[{"_1":2,"_399":-5,"_400":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/60d7d449-e7df-4539-8b45-718b3f99bb80?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_110":111,"_211":212,"_51":287,"_354":355,"_395":396,"_397":398},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_85":86,"_104":43,"_105":106,"_107":108,"_109":16},"correctOptionId","54c1a3db-0cd1-4813-9236-fb2aadb35ce5","difficulty","","id","60d7d449-e7df-4539-8b45-718b3f99bb80","metadata",{"_48":49,"_81":82,"_83":84},"pd",{"_50":-5,"_51":52,"_59":60,"_69":70,"_71":72,"_73":16,"_74":75,"_76":16,"_77":78,"_79":80},"area","tags",[53],{"_44":54,"_55":56,"_57":58},98,"name","Exercício","alias","exercicio","subjects",[61,65],{"_44":62,"_55":63,"_57":64},670683,"Mecânica dos Fluidos","mecanica-dos-fluidos",{"_44":66,"_55":67,"_57":68},1663620,"Resistência dos Materiais","resistencia-dos-materiais","materialId","120595386","answerCount",1,"isIndexable","mainSubject",{"_44":66,"_55":67,"_57":68},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","120792686","options",[87,93,96,100],{"_44":88,"_89":90,"_91":92},"8ba1573a-0f1f-44f8-8c7a-a84dafda40d5","label","A","text","

O fluido não tem estrutura interna.

",{"_44":41,"_89":94,"_91":95},"B","

O fluido é uniforme e contínuo.

",{"_44":97,"_89":98,"_91":99},"ea61a2e3-a3da-4755-8eb7-0f2377333aa5","C","

O fluido é constituído por partículas sólidas.

",{"_44":101,"_89":102,"_91":103},"7e3318b0-423a-4a90-93a6-3607da2ca27e","D","

O fluido é extremamente viscoso.

","solution_explanation","statement","

Introdução a Mecânica dos Fluidos. Definição de um Fluido. Qual é a hipótese do contínuo?

","status","pending_classification","hasRelatedVideo","relatedVideos",[112],{"_113":114,"_132":133,"_51":148,"_183":184,"_201":202},"content",{"_44":115,"_55":116,"_117":-5,"_118":119,"_120":121,"_122":-5,"_46":123,"_126":127,"_128":127,"_129":-5,"_130":131},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_124":125},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_134":135,"_141":142,"_143":144,"_145":146,"_28":147},"provider",{"_44":136,"_137":138,"_139":140},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[149],{"_44":150,"_55":151,"_57":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_46":157,"_130":152,"_164":165},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_158":159,"_160":161,"_162":163},"childrenCount",18,"content_count",0,"question_count",135489,"children",[166],{"_44":167,"_55":168,"_57":169,"_153":154,"_155":150,"_126":170,"_128":170,"_46":171,"_130":174,"_164":175},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_158":172,"_160":161,"_162":173},10,19948,"mecanica-2",[176],{"_44":177,"_55":67,"_57":68,"_153":154,"_155":167,"_126":178,"_128":178,"_46":179,"_130":181,"_164":182},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_158":161,"_160":161,"_162":180},3376,"resistencia-dos-materiais-4",[],"video",{"_44":121,"_13":116,"_117":-5,"_185":186,"_187":188,"_28":-5,"_189":-5,"_134":188,"_190":191,"_145":-5,"_192":-5,"_193":-5,"_194":-5,"_195":-5,"_46":196,"_197":161,"_198":-5,"_107":199,"_126":200,"_128":200},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_124":125},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_44":150,"_55":151,"_57":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_46":203,"_130":152,"_164":204},{"_158":159,"_160":161,"_162":163},[205],{"_44":167,"_55":168,"_57":169,"_153":154,"_155":150,"_126":170,"_128":170,"_46":206,"_130":174,"_164":207},{"_158":172,"_160":161,"_162":173},[208],{"_44":177,"_55":67,"_57":68,"_153":154,"_155":167,"_126":178,"_128":178,"_46":209,"_130":181,"_164":210},{"_158":161,"_160":161,"_162":180},[],"similarQuestions",[213,244,264],{"_40":214,"_42":43,"_44":215,"_85":216,"_104":232,"_105":233,"_51":234},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[217,220,223,226,229],{"_44":218,"_89":90,"_91":219},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":221,"_89":94,"_91":222},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":224,"_89":98,"_91":225},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":227,"_89":102,"_91":228},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":214,"_89":230,"_91":231},"E","y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[235],{"_44":236,"_55":237,"_57":238,"_153":154,"_155":239,"_126":240,"_128":240,"_46":241,"_130":238},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_158":242,"_160":161,"_162":243},4,12302,{"_40":245,"_42":43,"_44":246,"_85":247,"_104":259,"_105":260,"_51":261},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[248,251,254,256],{"_44":249,"_89":90,"_91":250},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":252,"_89":94,"_91":253},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":245,"_89":98,"_91":255},"

Verdadeiro, falso, verdadeiro

",{"_44":257,"_89":102,"_91":258},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[262],{"_44":236,"_55":237,"_57":238,"_153":154,"_155":239,"_126":240,"_128":240,"_46":263,"_130":238},{"_158":242,"_160":161,"_162":243},{"_40":265,"_42":43,"_44":266,"_85":267,"_104":282,"_105":283,"_51":284},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[268,271,274,276,279],{"_44":269,"_89":90,"_91":270},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":272,"_89":94,"_91":273},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":265,"_89":98,"_91":275},"Indeterminado",{"_44":277,"_89":102,"_91":278},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":280,"_89":230,"_91":281},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[285],{"_44":236,"_55":237,"_57":238,"_153":154,"_155":239,"_126":240,"_128":240,"_46":286,"_130":238},{"_158":242,"_160":161,"_162":243},[288,290,299,305,309,311,313,321,326,334,336,341,347],{"_44":236,"_55":237,"_57":238,"_153":154,"_155":239,"_126":240,"_128":240,"_46":289,"_130":238},{"_158":242,"_160":161,"_162":243},{"_44":291,"_55":292,"_57":293,"_153":154,"_155":294,"_126":170,"_128":170,"_46":295,"_130":298},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_158":296,"_160":161,"_162":297},5,30614,"engenharia-mecatronica-1",{"_44":300,"_55":67,"_57":68,"_153":154,"_155":301,"_126":302,"_128":302,"_46":303,"_130":304},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-6",{"_44":301,"_55":168,"_57":169,"_153":154,"_155":291,"_126":240,"_128":240,"_46":306,"_130":308},{"_158":296,"_160":161,"_162":307},25741,"mecanica-3",{"_44":150,"_55":151,"_57":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_46":310,"_130":152},{"_158":159,"_160":161,"_162":163},{"_44":177,"_55":67,"_57":68,"_153":154,"_155":167,"_126":178,"_128":178,"_46":312,"_130":181},{"_158":161,"_160":161,"_162":180},{"_44":314,"_55":315,"_57":316,"_153":154,"_155":294,"_126":170,"_128":170,"_46":317,"_130":320},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_158":318,"_160":161,"_162":319},21,45865,"engenharia-civil-3",{"_44":239,"_55":322,"_57":323,"_153":154,"_155":294,"_126":170,"_128":170,"_46":324,"_130":325},"Engenharia de Petróleo","engenharia-de-petroleo",{"_158":296,"_160":161,"_162":243},"engenharia-de-petroleo-1",{"_44":327,"_55":328,"_57":329,"_153":154,"_155":314,"_126":330,"_128":330,"_46":331,"_130":333},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_158":296,"_160":161,"_162":332},8852,"estruturas-1",{"_44":167,"_55":168,"_57":169,"_153":154,"_155":150,"_126":170,"_128":170,"_46":335,"_130":174},{"_158":172,"_160":161,"_162":173},{"_44":337,"_55":67,"_57":68,"_153":154,"_155":236,"_126":338,"_128":338,"_46":339,"_130":340},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-7",{"_44":342,"_55":343,"_57":68,"_153":154,"_155":327,"_126":344,"_128":344,"_46":345,"_130":346},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-5",{"_44":294,"_55":348,"_57":349,"_153":154,"_155":-5,"_126":350,"_128":350,"_46":351,"_130":349},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_158":352,"_160":161,"_162":353},29,351586,"tagsTree",[356,365],{"_44":150,"_55":151,"_57":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_46":357,"_130":152,"_164":358},{"_158":159,"_160":161,"_162":163},[359],{"_44":167,"_55":168,"_57":169,"_153":154,"_155":150,"_126":170,"_128":170,"_46":360,"_130":174,"_164":361},{"_158":172,"_160":161,"_162":173},[362],{"_44":177,"_55":67,"_57":68,"_153":154,"_155":167,"_126":178,"_128":178,"_46":363,"_130":181,"_164":364},{"_158":161,"_160":161,"_162":180},[],{"_44":294,"_55":348,"_57":349,"_153":154,"_155":-5,"_126":350,"_128":350,"_46":366,"_130":349,"_164":367},{"_158":352,"_160":161,"_162":353},[368,377,386],{"_44":291,"_55":292,"_57":293,"_153":154,"_155":294,"_126":170,"_128":170,"_46":369,"_130":298,"_164":370},{"_158":296,"_160":161,"_162":297},[371],{"_44":301,"_55":168,"_57":169,"_153":154,"_155":291,"_126":240,"_128":240,"_46":372,"_130":308,"_164":373},{"_158":296,"_160":161,"_162":307},[374],{"_44":300,"_55":67,"_57":68,"_153":154,"_155":301,"_126":302,"_128":302,"_46":375,"_130":304,"_164":376},{"_158":161,"_160":161,"_162":180},[],{"_44":314,"_55":315,"_57":316,"_153":154,"_155":294,"_126":170,"_128":170,"_46":378,"_130":320,"_164":379},{"_158":318,"_160":161,"_162":319},[380],{"_44":327,"_55":328,"_57":329,"_153":154,"_155":314,"_126":330,"_128":330,"_46":381,"_130":333,"_164":382},{"_158":296,"_160":161,"_162":332},[383],{"_44":342,"_55":343,"_57":68,"_153":154,"_155":327,"_126":344,"_128":344,"_46":384,"_130":346,"_164":385},{"_158":161,"_160":161,"_162":180},[],{"_44":239,"_55":322,"_57":323,"_153":154,"_155":294,"_126":170,"_128":170,"_46":387,"_130":325,"_164":388},{"_158":296,"_160":161,"_162":243},[389],{"_44":236,"_55":237,"_57":238,"_153":154,"_155":239,"_126":240,"_128":240,"_46":390,"_130":238,"_164":391},{"_158":242,"_160":161,"_162":243},[392],{"_44":337,"_55":67,"_57":68,"_153":154,"_155":236,"_126":338,"_128":338,"_46":393,"_130":340,"_164":394},{"_158":161,"_160":161,"_162":180},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários