{"id":498,"date":"2017-12-02T07:20:36","date_gmt":"2017-12-02T12:20:36","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=498"},"modified":"2026-04-05T05:43:00","modified_gmt":"2026-04-05T10:43:00","slug":"1eva2017ti_t2-tanque-esferico-volumen","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-1eva20\/1eva2017ti_t2-tanque-esferico-volumen\/","title":{"rendered":"1Eva2017TI_T2 Tanque esf\u00e9rico-volumen"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">1ra Evaluaci\u00f3n I T\u00e9rmino 2017-2018. 26\/junio\/2017. MATG1013<\/h2>\n\n\n\n<p><strong>Tema 2<\/strong> (25 puntos). <\/p>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"214\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/12\/tanqueEsferico01.png\" alt=\"tanque Esf\u00e9rico\" class=\"wp-image-14121\" \/><\/figure>\n\n\n\n<p>El volumen <strong>V<\/strong> del l\u00edquido contenido en un tanque esf\u00e9rico de radio <strong>r<\/strong> est\u00e1 relacionado con la profundidad <strong>h<\/strong> del l\u00edquido por la ecuaci\u00f3n<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> V = \\frac{\\pi h^{2} (3r-h)}{3} <\/span>\n\n\n\n<p>Es posible desarrollar las siguientes dos f\u00f3rmulas para \u00e9l m\u00e9todo de punto fijo:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> h = \\sqrt{\\frac{h^{3}+(3V\/\\pi)}{3r}} <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> h = \\sqrt[3]{3(rh^{2}-V\/\\pi)} <\/span>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"265\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/12\/tanqueesferico03.png\" alt=\"tanque esf\u00e9rico diagrama\" class=\"wp-image-14123\" \/><\/figure>\n\n\n\n<p>Si <strong>r<\/strong>=1 m y <strong>V<\/strong>=0.75 m<sup>3<\/sup>, determine si las dos alternativas son estables (convergen), realice las iteraciones para aproximar <strong>h<\/strong> con un error menor o igual 0.01 m.<\/p>\n\n\n\n<p><em><strong>R\u00fabrica<\/strong><\/em>: C\u00e1lculo de las derivadas (10 puntos), determinaci\u00f3n de la estabilidad (5 puntos), iteraciones con el error (10 puntos).<\/p>\n\n\n\n<p><em><strong>Referencia<\/strong><\/em>: Ejercicio 5.17. p143 Steven C. Chapra. Numerical Methods 7<sup>th<\/sup> Edition.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1ra Evaluaci\u00f3n I T\u00e9rmino 2017-2018. 26\/junio\/2017. MATG1013 Tema 2 (25 puntos). El volumen V del l\u00edquido contenido en un tanque esf\u00e9rico de radio r est\u00e1 relacionado con la profundidad h del l\u00edquido por la ecuaci\u00f3n Es posible desarrollar las siguientes dos f\u00f3rmulas para \u00e9l m\u00e9todo de punto fijo: Si r=1 m y V=0.75 m3, determine [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[66],"class_list":["post-498","post","type-post","status-publish","format-standard","hentry","category-mn-1eva20","tag-raices"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/498","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=498"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/498\/revisions"}],"predecessor-version":[{"id":14126,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/498\/revisions\/14126"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}