{"id":26276,"date":"2023-06-06T19:15:03","date_gmt":"2023-06-06T18:15:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26276"},"modified":"2023-06-07T22:49:07","modified_gmt":"2023-06-07T21:49:07","slug":"o-valor-de-cada-simbolo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26276","title":{"rendered":"O valor de cada s\u00edmbolo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26276' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26276' class='GTTabs_curr'><a  id=\"26276_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26276' ><a  id=\"26276_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_26276'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Que resposta d\u00e1s ao professor Pedro?<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26277\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26277\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26277\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png\" data-orig-size=\"826,515\" 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=\"8_Pag211-T15\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png\" class=\"aligncenter wp-image-26277\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-300x187.png\" alt=\"\" width=\"640\" height=\"399\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-300x187.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-768x479.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png 826w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26276' onClick='GTTabs_show(1,26276)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26276'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Que resposta d\u00e1s ao professor Pedro?<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26277\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26277\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26277\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png\" data-orig-size=\"826,515\" 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=\"8_Pag211-T15\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png\" class=\"aligncenter wp-image-26277\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-300x187.png\" alt=\"\" width=\"640\" height=\"399\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-300x187.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15-768x479.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15.png 826w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<p><br>Para simplificar a escrita, comecemos por substituir os s\u00edmbolos por letras mai\u00fasculas. E designemos os valores a calcular pelas vari\u00e1veis: <em>u<\/em>, <em>v<\/em>, <em>x<\/em>, <em>y<\/em> e <em>z<\/em>.<\/p>\n<p>Acrescentemos ainda uma terceira linha \u00e0 tabela, onde anotaremos a vermelho os valores sucessivamente calculados.<\/p>\n<table class=\" aligncenter\" style=\"height: 40px; width: 80%; border-collapse: collapse;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"width: 14.2857%; height: 20px;\"><strong>A<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>B<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>C<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>D<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>E<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>F<\/strong><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><strong>G<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 14.2857%; height: 20px;\">91<\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><em>u<\/em><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><em>v<\/em><\/td>\n<td style=\"width: 14.2857%; height: 20px;\">148<\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><em>x<\/em><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><em>y<\/em><\/td>\n<td style=\"width: 14.2857%; height: 20px;\"><em>z<\/em><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.2857%;\">&nbsp;<\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ff0000;\">110<\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ff0000;\">129<\/span><\/td>\n<td style=\"width: 14.2857%;\">&nbsp;<\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ff0000;\">167<\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ff0000;\">186<\/span><\/td>\n<td style=\"width: 14.2857%;\"><strong><span style=\"color: #ff0000;\">205<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><br>Comecemos por determinar os valores das <em>u<\/em> e de <em>v<\/em>: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{u = \\frac{{91 + v}}{2}}\\\\{v = \\frac{{u + 148}}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{v = 2u &#8211; 91}\\\\{2u &#8211; 91 = \\frac{{u + 148}}{2}}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{4u &#8211; 182 = u + 148}\\\\{v = 2u &#8211; 91}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{3u = 330}\\\\{v = 2u &#8211; 91}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{u = 110}\\\\{y = 129}\\end{array}} \\right.}&amp;{}\\end{array}\\]<\/p>\n<p>Agora, calculemos sucessivamente os valores de <em>x<\/em>, <em>y<\/em> e <em>z<\/em>:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{129 + x}}{2} = 148}&amp; \\Leftrightarrow &amp;{x = 2 \\times 148 &#8211; 129}\\\\{}&amp; \\Leftrightarrow &amp;{x = 167}\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{148 + y}}{2} = 167}&amp; \\Leftrightarrow &amp;{x = 2 \\times 167 &#8211; 148}\\\\{}&amp; \\Leftrightarrow &amp;{x = 186}\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{167 + z}}{2} = 186}&amp; \\Leftrightarrow &amp;{x = 2 \\times 186 &#8211; 167}\\\\{}&amp; \\Leftrightarrow &amp;{x = 205}\\end{array}\\]<\/p>\n<p>Portanto, <img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26291\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26291\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15_b.png\" data-orig-size=\"165,68\" 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=\"8_Pag211-T15_b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15_b.png\" class=\"alignnone wp-image-26291\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15_b.png\" alt=\"\" width=\"100\" height=\"41\">.<\/p>\n<p><strong>Nota<\/strong>:<br>Repara que esses sete valores s\u00e3o termos de uma sequ\u00eancia que pode ser definida por \\({u_n} = 19n + 72\\), na qual&nbsp; cada termo, a partir do primeiro, \u00e9 19 unidades superior ao termo anterior.<br>Assim, o valor pretendido \u00e9 o s\u00e9timo termo da sequ\u00eancia: \\({u_7} = 19 \\times 7 + 72 = 205\\).<\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26276' onClick='GTTabs_show(0,26276)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Que resposta d\u00e1s ao professor Pedro? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":26278,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,716,239],"series":[],"class_list":["post-26276","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-media","tag-sistema-de-equacoes"],"views":91,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag211-T15_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26276","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=26276"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26276\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26278"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26276"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}