[{"_1":2,"_274":-5,"_275":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e2fbcad5-b3e0-4d5a-9e02-5ea1a334eef1","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":246,"_247":248},"comments",[],"question",{"_14":15,"_16":17,"_18":19,"_20":21,"_43":17,"_44":45},"correctOptionId","dbe7fc16-74cb-46ad-bc07-f8baed5a5912","difficulty","","id","e2fbcad5-b3e0-4d5a-9e02-5ea1a334eef1","options",[22,28,32,35,39],{"_18":23,"_24":25,"_26":27},"48783e56-1af6-411d-9e03-7968a3aeb337","label","A","text","

20%

",{"_18":29,"_24":30,"_26":31},"77505ebe-3576-44aa-9af9-8eab083c7923","B","

30%

",{"_18":15,"_24":33,"_26":34},"C","

40%

",{"_18":36,"_24":37,"_26":38},"66d7754f-7d98-4848-8abc-ededbf0d78a2","D","

50%

",{"_18":40,"_24":41,"_26":42},"135c5ad9-3bbf-4a8a-973c-2521042cb62c","E","

60%

","solution_explanation","statement","

A eficiência de um motor térmico é dada pela razão entre o trabalho útil e a energia fornecida. Se um motor recebe 500 \text{ J} e realiza 200 \text{ J} de trabalho, qual é sua eficiência?

","relatedVideos",[],"similarQuestions",[50,172,189,206,226],{"_14":17,"_16":17,"_18":51,"_20":52,"_43":17,"_44":68,"_69":70},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_18":54,"_24":25,"_26":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_18":57,"_24":30,"_26":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_18":60,"_24":33,"_26":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_18":63,"_24":37,"_26":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_18":66,"_24":41,"_26":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],{"_18":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",{"_18":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",{"_18":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",{"_18":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",{"_18":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",{"_18":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,{"_18":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,{"_18":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",{"_18":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",{"_18":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",{"_18":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,{"_18":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":17,"_16":17,"_18":173,"_20":174,"_43":17,"_44":187,"_69":188},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[175,178,181,184],{"_18":176,"_24":25,"_26":177},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_18":179,"_24":30,"_26":180},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_18":182,"_24":33,"_26":183},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_18":185,"_24":37,"_26":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":17,"_16":17,"_18":190,"_20":191,"_43":17,"_44":204,"_69":205},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[192,195,198,201],{"_18":193,"_24":25,"_26":194},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_18":196,"_24":30,"_26":197},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_18":199,"_24":33,"_26":200},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_18":202,"_24":37,"_26":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":17,"_16":17,"_18":207,"_20":208,"_43":17,"_44":224,"_69":225},"996628fc-4ac3-4821-86bd-839f86a97a6d",[209,212,215,218,221],{"_18":210,"_24":25,"_26":211},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_18":213,"_24":30,"_26":214},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_18":216,"_24":33,"_26":217},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_18":219,"_24":37,"_26":220},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_18":222,"_24":41,"_26":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":17,"_16":17,"_18":227,"_20":228,"_43":17,"_44":244,"_69":245},"c478a46c-46a8-4942-ae14-2e79def3dda2",[229,232,235,238,241],{"_18":230,"_24":25,"_26":231},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_18":233,"_24":30,"_26":234},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_18":236,"_24":33,"_26":237},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_18":239,"_24":37,"_26":240},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_18":242,"_24":41,"_26":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],{"_18":136,"_73":137,"_75":138,"_77":78,"_79":-5,"_81":139,"_83":139,"_84":140,"_92":138,"_250":251},"children",[252],{"_18":131,"_73":155,"_75":156,"_77":78,"_79":136,"_81":108,"_83":108,"_84":157,"_92":159,"_250":253},[254],{"_18":128,"_73":129,"_75":130,"_77":78,"_79":131,"_81":98,"_83":98,"_84":132,"_92":130,"_250":255},[],{"_18":107,"_73":161,"_75":162,"_77":78,"_79":-5,"_81":163,"_83":163,"_84":164,"_92":162,"_250":257},[258,264,268],{"_18":104,"_73":105,"_75":106,"_77":78,"_79":107,"_81":108,"_83":108,"_84":109,"_92":112,"_250":259},[260],{"_18":114,"_73":115,"_75":116,"_77":78,"_79":104,"_81":82,"_83":82,"_84":117,"_92":119,"_250":261},[262],{"_18":168,"_73":95,"_75":96,"_77":78,"_79":114,"_81":169,"_83":169,"_84":170,"_92":171,"_250":263},[],{"_18":97,"_73":121,"_75":122,"_77":78,"_79":107,"_81":108,"_83":108,"_84":123,"_92":126,"_250":265},[266],{"_18":94,"_73":95,"_75":96,"_77":78,"_79":97,"_81":98,"_83":98,"_84":99,"_92":102,"_250":267},[],{"_18":80,"_73":150,"_75":151,"_77":78,"_79":107,"_81":108,"_83":108,"_84":152,"_92":153,"_250":269},[270],{"_18":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76,"_250":271},[272],{"_18":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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