[{"_1":2,"_274":-5,"_275":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/f97a66bb-30fe-45d0-af93-55940e197f99","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_112":113,"_114":115,"_30":195,"_249":250,"_270":271,"_272":273},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":21,"_22":23,"_24":25,"_83":84,"_106":21,"_107":108,"_109":110,"_111":14},"correctOptionId","2239f433-11ea-4c63-825f-2f7a4a518f59","difficulty","","id","f97a66bb-30fe-45d0-af93-55940e197f99","metadata",{"_26":27,"_79":80,"_81":82},"pd",{"_28":29,"_30":31,"_56":57,"_66":67,"_68":69,"_70":71,"_72":73,"_74":71,"_75":76,"_77":78},"area","Outros","tags",[32,37,41,45,49,53],{"_22":33,"_34":35,"_36":35},32,"name","prova","alias",{"_22":38,"_34":39,"_36":40},720,"Concurso","concurso",{"_22":42,"_34":43,"_36":44},845,"Engenharia","engenharia",{"_22":46,"_34":47,"_36":48},846,"Petróleo","petroleo",{"_22":50,"_34":51,"_36":52},40987,"Petrobrás","petrobras",{"_22":54,"_34":55,"_36":55},453167,"prova-petrobras","subjects",[58,62],{"_22":59,"_34":60,"_36":61},669639,"Termodinâmica","termodinamica",{"_22":63,"_34":64,"_36":65},5122557,"Engenharia Química","engenharia-quimica","materialId","41886316","answerCount",1,"isIndexable",true,"mainSubject",{"_22":59,"_34":60,"_36":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","131165522","options",[85,91,95,99,102],{"_22":86,"_87":88,"_89":90},"7d4545e3-5f47-452e-babe-e5b2a80f71c9","label","A","text","

Ensinar implica à necessidade de também aprender.

",{"_22":92,"_87":93,"_89":94},"02a67f11-3d00-4f66-b890-a04e78c25fdf","B","

Os professores sempre visam à evolução dos alunos.

",{"_22":96,"_87":97,"_89":98},"5643a0eb-493c-4d17-8051-23739f6a4a4f","C","

A educação se constrói à duras penas.

",{"_22":19,"_87":100,"_89":101},"D","

Recorrer à métodos pedagógicos alternativos é fundamental.

",{"_22":103,"_87":104,"_89":105},"10e42d5c-a575-4536-b6e5-8102cd41724f","E","

É importante criar discussões àcerca do ensino.

","solution_explanation","statement","

O acento grave está empregado de acordo com a norma-padrão em:

","status","pending_classification","hasRelatedVideo","relatedVideos",[],"similarQuestions",[116,156,174],{"_18":117,"_20":21,"_22":118,"_83":119,"_106":134,"_107":135,"_30":136},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[120,123,126,129,132],{"_22":121,"_87":88,"_89":122},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":124,"_87":93,"_89":125},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":127,"_87":97,"_89":128},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":130,"_87":100,"_89":131},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":117,"_87":104,"_89":133},"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

",[137],{"_22":138,"_34":139,"_36":140,"_141":142,"_143":144,"_145":146,"_147":146,"_24":148,"_155":140},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","b787e438-0ab3-454c-ab43-5d3d14c2720d","created_at","2025-04-29T03:44:35.328997+00:00","updated_at",{"_149":150,"_151":152,"_153":154},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_18":157,"_20":21,"_22":158,"_83":159,"_106":171,"_107":172,"_30":173},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[160,163,166,168],{"_22":161,"_87":88,"_89":162},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":164,"_87":93,"_89":165},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":157,"_87":97,"_89":167},"

Verdadeiro, falso, verdadeiro

",{"_22":169,"_87":100,"_89":170},"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?

",[137],{"_18":175,"_20":21,"_22":176,"_83":177,"_106":192,"_107":193,"_30":194},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[178,181,184,186,189],{"_22":179,"_87":88,"_89":180},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":182,"_87":93,"_89":183},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":175,"_87":97,"_89":185},"Indeterminado",{"_22":187,"_87":100,"_89":188},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":190,"_87":104,"_89":191},"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????",[137],[137,196,204,214,221,228,234,239,244],{"_22":197,"_34":60,"_36":61,"_141":142,"_143":198,"_145":199,"_147":199,"_24":200,"_155":203},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_149":201,"_151":152,"_153":202},2,11846,"termodinamica-3",{"_22":205,"_34":206,"_36":207,"_141":142,"_143":208,"_145":209,"_147":209,"_24":210,"_155":213},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_149":211,"_151":152,"_153":212},5,30614,"engenharia-mecatronica-1",{"_22":215,"_34":216,"_36":217,"_141":142,"_143":205,"_145":146,"_147":146,"_24":218,"_155":220},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_149":211,"_151":152,"_153":219},25741,"mecanica-3",{"_22":198,"_34":222,"_36":223,"_141":142,"_143":208,"_145":209,"_147":209,"_24":224,"_155":227},"Engenharia Mecânica","engenharia-mecanica",{"_149":225,"_151":152,"_153":226},11,36318,"engenharia-mecanica-2",{"_22":229,"_34":60,"_36":61,"_141":142,"_143":138,"_145":230,"_147":230,"_24":231,"_155":233},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_149":152,"_151":152,"_153":232},8597,"termodinamica-5",{"_22":144,"_34":235,"_36":236,"_141":142,"_143":208,"_145":209,"_147":209,"_24":237,"_155":238},"Engenharia de Petróleo","engenharia-de-petroleo",{"_149":211,"_151":152,"_153":154},"engenharia-de-petroleo-1",{"_22":208,"_34":43,"_36":44,"_141":142,"_143":-5,"_145":240,"_147":240,"_24":241,"_155":44},"2025-04-29T01:55:38.635246+00:00",{"_149":242,"_151":152,"_153":243},29,351586,{"_22":245,"_34":60,"_36":61,"_141":142,"_143":215,"_145":246,"_147":246,"_24":247,"_155":248},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_149":152,"_151":152,"_153":232},"termodinamica-4","tagsTree",[251],{"_22":208,"_34":43,"_36":44,"_141":142,"_143":-5,"_145":240,"_147":240,"_24":241,"_155":44,"_252":253},"children",[254,260,264],{"_22":205,"_34":206,"_36":207,"_141":142,"_143":208,"_145":209,"_147":209,"_24":210,"_155":213,"_252":255},[256],{"_22":215,"_34":216,"_36":217,"_141":142,"_143":205,"_145":146,"_147":146,"_24":218,"_155":220,"_252":257},[258],{"_22":245,"_34":60,"_36":61,"_141":142,"_143":215,"_145":246,"_147":246,"_24":247,"_155":248,"_252":259},[],{"_22":198,"_34":222,"_36":223,"_141":142,"_143":208,"_145":209,"_147":209,"_24":224,"_155":227,"_252":261},[262],{"_22":197,"_34":60,"_36":61,"_141":142,"_143":198,"_145":199,"_147":199,"_24":200,"_155":203,"_252":263},[],{"_22":144,"_34":235,"_36":236,"_141":142,"_143":208,"_145":209,"_147":209,"_24":237,"_155":238,"_252":265},[266],{"_22":138,"_34":139,"_36":140,"_141":142,"_143":144,"_145":146,"_147":146,"_24":148,"_155":140,"_252":267},[268],{"_22":229,"_34":60,"_36":61,"_141":142,"_143":138,"_145":230,"_147":230,"_24":231,"_155":233,"_252":269},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários