha retangular de metal com 20 cm de largura vai ser dobrada para se fabricarem caleiras, como mostra a figura.<\/p>\n<p>Por onde devem ser feitas as dobragens para que a caleira transporte a maior quantidade poss\u00edvel de \u00e1gua?<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6638\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6638\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2.jpg\" data-orig-size=\"363,178\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Caleira\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2.jpg\" class=\"aligncenter size-medium wp-image-6638\" title=\"Caleira\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2-300x147.jpg\" alt=\"\" width=\"240\" height=\"118\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2-300x147.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2-150x73.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira2.jpg 363w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6636' onClick='GTTabs_show(1,6636)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6636'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6637\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6637\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\" data-orig-size=\"234,427\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Caleira\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg\" class=\"alignright size-medium wp-image-6637\" title=\"Caleira\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-164x300.jpg\" alt=\"\" width=\"131\" height=\"240\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-164x300.jpg 164w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1-82x150.jpg 82w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/caleira1.jpg 234w\" sizes=\"auto, (max-width: 131px) 100vw, 131px\" \/><\/a>Para que a caleira transporte a maior quantidade poss\u00edvel de \u00e1gua, a sua sec\u00e7\u00e3o deve ser m\u00e1xima.<\/p>\n<p>A \u00e1rea da sec\u00e7\u00e3o da caleira, em cent\u00edmetros quadrados, \u00e9 dada por $A(x)=(20-2x)x$, com $0&lt;x&lt;10$.<\/p>\n<p>Ora, $A'(x)=(20x-2{{x}^{2}})&#8217;=20-4x$.<\/p>\n<p>Assim, temos:<\/p>\n<table class=\"aligncenter\" style=\"width: 60%;\" border=\"4\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$<\/td>\n<td style=\"text-align: center;\">$0$<\/td>\n<td><\/td>\n<td style=\"text-align: center;\">$5$<\/td>\n<td><\/td>\n<td style=\"text-align: center;\">$10$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$A'(x)$<\/td>\n<td style=\"text-align: center;\">n.d.<\/td>\n<td style=\"text-align: center;\">+<\/td>\n<td style=\"text-align: center;\">$0$<\/td>\n<td style=\"text-align: center;\">&#8211;<\/td>\n<td style=\"text-align: center;\">n.d.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$A(x)$<\/td>\n<td style=\"text-align: center;\">n.d.<\/td>\n<td style=\"text-align: center;\">$\\nearrow $<\/td>\n<td style=\"text-align: center;\">$50$<\/td>\n<td style=\"text-align: center;\">$\\searrow $<\/td>\n<td style=\"text-align: center;\">n.d.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Portanto, a \u00e1rea da sec\u00e7\u00e3o \u00e9 m\u00e1xima ($50\\,c{{m}^{2}}$) para $x=5\\,cm$.<\/p>\n<p>Logo, para que a caleira transporte a maior quantidade poss\u00edvel de \u00e1gua, as dobragens devem ser feitas a 5 cm das extremidades laterais da folha retangular.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6639\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6639\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001.png\" data-orig-size=\"690,468\" 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=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001.png\" class=\"aligncenter wp-image-6639\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001.png\" alt=\"\" width=\"540\" height=\"366\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001.png 690w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001-150x101.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/22-03-2001-Ecra001-400x271.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6636' onClick='GTTabs_show(0,6636)'>&lt;&lt; Resolu\u00e7\u00e3o<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Resolu\u00e7\u00e3o Resolu\u00e7\u00e3o Resolu\u00e7\u00e3o Uma folha retangular de metal com 20 cm de largura vai ser dobrada para se fabricarem caleiras, como mostra a figura. Por onde devem ser feitas as dobragens para que a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20927,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[145,144],"series":[],"class_list":["post-6636","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivadas-2","tag-extremos-relativos"],"views":2719,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11V2Pag198-48_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6636","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=6636"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6636\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20927"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6636"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}