{"id":26156,"date":"2023-06-04T11:28:42","date_gmt":"2023-06-04T10:28:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26156"},"modified":"2023-06-04T21:37:42","modified_gmt":"2023-06-04T20:37:42","slug":"a-festa-de-final-de-ano","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26156","title":{"rendered":"A festa de final de ano"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26156' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26156' class='GTTabs_curr'><a  id=\"26156_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26156' ><a  id=\"26156_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_26156'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A Associa\u00e7\u00e3o de Estudantes da Escola Descobrir est\u00e1 a organizar a festa de final de ano, a realizar no gin\u00e1sio. Vai ser uma festa em grande, j\u00e1 que o gin\u00e1sio da escola tem capacidade para 400 alunos.<\/p>\n<p>A Associa\u00e7\u00e3o de Estudantes gastou 500 euros, na decora\u00e7\u00e3o e nos equipamentos de som e ilumina\u00e7\u00e3o, e decidiu cobrar 2 euros por cada bilhete. O Jo\u00e3o e a Teresa est\u00e3o encarregados de fazer a an\u00e1lise financeira da festa. Arranjaram uma express\u00e3o para calcular o saldo monet\u00e1rio da festa (<em>S<\/em>) em fun\u00e7\u00e3o do n\u00famero de bilhetes vendidos (<em>n<\/em>): \\[S = 2n &#8211; 500\\]<\/p>\n<ol>\n<li>Qual \u00e9 o lucro que a Associa\u00e7\u00e3o pode esperar?<br \/><strong>[A]<\/strong> 400 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 800 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 500 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 300 \u20ac<\/li>\n<li>No contexto da situa\u00e7\u00e3o, a express\u00e3o \\(2n\\) significa:<br \/><strong>[A]<\/strong> O lucro m\u00e1ximo que a Associa\u00e7\u00e3o pode ter.<br \/><strong>[B]<\/strong> O n\u00famero de bilhetes comprados.<br \/><strong>[C]<\/strong> O dinheiro obtido com a venda dos bilhetes.<br \/><strong>[D]<\/strong> O preju\u00edzo que a Associa\u00e7\u00e3o pode ter.<\/li>\n<li>Qual \u00e9 o saldo monet\u00e1rio a apurar se forem vendidos 120 bilhetes?<br \/><strong>[A]<\/strong> 260 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> \u2212260 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 740 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \u2212380 \u20ac<\/li>\n<li>Quantos bilhetes, no m\u00ednimo, \u00e9 necess\u00e1rio vender para que n\u00e3o haja preju\u00edzo?<br \/><strong>[A]<\/strong> 250\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 400\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 500\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 300<\/li>\n<li>Qual dos gr\u00e1ficos poder\u00e1 representar a rela\u00e7\u00e3o entre o saldo monet\u00e1rio, <em>S<\/em>, e o n\u00famero de bilhetes vendidos, <em>n<\/em>?<br \/><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26159\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26159\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\" data-orig-size=\"562,494\" 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_Pag206-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\" class=\"aligncenter wp-image-26159\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4-300x264.png\" alt=\"\" width=\"480\" height=\"422\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4-300x264.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png 562w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26156' onClick='GTTabs_show(1,26156)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26156'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A Associa\u00e7\u00e3o de Estudantes da Escola Descobrir est\u00e1 a organizar a festa de final de ano, a realizar no gin\u00e1sio. Vai ser uma festa em grande, j\u00e1 que o gin\u00e1sio da escola tem capacidade para 400 alunos.<\/p>\n<p>A Associa\u00e7\u00e3o de Estudantes gastou 500 euros, na decora\u00e7\u00e3o e nos equipamentos de som e ilumina\u00e7\u00e3o, e decidiu cobrar 2 euros por cada bilhete. O Jo\u00e3o e a Teresa est\u00e3o encarregados de fazer a an\u00e1lise financeira da festa. Arranjaram uma express\u00e3o para calcular o saldo monet\u00e1rio da festa (<em>S<\/em>) em fun\u00e7\u00e3o do n\u00famero de bilhetes vendidos (<em>n<\/em>): \\[S = 2n &#8211; 500\\]<\/p>\n<\/blockquote>\n<ol>\n<li>Qual \u00e9 o lucro que a Associa\u00e7\u00e3o pode esperar?<br \/><strong>[A]<\/strong> 400 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 800 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 500 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color: #0000ff;\"><strong>[D]<\/strong> 300 \u20ac<\/span><br \/><span style=\"color: #0000ff;\">Pode esperar um lucro m\u00e1ximo de 300 \u20ac, na suposi\u00e7\u00e3o de esgotar a capacidade do gin\u00e1sio da escola (venda de 400 bilhetes).<\/span><\/li>\n<li>No contexto da situa\u00e7\u00e3o, a express\u00e3o \\(2n\\) significa:<br \/><strong>[A]<\/strong> O lucro m\u00e1ximo que a Associa\u00e7\u00e3o pode ter.<br \/><strong>[B]<\/strong> O n\u00famero de bilhetes comprados.<br \/><span style=\"color: #0000ff;\"><strong>[C]<\/strong> O dinheiro obtido com a venda dos bilhetes.<\/span><br \/><strong>[D]<\/strong> O preju\u00edzo que a Associa\u00e7\u00e3o pode ter.<\/li>\n<li>Qual \u00e9 o saldo monet\u00e1rio a apurar se forem vendidos 120 bilhetes?<br \/><strong>[A]<\/strong> 260 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color: #0000ff;\"><strong>[B]<\/strong> \u2212260 \u20ac<\/span>\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 740 \u20ac\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \u2212380 \u20ac<br \/><span style=\"color: #0000ff;\">Se forem vendidos 120 bilhetes, o saldo monet\u00e1rio a apurar \u00e9 de \\(S\\left( {120} \\right) = 2 \\times 120 &#8211; 500 = &#8211; 260\\) euros.<\/span><\/li>\n<li>Quantos bilhetes, no m\u00ednimo, \u00e9 necess\u00e1rio vender para que n\u00e3o haja preju\u00edzo?<br \/><span style=\"color: #0000ff;\"><strong>[A]<\/strong> 250<\/span>\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> 400\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> 500\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> 300<br \/><span style=\"color: #0000ff;\">Para que n\u00e3o haja preju\u00edzo, no m\u00ednimo, \u00e9 necess\u00e1rio vender 250 bilhetes para que n\u00e3o haja preju\u00edzo, pois \\(\\begin{array}{*{20}{c}}{S = 0}&amp; \\Leftrightarrow &amp;{2n &#8211; 500 = 0}&amp; \\Leftrightarrow &amp;{n = 250}\\end{array}\\) e a fun\u00e7\u00e3o <em>S<\/em> \u00e9 crescente.<\/span><\/li>\n<li>Qual dos gr\u00e1ficos poder\u00e1 representar a rela\u00e7\u00e3o entre o saldo monet\u00e1rio, <em>S<\/em>, e o n\u00famero de bilhetes vendidos, <em>n<\/em>?<br \/><span style=\"color: #0000ff;\">Pelas respostas anteriores, conclui-se que apenas a op\u00e7\u00e3o (D) satisfaz esses requisitos.<br \/>(Em alternativa, basta ter em considera\u00e7\u00e3o os valores do declive (2) e da ordenada na origem (\u2212500) da reta que cont\u00e9m o gr\u00e1fico da fun\u00e7\u00e3o <em>S<\/em>.)<\/span><br \/><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26159\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26159\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\" data-orig-size=\"562,494\" 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_Pag206-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png\" class=\"aligncenter wp-image-26159\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4-300x264.png\" alt=\"\" width=\"480\" height=\"422\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4-300x264.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4.png 562w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26156' onClick='GTTabs_show(0,26156)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Associa\u00e7\u00e3o de Estudantes da Escola Descobrir est\u00e1 a organizar a festa de final de ano, a realizar no gin\u00e1sio. Vai ser uma festa em grande, j\u00e1 que o gin\u00e1sio da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26160,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,192,345,344],"series":[],"class_list":["post-26156","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-equacoes-literais","tag-funcao-afim","tag-grafico"],"views":148,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag206-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26156","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=26156"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26156\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26160"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26156"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}