{"id":14647,"date":"2018-04-18T10:28:00","date_gmt":"2018-04-18T09:28:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14647"},"modified":"2026-04-24T17:30:27","modified_gmt":"2026-04-24T16:30:27","slug":"uma-funcao-definida-por-y-frac10x","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14647","title":{"rendered":"Uma fun\u00e7\u00e3o definida por \\(y = \\frac{{10}}{x}\\)"},"content":{"rendered":"<p><ul id='GTTabs_ul_14647' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14647' class='GTTabs_curr'><a  id=\"14647_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14647' ><a  id=\"14647_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_14647'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14648\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14648\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png\" data-orig-size=\"446,321\" 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\/9V2Pag107-7.png\" class=\"alignright wp-image-14648\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7-300x216.png\" alt=\"\" width=\"400\" height=\"288\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7-300x216.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png 446w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>No referencial cartesiano da figura, est\u00e1 representada parte do gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> definida por\u00a0\\(y = \\frac{{10}}{x}\\), com\u00a0\\(x &gt; 0\\).<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>os pontos <em>P<\/em> e <em>Q<\/em> pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>;<\/li>\n<li>os pontos <em>A<\/em> e <em>B<\/em> pertencem ao eixo das abcissas;<\/li>\n<li>o ponto <em>C<\/em> pertence ao eixo das ordenadas;<\/li>\n<li>as abcissas dos pontos <em>A<\/em> e <em>P<\/em> s\u00e3o iguais,<\/li>\n<li>as abcissas dos pontos <em>B<\/em> e <em>Q<\/em> s\u00e3o iguais.<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 a \u00e1rea do ret\u00e2ngulo [OAPC]?<br \/>\n[A] 5 \u00a0 \u00a0 \u00a0 \u00a0 [B] 10 \u00a0 \u00a0 \u00a0 \u00a0 [C] 15 \u00a0 \u00a0 \u00a0 \u00a0 [D] 20<\/li>\n<li>Admite que\u00a0\\(\\overline {OB} = 4\\).<br \/>\nDetermina o per\u00edmetro do tri\u00e2ngulo [<em>OBQ<\/em>].<br \/>\nApresenta o resultado arredondado \u00e0s d\u00e9cimas.<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14647' onClick='GTTabs_show(1,14647)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14647'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote><p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14648\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14648\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png\" data-orig-size=\"446,321\" 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\/9V2Pag107-7.png\" class=\"alignright wp-image-14648\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7-300x216.png\" alt=\"\" width=\"400\" height=\"288\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7-300x216.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7.png 446w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>No referencial cartesiano da figura, est\u00e1 representada parte do gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em> definida por\u00a0\\(y = \\frac{{10}}{x}\\), com\u00a0\\(x &gt; 0\\).<br \/>\nSabe-se que:<\/p><\/blockquote>\n<ul>\n<li>\n<blockquote><p>os pontos <em>P<\/em> e <em>Q<\/em> pertencem ao gr\u00e1fico da fun\u00e7\u00e3o <em>f<\/em>;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>os pontos <em>A<\/em> e <em>B<\/em> pertencem ao eixo das abcissas;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>o ponto <em>C<\/em> pertence ao eixo das ordenadas;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>as abcissas dos pontos <em>A<\/em> e <em>P<\/em> s\u00e3o iguais,<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>as abcissas dos pontos <em>B<\/em> e <em>Q<\/em> s\u00e3o iguais.<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Como a fun\u00e7\u00e3o \u00e9 de proporcionalidade inversa e a constante de proporcionalidade \u00e9 10 (pois \\(x \\times y = 10\\)), ent\u00e3o\u00a0\\({A_{\\left[ {OAPC} \\right]}} = \\overline {OA} \\times \\overline {OC} = {x_P} \\times {y_P} = 10\\).<br \/>\nLogo, a alternativa correta \u00e9 a [B].<br \/>\n\u00ad<\/li>\n<li>Se\u00a0\\(\\overline {OB} = 4\\), ent\u00e3o\u00a0\\({x_Q} = 4\\).<br \/>\nLogo, \\({y_Q} = f\\left( {{x_Q}} \\right) = f\\left( 4 \\right) = \\frac{{10}}{4} = \\frac{5}{2}\\).<br \/>\nAplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [OBQ], vem:\\[\\overline {OQ} = \\sqrt {{{\\overline {OB} }^2} + {{\\overline {BQ} }^2}} = \\sqrt {{4^2} + {{\\left( {{\\textstyle{5 \\over 2}}} \\right)}^2}} = \\sqrt {\\frac{{89}}{4}} = \\frac{{\\sqrt {89} }}{2}\\]<br \/>\nAssim, o per\u00edmetro do tri\u00e2ngulo [<em>OBQ<\/em>] \u00e9 \\({P_{\\left[ {OBQ} \\right]}} = \\overline {OB} + \\overline {BQ} + \\overline {OQ} = 4 + \\frac{5}{2} + \\frac{{\\sqrt {89} }}{2} = \\frac{{13 + \\sqrt {89} }}{2} \\approx 11,2\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14647' onClick='GTTabs_show(0,14647)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No referencial cartesiano da figura, est\u00e1 representada parte do gr\u00e1fico da fun\u00e7\u00e3o f definida por\u00a0\\(y = \\frac{{10}}{x}\\), com\u00a0\\(x &gt; 0\\). Sabe-se que: os pontos P e Q pertencem ao gr\u00e1fico da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14650,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,250],"series":[],"class_list":["post-14647","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-proporcionalidade-inversa-2"],"views":2526,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag107-7a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14647","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=14647"}],"version-history":[{"count":1,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14647\/revisions"}],"predecessor-version":[{"id":27681,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14647\/revisions\/27681"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14650"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14647"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}