{"id":14624,"date":"2018-04-17T22:21:26","date_gmt":"2018-04-17T21:21:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14624"},"modified":"2022-01-09T22:14:08","modified_gmt":"2022-01-09T22:14:08","slug":"considera-a-funcao-f-de-proporcionalidade-inversa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14624","title":{"rendered":"Considera a fun\u00e7\u00e3o <em>f<\/em> de proporcionalidade inversa"},"content":{"rendered":"<p><ul id='GTTabs_ul_14624' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14624' class='GTTabs_curr'><a  id=\"14624_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14624' ><a  id=\"14624_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_14624'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14628\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14628\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png\" data-orig-size=\"443,351\" 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\/9V2Pag106-4.png\" class=\"alignright size-medium wp-image-14628\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4-300x238.png\" alt=\"\" width=\"300\" height=\"238\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4-300x238.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png 443w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera a fun\u00e7\u00e3o <em>f<\/em> de proporcionalidade inversa representada graficamente no referencial cartesiano da figura.<\/p>\n<ol>\n<li>Tendo em conta os dados da figura, determina o valor de <em>b<\/em>.<\/li>\n<li>Se \\(a = 4\\), indica a constante de proporcionalidade inversa e uma express\u00e3o alg\u00e9brica da fun\u00e7\u00e3o <em>f<\/em>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14624' onClick='GTTabs_show(1,14624)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14624'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14628\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14628\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png\" data-orig-size=\"443,351\" 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\/9V2Pag106-4.png\" class=\"alignright size-medium wp-image-14628\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4-300x238.png\" alt=\"\" width=\"300\" height=\"238\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4-300x238.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4.png 443w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Como as grandezas s\u00e3o inversamente proporcionais, ent\u00e3o \u00e9 constante o produto das medidas correspondentes dessas grandezas. Assim, tendo em considera\u00e7\u00e3o que \\(a &gt; 0\\) e, por isso, \\(a \\ne 0\\), temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{a \\times b = 3a \\times \\left( {b &#8211; 1} \\right)}&amp; \\Leftrightarrow &amp;{ab = 3ab &#8211; 3a}\\\\{}&amp; \\Leftrightarrow &amp;{2ab = 3a}\\\\{}&amp; \\Leftrightarrow &amp;{b = \\frac{{3a}}{{2a}}}\\\\{}&amp; \\Leftrightarrow &amp;{b = \\frac{3}{2}}\\end{array}\\]<\/li>\n<li>J\u00e1 vimos que\u00a0\\({b = \\frac{3}{2}}\\).<br \/>\nLogo, se\u00a0 \\(a = 4\\), ent\u00e3o a constante de proporcionalidade inversa \u00e9\u00a0\\(k = 4 \\times \\frac{3}{2} = 6\\) e a fun\u00e7\u00e3o <em>f<\/em> pode ser definida por \\(f\\left( x \\right) = \\frac{6}{x}\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14624' onClick='GTTabs_show(0,14624)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a fun\u00e7\u00e3o f de proporcionalidade inversa representada graficamente no referencial cartesiano da figura. Tendo em conta os dados da figura, determina o valor de b. Se \\(a = 4\\), indica&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14629,"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-14624","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":5060,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag106-4a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14624","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=14624"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14624\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14629"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14624"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}