[{"_1":2,"_262":-5,"_263":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e57a5d78-f68e-4c66-a717-d41f56af5b65","user","pages/questions/show/index",{"_10":11,"_12":13,"_30":31,"_32":33,"_57":234,"_235":236},"comments",[],"question",{"_14":15,"_16":17,"_18":19,"_20":21,"_27":17,"_28":29},"correctOptionId","bc9a97c5-1f62-4575-90ea-70f8ae914c13","difficulty","","id","e57a5d78-f68e-4c66-a717-d41f56af5b65","options",[22],{"_18":15,"_23":24,"_25":26},"label","A","text","Não é uma questão","solution_explanation","statement","

(c) o funcionamento ćıclico de todos os moto- res. A repetição cont́ınua dos movimentos exige que parte da energia seja transferida ao próximo ciclo.

","relatedVideos",[],"similarQuestions",[34,160,177,194,214],{"_14":17,"_16":17,"_18":35,"_20":36,"_27":17,"_28":56,"_57":58},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[37,40,44,48,52],{"_18":38,"_23":24,"_25":39},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_18":41,"_23":42,"_25":43},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","B","6y'' - y' - y = 0",{"_18":45,"_23":46,"_25":47},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_18":49,"_23":50,"_25":51},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_18":53,"_23":54,"_25":55},"112831da-be9c-458e-94cb-e8292d0dba12","E","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",[59,81,91,101,108,115,123,131,137,142,148,155],{"_18":60,"_61":62,"_63":64,"_65":66,"_67":68,"_69":70,"_71":70,"_72":73,"_80":64},"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",{"_74":75,"_76":77,"_78":79},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_18":82,"_61":83,"_63":84,"_65":66,"_67":85,"_69":86,"_71":86,"_72":87,"_80":90},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_74":88,"_76":77,"_78":89},2,11846,"termodinamica-3",{"_18":92,"_61":93,"_63":94,"_65":66,"_67":95,"_69":96,"_71":96,"_72":97,"_80":100},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_74":98,"_76":77,"_78":99},5,30614,"engenharia-mecatronica-1",{"_18":102,"_61":103,"_63":104,"_65":66,"_67":92,"_69":70,"_71":70,"_72":105,"_80":107},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_74":98,"_76":77,"_78":106},25741,"mecanica-3",{"_18":85,"_61":109,"_63":110,"_65":66,"_67":95,"_69":96,"_71":96,"_72":111,"_80":114},"Engenharia Mecânica","engenharia-mecanica",{"_74":112,"_76":77,"_78":113},11,36318,"engenharia-mecanica-2",{"_18":116,"_61":117,"_63":118,"_65":66,"_67":119,"_69":86,"_71":86,"_72":120,"_80":118},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_74":121,"_76":77,"_78":122},10,8575,{"_18":124,"_61":125,"_63":126,"_65":66,"_67":-5,"_69":127,"_71":127,"_72":128,"_80":126},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_74":129,"_76":77,"_78":130},18,135489,{"_18":132,"_61":83,"_63":84,"_65":66,"_67":60,"_69":133,"_71":133,"_72":134,"_80":136},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_74":77,"_76":77,"_78":135},8597,"termodinamica-5",{"_18":68,"_61":138,"_63":139,"_65":66,"_67":95,"_69":96,"_71":96,"_72":140,"_80":141},"Engenharia de Petróleo","engenharia-de-petroleo",{"_74":98,"_76":77,"_78":79},"engenharia-de-petroleo-1",{"_18":119,"_61":143,"_63":144,"_65":66,"_67":124,"_69":96,"_71":96,"_72":145,"_80":147},"Física","fisica",{"_74":112,"_76":77,"_78":146},13777,"fisica-4",{"_18":95,"_61":149,"_63":150,"_65":66,"_67":-5,"_69":151,"_71":151,"_72":152,"_80":150},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_74":153,"_76":77,"_78":154},29,351586,{"_18":156,"_61":83,"_63":84,"_65":66,"_67":102,"_69":157,"_71":157,"_72":158,"_80":159},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_74":77,"_76":77,"_78":135},"termodinamica-4",{"_14":17,"_16":17,"_18":161,"_20":162,"_27":17,"_28":175,"_57":176},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[163,166,169,172],{"_18":164,"_23":24,"_25":165},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_18":167,"_23":42,"_25":168},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_18":170,"_23":46,"_25":171},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_18":173,"_23":50,"_25":174},"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.

",[59,81,91,101,108,115,123,131,137,142,148,155],{"_14":17,"_16":17,"_18":178,"_20":179,"_27":17,"_28":192,"_57":193},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[180,183,186,189],{"_18":181,"_23":24,"_25":182},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_18":184,"_23":42,"_25":185},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_18":187,"_23":46,"_25":188},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_18":190,"_23":50,"_25":191},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[59,81,91,101,108,115,123,131,137,142,148,155],{"_14":17,"_16":17,"_18":195,"_20":196,"_27":17,"_28":212,"_57":213},"996628fc-4ac3-4821-86bd-839f86a97a6d",[197,200,203,206,209],{"_18":198,"_23":24,"_25":199},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_18":201,"_23":42,"_25":202},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_18":204,"_23":46,"_25":205},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_18":207,"_23":50,"_25":208},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_18":210,"_23":54,"_25":211},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[59,81,91,101,108,115,123,131,137,142,148,155],{"_14":17,"_16":17,"_18":215,"_20":216,"_27":17,"_28":232,"_57":233},"c478a46c-46a8-4942-ae14-2e79def3dda2",[217,220,223,226,229],{"_18":218,"_23":24,"_25":219},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_18":221,"_23":42,"_25":222},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_18":224,"_23":46,"_25":225},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_18":227,"_23":50,"_25":228},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_18":230,"_23":54,"_25":231},"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????",[59,81,91,101,108,115,123,131,137,142,148,155],[59,81,91,101,108,115,123,131,137,142,148,155],"tagsTree",[237,244],{"_18":124,"_61":125,"_63":126,"_65":66,"_67":-5,"_69":127,"_71":127,"_72":128,"_80":126,"_238":239},"children",[240],{"_18":119,"_61":143,"_63":144,"_65":66,"_67":124,"_69":96,"_71":96,"_72":145,"_80":147,"_238":241},[242],{"_18":116,"_61":117,"_63":118,"_65":66,"_67":119,"_69":86,"_71":86,"_72":120,"_80":118,"_238":243},[],{"_18":95,"_61":149,"_63":150,"_65":66,"_67":-5,"_69":151,"_71":151,"_72":152,"_80":150,"_238":245},[246,252,256],{"_18":92,"_61":93,"_63":94,"_65":66,"_67":95,"_69":96,"_71":96,"_72":97,"_80":100,"_238":247},[248],{"_18":102,"_61":103,"_63":104,"_65":66,"_67":92,"_69":70,"_71":70,"_72":105,"_80":107,"_238":249},[250],{"_18":156,"_61":83,"_63":84,"_65":66,"_67":102,"_69":157,"_71":157,"_72":158,"_80":159,"_238":251},[],{"_18":85,"_61":109,"_63":110,"_65":66,"_67":95,"_69":96,"_71":96,"_72":111,"_80":114,"_238":253},[254],{"_18":82,"_61":83,"_63":84,"_65":66,"_67":85,"_69":86,"_71":86,"_72":87,"_80":90,"_238":255},[],{"_18":68,"_61":138,"_63":139,"_65":66,"_67":95,"_69":96,"_71":96,"_72":140,"_80":141,"_238":257},[258],{"_18":60,"_61":62,"_63":64,"_65":66,"_67":68,"_69":70,"_71":70,"_72":73,"_80":64,"_238":259},[260],{"_18":132,"_61":83,"_63":84,"_65":66,"_67":60,"_69":133,"_71":133,"_72":134,"_80":136,"_238":261},[],"actionData","errors"]

Aulas em vídeo Em breve

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