[{"_1":2,"_274":-5,"_275":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f3a985e9-6b4d-4af2-9fab-b094f9635385","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":246,"_247":248},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45},"correctOptionId","","difficulty","id","f3a985e9-6b4d-4af2-9fab-b094f9635385","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"40b4f293-957e-43c7-94d5-d82cf324e2ee","label","A","text","44%",{"_17":28,"_23":29,"_25":30},"17f44f5c-5e3e-453f-a329-70e7d87756f7","B","56%",{"_17":32,"_23":33,"_25":34},"8013f7f1-429d-4a08-8163-afce088a7e50","C","80%",{"_17":36,"_23":37,"_25":38},"d8cb86a3-2bdc-4620-a44e-b50f4b828778","D","10%",{"_17":40,"_23":41,"_25":42},"69f7a543-5bb0-4b12-bd1e-678ef59fa1c6","E","20%","solution_explanation","statement","Certa máquina ideal funciona realizando o ciclo de Carnot. Em cada ciclo o trabalho útil fornecido pela máquina é 1 \\, 500 \\, \\text{joules}. Sendo as temperaturas das fontes térmicas 227^{\\circ}C e 127^{\\circ}C, o rendimento da referida máquina é de:","relatedVideos",[],"similarQuestions",[50,172,189,206,226],{"_14":15,"_16":15,"_17":51,"_19":52,"_43":15,"_44":68,"_69":70},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_17":54,"_23":24,"_25":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":57,"_23":29,"_25":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":60,"_23":33,"_25":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":63,"_23":37,"_25":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":66,"_23":41,"_25":67},"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",[71,93,103,113,120,127,135,143,149,154,160,167],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76},"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",{"_86":87,"_88":89,"_90":91},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":94,"_73":95,"_75":96,"_77":78,"_79":97,"_81":98,"_83":98,"_84":99,"_92":102},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_86":100,"_88":89,"_90":101},2,11846,"termodinamica-3",{"_17":104,"_73":105,"_75":106,"_77":78,"_79":107,"_81":108,"_83":108,"_84":109,"_92":112},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_86":110,"_88":89,"_90":111},5,30614,"engenharia-mecatronica-1",{"_17":114,"_73":115,"_75":116,"_77":78,"_79":104,"_81":82,"_83":82,"_84":117,"_92":119},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_86":110,"_88":89,"_90":118},25741,"mecanica-3",{"_17":97,"_73":121,"_75":122,"_77":78,"_79":107,"_81":108,"_83":108,"_84":123,"_92":126},"Engenharia Mecânica","engenharia-mecanica",{"_86":124,"_88":89,"_90":125},11,36318,"engenharia-mecanica-2",{"_17":128,"_73":129,"_75":130,"_77":78,"_79":131,"_81":98,"_83":98,"_84":132,"_92":130},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_86":133,"_88":89,"_90":134},10,8575,{"_17":136,"_73":137,"_75":138,"_77":78,"_79":-5,"_81":139,"_83":139,"_84":140,"_92":138},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_86":141,"_88":89,"_90":142},18,135489,{"_17":144,"_73":95,"_75":96,"_77":78,"_79":72,"_81":145,"_83":145,"_84":146,"_92":148},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_86":89,"_88":89,"_90":147},8597,"termodinamica-5",{"_17":80,"_73":150,"_75":151,"_77":78,"_79":107,"_81":108,"_83":108,"_84":152,"_92":153},"Engenharia de Petróleo","engenharia-de-petroleo",{"_86":110,"_88":89,"_90":91},"engenharia-de-petroleo-1",{"_17":131,"_73":155,"_75":156,"_77":78,"_79":136,"_81":108,"_83":108,"_84":157,"_92":159},"Física","fisica",{"_86":124,"_88":89,"_90":158},13777,"fisica-4",{"_17":107,"_73":161,"_75":162,"_77":78,"_79":-5,"_81":163,"_83":163,"_84":164,"_92":162},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_86":165,"_88":89,"_90":166},29,351586,{"_17":168,"_73":95,"_75":96,"_77":78,"_79":114,"_81":169,"_83":169,"_84":170,"_92":171},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_86":89,"_88":89,"_90":147},"termodinamica-4",{"_14":15,"_16":15,"_17":173,"_19":174,"_43":15,"_44":187,"_69":188},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[175,178,181,184],{"_17":176,"_23":24,"_25":177},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":179,"_23":29,"_25":180},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":182,"_23":33,"_25":183},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":185,"_23":37,"_25":186},"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.

",[71,93,103,113,120,127,135,143,149,154,160,167],{"_14":15,"_16":15,"_17":190,"_19":191,"_43":15,"_44":204,"_69":205},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[192,195,198,201],{"_17":193,"_23":24,"_25":194},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":196,"_23":29,"_25":197},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":199,"_23":33,"_25":200},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":202,"_23":37,"_25":203},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[71,93,103,113,120,127,135,143,149,154,160,167],{"_14":15,"_16":15,"_17":207,"_19":208,"_43":15,"_44":224,"_69":225},"996628fc-4ac3-4821-86bd-839f86a97a6d",[209,212,215,218,221],{"_17":210,"_23":24,"_25":211},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":213,"_23":29,"_25":214},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":216,"_23":33,"_25":217},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":219,"_23":37,"_25":220},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":222,"_23":41,"_25":223},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[71,93,103,113,120,127,135,143,149,154,160,167],{"_14":15,"_16":15,"_17":227,"_19":228,"_43":15,"_44":244,"_69":245},"c478a46c-46a8-4942-ae14-2e79def3dda2",[229,232,235,238,241],{"_17":230,"_23":24,"_25":231},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":233,"_23":29,"_25":234},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":236,"_23":33,"_25":237},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":239,"_23":37,"_25":240},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":242,"_23":41,"_25":243},"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????",[71,93,103,113,120,127,135,143,149,154,160,167],[71,93,103,113,120,127,135,143,149,154,160,167],"tagsTree",[249,256],{"_17":136,"_73":137,"_75":138,"_77":78,"_79":-5,"_81":139,"_83":139,"_84":140,"_92":138,"_250":251},"children",[252],{"_17":131,"_73":155,"_75":156,"_77":78,"_79":136,"_81":108,"_83":108,"_84":157,"_92":159,"_250":253},[254],{"_17":128,"_73":129,"_75":130,"_77":78,"_79":131,"_81":98,"_83":98,"_84":132,"_92":130,"_250":255},[],{"_17":107,"_73":161,"_75":162,"_77":78,"_79":-5,"_81":163,"_83":163,"_84":164,"_92":162,"_250":257},[258,264,268],{"_17":104,"_73":105,"_75":106,"_77":78,"_79":107,"_81":108,"_83":108,"_84":109,"_92":112,"_250":259},[260],{"_17":114,"_73":115,"_75":116,"_77":78,"_79":104,"_81":82,"_83":82,"_84":117,"_92":119,"_250":261},[262],{"_17":168,"_73":95,"_75":96,"_77":78,"_79":114,"_81":169,"_83":169,"_84":170,"_92":171,"_250":263},[],{"_17":97,"_73":121,"_75":122,"_77":78,"_79":107,"_81":108,"_83":108,"_84":123,"_92":126,"_250":265},[266],{"_17":94,"_73":95,"_75":96,"_77":78,"_79":97,"_81":98,"_83":98,"_84":99,"_92":102,"_250":267},[],{"_17":80,"_73":150,"_75":151,"_77":78,"_79":107,"_81":108,"_83":108,"_84":152,"_92":153,"_250":269},[270],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76,"_250":271},[272],{"_17":144,"_73":95,"_75":96,"_77":78,"_79":72,"_81":145,"_83":145,"_84":146,"_92":148,"_250":273},[],"actionData","errors"]

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