[{"_1":2,"_276":-5,"_277":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ff35f023-5e14-4a40-a49f-007ab4ec4e7d","user","pages/questions/show/index",{"_10":11,"_12":13,"_48":49,"_50":51,"_71":248,"_249":250},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45,"_46":47},"correctOptionId","","difficulty","id","ff35f023-5e14-4a40-a49f-007ab4ec4e7d","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"2875f4a7-0274-496d-9943-87e64801bd01","label","A","text","3448,28 J",{"_17":28,"_23":29,"_25":30},"5f114964-2282-440b-a3ca-55aa6ee9440d","B","1000,00 J",{"_17":32,"_23":33,"_25":34},"09ed74e4-0ff6-4220-94b7-a9f5da49f3a1","C","2516,35 J",{"_17":36,"_23":37,"_25":38},"6c9b8e06-3309-4d63-9ce7-6f8e7d954c46","D","6892,37 J",{"_17":40,"_23":41,"_25":42},"a3e08130-7108-4114-ae57-c56e08f3c064","E","5017,24 J","solution_explanation","statement","

Uma máquina térmica que opera entre reservatórios de energia a 20^\text{ºC} e 600^\text{ºC} tem 30\\\\% do máximo rendimento possível. Que quantidade de energia esta máquina deve extrair do reservatório quente para realizar 1.000 \\, \text{J} de trabalho?

","status","has_issues","relatedVideos",[],"similarQuestions",[52,174,191,208,228],{"_14":15,"_16":15,"_17":53,"_19":54,"_43":15,"_44":70,"_71":72},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[55,58,61,64,67],{"_17":56,"_23":24,"_25":57},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":59,"_23":29,"_25":60},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":62,"_23":33,"_25":63},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":65,"_23":37,"_25":66},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":68,"_23":41,"_25":69},"112831da-be9c-458e-94cb-e8292d0dba12","y'' - 2y' + 6y = 0","

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

","tags",[73,95,105,115,122,129,137,145,151,156,162,169],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78},"6516bbbd-f2a3-4710-8382-702240b17836","name","Mecânica na Engenharia de Petróleo","alias","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","metadata",{"_88":89,"_90":91,"_92":93},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":96,"_75":97,"_77":98,"_79":80,"_81":99,"_83":100,"_85":100,"_86":101,"_94":104},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_88":102,"_90":91,"_92":103},2,11846,"termodinamica-3",{"_17":106,"_75":107,"_77":108,"_79":80,"_81":109,"_83":110,"_85":110,"_86":111,"_94":114},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_88":112,"_90":91,"_92":113},5,30614,"engenharia-mecatronica-1",{"_17":116,"_75":117,"_77":118,"_79":80,"_81":106,"_83":84,"_85":84,"_86":119,"_94":121},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_88":112,"_90":91,"_92":120},25741,"mecanica-3",{"_17":99,"_75":123,"_77":124,"_79":80,"_81":109,"_83":110,"_85":110,"_86":125,"_94":128},"Engenharia Mecânica","engenharia-mecanica",{"_88":126,"_90":91,"_92":127},11,36318,"engenharia-mecanica-2",{"_17":130,"_75":131,"_77":132,"_79":80,"_81":133,"_83":100,"_85":100,"_86":134,"_94":132},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_88":135,"_90":91,"_92":136},10,8575,{"_17":138,"_75":139,"_77":140,"_79":80,"_81":-5,"_83":141,"_85":141,"_86":142,"_94":140},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_88":143,"_90":91,"_92":144},18,135489,{"_17":146,"_75":97,"_77":98,"_79":80,"_81":74,"_83":147,"_85":147,"_86":148,"_94":150},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_88":91,"_90":91,"_92":149},8597,"termodinamica-5",{"_17":82,"_75":152,"_77":153,"_79":80,"_81":109,"_83":110,"_85":110,"_86":154,"_94":155},"Engenharia de Petróleo","engenharia-de-petroleo",{"_88":112,"_90":91,"_92":93},"engenharia-de-petroleo-1",{"_17":133,"_75":157,"_77":158,"_79":80,"_81":138,"_83":110,"_85":110,"_86":159,"_94":161},"Física","fisica",{"_88":126,"_90":91,"_92":160},13777,"fisica-4",{"_17":109,"_75":163,"_77":164,"_79":80,"_81":-5,"_83":165,"_85":165,"_86":166,"_94":164},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_88":167,"_90":91,"_92":168},29,351586,{"_17":170,"_75":97,"_77":98,"_79":80,"_81":116,"_83":171,"_85":171,"_86":172,"_94":173},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_88":91,"_90":91,"_92":149},"termodinamica-4",{"_14":15,"_16":15,"_17":175,"_19":176,"_43":15,"_44":189,"_71":190},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[177,180,183,186],{"_17":178,"_23":24,"_25":179},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":181,"_23":29,"_25":182},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":184,"_23":33,"_25":185},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":187,"_23":37,"_25":188},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[73,95,105,115,122,129,137,145,151,156,162,169],{"_14":15,"_16":15,"_17":192,"_19":193,"_43":15,"_44":206,"_71":207},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[194,197,200,203],{"_17":195,"_23":24,"_25":196},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":198,"_23":29,"_25":199},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":201,"_23":33,"_25":202},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":204,"_23":37,"_25":205},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[73,95,105,115,122,129,137,145,151,156,162,169],{"_14":15,"_16":15,"_17":209,"_19":210,"_43":15,"_44":226,"_71":227},"996628fc-4ac3-4821-86bd-839f86a97a6d",[211,214,217,220,223],{"_17":212,"_23":24,"_25":213},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":215,"_23":29,"_25":216},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":218,"_23":33,"_25":219},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":221,"_23":37,"_25":222},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":224,"_23":41,"_25":225},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[73,95,105,115,122,129,137,145,151,156,162,169],{"_14":15,"_16":15,"_17":229,"_19":230,"_43":15,"_44":246,"_71":247},"c478a46c-46a8-4942-ae14-2e79def3dda2",[231,234,237,240,243],{"_17":232,"_23":24,"_25":233},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":235,"_23":29,"_25":236},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":238,"_23":33,"_25":239},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":241,"_23":37,"_25":242},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":244,"_23":41,"_25":245},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[73,95,105,115,122,129,137,145,151,156,162,169],[73,95,105,115,122,129,137,145,151,156,162,169],"tagsTree",[251,258],{"_17":138,"_75":139,"_77":140,"_79":80,"_81":-5,"_83":141,"_85":141,"_86":142,"_94":140,"_252":253},"children",[254],{"_17":133,"_75":157,"_77":158,"_79":80,"_81":138,"_83":110,"_85":110,"_86":159,"_94":161,"_252":255},[256],{"_17":130,"_75":131,"_77":132,"_79":80,"_81":133,"_83":100,"_85":100,"_86":134,"_94":132,"_252":257},[],{"_17":109,"_75":163,"_77":164,"_79":80,"_81":-5,"_83":165,"_85":165,"_86":166,"_94":164,"_252":259},[260,266,270],{"_17":106,"_75":107,"_77":108,"_79":80,"_81":109,"_83":110,"_85":110,"_86":111,"_94":114,"_252":261},[262],{"_17":116,"_75":117,"_77":118,"_79":80,"_81":106,"_83":84,"_85":84,"_86":119,"_94":121,"_252":263},[264],{"_17":170,"_75":97,"_77":98,"_79":80,"_81":116,"_83":171,"_85":171,"_86":172,"_94":173,"_252":265},[],{"_17":99,"_75":123,"_77":124,"_79":80,"_81":109,"_83":110,"_85":110,"_86":125,"_94":128,"_252":267},[268],{"_17":96,"_75":97,"_77":98,"_79":80,"_81":99,"_83":100,"_85":100,"_86":101,"_94":104,"_252":269},[],{"_17":82,"_75":152,"_77":153,"_79":80,"_81":109,"_83":110,"_85":110,"_86":154,"_94":155,"_252":271},[272],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78,"_252":273},[274],{"_17":146,"_75":97,"_77":98,"_79":80,"_81":74,"_83":147,"_85":147,"_86":148,"_94":150,"_252":275},[],"actionData","errors"]

Aulas em vídeo Em breve

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