{"id":14784,"date":"2018-04-22T18:20:39","date_gmt":"2018-04-22T17:20:39","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14784"},"modified":"2022-01-10T00:01:05","modified_gmt":"2022-01-10T00:01:05","slug":"parte-do-grafico-de-uma-funcao-e-um-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14784","title":{"rendered":"Parte do gr\u00e1fico de uma fun\u00e7\u00e3o e um ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14784' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14784' class='GTTabs_curr'><a  id=\"14784_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14784' ><a  id=\"14784_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_14784'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14785\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14785\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\" data-orig-size=\"500,392\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\" class=\"alignright wp-image-14785\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3-300x235.png\" alt=\"\" width=\"340\" height=\"267\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3-300x235.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png 500w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Na figura, est\u00e1 representada, num referencial cartesiano de origem <em>O<\/em>, parte do gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>, bem como o ret\u00e2ngulo [<em>OBCD<\/em>].<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>o ponto <em>B<\/em> pertence ao eixo das ordenadas;<\/li>\n<li>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/li>\n<li>os pontos <em>A<\/em> e <em>C<\/em> pertencem ao gr\u00e1fico de fun\u00e7\u00e3o <em>f<\/em>;<\/li>\n<li>o ponto <em>D<\/em> pertence o eixo das abcissas e tem abcissa 5;<\/li>\n<li>o ponto <em>A<\/em> tem coordenadas\u00a0\\(\\left( {2,\\;4} \\right)\\).<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 o valor de\u00a0\\(f\\left( 2 \\right)\\)?<\/li>\n<li>Determina o per\u00edmetro do ret\u00e2ngulo [<em>OBCD<\/em>].<br \/>\nApresenta a resposta na forma de d\u00edzima.<br \/>\nApresenta todos os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14784' onClick='GTTabs_show(1,14784)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14784'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14785\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14785\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\" data-orig-size=\"500,392\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png\" class=\"alignright wp-image-14785\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3-300x235.png\" alt=\"\" width=\"340\" height=\"267\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3-300x235.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3.png 500w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Na figura, est\u00e1 representada, num referencial cartesiano de origem <em>O<\/em>, parte do gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>, bem como o ret\u00e2ngulo [<em>OBCD<\/em>].<br \/>\nSabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote><p>o ponto <em>B<\/em> pertence ao eixo das ordenadas;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>a fun\u00e7\u00e3o <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade inversa;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>os pontos <em>A<\/em> e <em>C<\/em> pertencem ao gr\u00e1fico de fun\u00e7\u00e3o <em>f<\/em>;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>o ponto <em>D<\/em> pertence o eixo das abcissas e tem abcissa 5;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>o ponto <em>A<\/em> tem coordenadas\u00a0\\(\\left( {2,\\;4} \\right)\\).<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Ora,\u00a0\\(f\\left( 2 \\right) = 4\\), pois o\u00a0ponto <em>A<\/em> tem coordenadas\u00a0\\(\\left( {2,\\;4} \\right)\\) e pertence\u00a0ao gr\u00e1fico de fun\u00e7\u00e3o <em>f<\/em>.<br \/>\n\u00ad<\/li>\n<li>Como\u00a0 <em>f<\/em> \u00e9 uma fun\u00e7\u00e3o de proporcionalidade direta, ent\u00e3o \u00e9 do tipo\u00a0\\(f\\left( x \\right) = \\frac{k}{x}\\), sendo <em>k<\/em> a constante de proporcionalidade, que, no caso presente, \u00e9\u00a0\\(k = 2 \\times f\\left( 2 \\right) = 2 \\times 4 = 8\\).<br \/>\nAssim, tem-se\u00a0\\(f\\left( x \\right) = \\frac{8}{x}\\).<br \/>\nA ordenada do ponto <em>D<\/em> \u00e9\u00a0\\({y_D} = f\\left( {{x_D}} \\right) = f\\left( 5 \\right) = \\frac{8}{5}\\).<br \/>\nPortanto,\u00a0\u00a0\\({P_{\\left[ {OBCD} \\right]}} = 2 \\times \\left( {\\overline {OD} + \\overline {OB} } \\right) = 2 \\times \\left( {5 + \\frac{8}{5}} \\right) = 2 \\times \\left( {5 + 1,6} \\right) = 13,2\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14784' onClick='GTTabs_show(0,14784)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e1 representada, num referencial cartesiano de origem O, parte do gr\u00e1fico da fun\u00e7\u00e3o f, bem como o ret\u00e2ngulo [OBCD]. Sabe-se que: o ponto B pertence ao eixo das ordenadas;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14787,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,503,250],"series":[],"class_list":["post-14784","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-funcao-de-proporcionalidade-inversa","tag-proporcionalidade-inversa-2"],"views":3036,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag120-3a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14784","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=14784"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14784\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14787"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14784"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}