{"id":3938,"date":"2010-10-09T19:48:33","date_gmt":"2010-10-09T18:48:33","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3938"},"modified":"2022-01-21T02:00:18","modified_gmt":"2022-01-21T02:00:18","slug":"rascunho-7","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3938","title":{"rendered":"Num certo pist\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_3938' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3938' class='GTTabs_curr'><a  id=\"3938_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3938' ><a  id=\"3938_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_3938'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3944\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3944\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" data-orig-size=\"335,278\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Pist\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" class=\"alignright wp-image-3944 size-full\" title=\"Pist\u00e3o\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" alt=\"\" width=\"335\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg 335w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao-300x248.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao-150x124.jpg 150w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/a>Observe a figura ao lado.<\/p>\n<p>Num certo pist\u00e3o, pe\u00e7a usada em mec\u00e2nica na transmiss\u00e3o de certos movimentos, a dist\u00e2ncia x, em metros, do centro do eixo \u00e0 cabe\u00e7a do pist\u00e3o, conforme se assinala na figura, \u00e9 dado pela f\u00f3rmula \\[x=\\cos \\theta +\\sqrt{16+0,5\\cos (2\\theta )}\\] em que $\\theta $ \u00e9\u00a0a amplitude do \u00e2ngulo representado na figura.<\/p>\n<p>Determine o valor exato de x, quando:<\/p>\n<ol>\n<li>$\\theta =30{}^\\text{o}$;<\/li>\n<li>$\\theta =45{}^\\text{o}$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3938' onClick='GTTabs_show(1,3938)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3938'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3944\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3944\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" data-orig-size=\"335,278\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Pist\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" class=\"alignright wp-image-3944 size-full\" title=\"Pist\u00e3o\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg\" alt=\"\" width=\"335\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao.jpg 335w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao-300x248.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pistao-150x124.jpg 150w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/a>Observe a figura ao lado.<\/p>\n<p>Num certo pist\u00e3o, pe\u00e7a usada em mec\u00e2nica na transmiss\u00e3o de certos movimentos, a dist\u00e2ncia x, em metros, do centro do eixo \u00e0 cabe\u00e7a do pist\u00e3o, conforme se assinala na figura, \u00e9 dado pela f\u00f3rmula \\[x=\\cos \\theta +\\sqrt{16+0,5\\cos (2\\theta )}\\] em que $\\theta $ \u00e9\u00a0a amplitude do \u00e2ngulo representado na figura.<\/p>\n<p>Determine o valor exato de x, quando:<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>\n<p>$\\theta =30{}^\\text{o}$;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>$\\theta =45{}^\\text{o}$.<\/p>\n<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00ad<\/p>\n<ol>\n<li>Para $\\theta =30{}^\\text{o}$, vem: \\[\\begin{array}{*{35}{l}}<br \/>\nx(30{}^\\text{o}) &amp; = &amp; \\cos 30{}^\\text{o}+\\sqrt{16+0,5\\cos (2\\times 30{}^\\text{o})}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}}{2}+\\sqrt{16+0,5\\times \\frac{1}{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}}{2}+\\sqrt{\\frac{65}{4}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}}{2}+\\frac{\\sqrt{65}}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{3}+\\sqrt{65}}{2}\\,\\,(m)\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\n\u00ad<\/li>\n<li>Para $\\theta =45{}^\\text{o}$, vem: \\[\\begin{array}{*{35}{l}}<br \/>\nx(45{}^\\text{o}) &amp; = &amp; \\cos 45{}^\\text{o}+\\sqrt{16+0,5\\cos (2\\times 45{}^\\text{o})}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{2}}{2}+\\sqrt{16+0,5\\times 0}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{\\sqrt{2}}{2}+4\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{8+\\sqrt{2}}{2}\\,\\,(m)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3938' onClick='GTTabs_show(0,3938)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observe a figura ao lado. Num certo pist\u00e3o, pe\u00e7a usada em mec\u00e2nica na transmiss\u00e3o de certos movimentos, a dist\u00e2ncia x, em metros, do centro do eixo \u00e0 cabe\u00e7a do pist\u00e3o, conforme&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20801,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,99],"tags":[422,423],"series":[],"class_list":["post-3938","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-trigonometria","tag-11-o-ano","tag-trigonometria"],"views":1651,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/11V1Pag095-46_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3938","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=3938"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3938\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20801"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3938"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}