{"id":22851,"date":"2022-11-01T11:28:02","date_gmt":"2022-11-01T11:28:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22851"},"modified":"2022-11-01T11:52:01","modified_gmt":"2022-11-01T11:52:01","slug":"seja-r-um-numero-real-positivo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22851","title":{"rendered":"Seja <em>r<\/em> um n\u00famero real positivo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22851' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22851' class='GTTabs_curr'><a  id=\"22851_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22851' ><a  id=\"22851_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_22851'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja <em>r<\/em> um n\u00famero real positivo.<\/p>\n<p>Sabe-se que as express\u00f5es \\(\\frac{1}{{2r}} \\times {10^{ &#8211; 20}}\\) e \\(r \\times {10^{30}}\\) representam as medidas dos comprimentos de dois lados consecutivos de um certo ret\u00e2ngulo.<\/p>\n<p>Qual das express\u00f5es seguintes \u00e9 a medida da \u00e1rea desse ret\u00e2ngulo?<br \/>Transcreve a op\u00e7\u00e3o correta.<\/p>\n<p><strong>[A]<\/strong> \\(2 \\times {10^9}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> \\(2 \\times {10^{10}}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> \\(5 \\times {10^9}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \\(5 \\times {10^{10}}\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22851' onClick='GTTabs_show(1,22851)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22851'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Seja <em>r<\/em> um n\u00famero real positivo.<\/p>\n<p>Sabe-se que as express\u00f5es \\(\\frac{1}{{2r}} \\times {10^{ &#8211; 20}}\\) e \\(r \\times {10^{30}}\\) representam as medidas dos comprimentos de dois lados consecutivos de um certo ret\u00e2ngulo.<\/p>\n<p>Qual das express\u00f5es seguintes \u00e9 a medida da \u00e1rea desse ret\u00e2ngulo?<br \/>Transcreve a op\u00e7\u00e3o correta.<\/p>\n<p><strong>[A]<\/strong> \\(2 \\times {10^9}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> \\(2 \\times {10^{10}}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> \\(5 \\times {10^9}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \\(5 \\times {10^{10}}\\)<\/p>\n<\/blockquote>\n<p>Ora, a medida da \u00e1rea desse ret\u00e2ngulo \u00e9:<\/p>\n<p>\\[{A_R} = \\left( {\\frac{1}{{2r}} \\times {{10}^{ &#8211; 20}}} \\right) \\times \\left( {r \\times {{10}^{30}}} \\right) = \\left( {\\frac{1}{{2r}} \\times r} \\right) \\times \\left( {{{10}^{ &#8211; 20}} \\times {{10}^{30}}} \\right) = \\frac{1}{2} \\times {10^{10}} = 0,5 \\times {10^{10}} = 5 \\times {10^9}\\]<\/p>\n<p>Logo, a op\u00e7\u00e3o correta \u00e9 <strong>[C]<\/strong> \\(5 \\times {10^9}\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22851' onClick='GTTabs_show(0,22851)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja r um n\u00famero real positivo. Sabe-se que as express\u00f5es \\(\\frac{1}{{2r}} \\times {10^{ &#8211; 20}}\\) e \\(r \\times {10^{30}}\\) representam as medidas dos comprimentos de dois lados consecutivos de um certo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,143],"series":[],"class_list":["post-22851","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-notacao-cientifica"],"views":203,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22851","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=22851"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22851\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22851"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}