[{"_1":2,"_272":-5,"_273":-5},"loaderData",{"_3":4,"_6":7},"root",{"_5":-5},"user","pages/questions/show/index",{"_8":9,"_10":11,"_44":45,"_46":47,"_67":244,"_245":246},"comments",[],"question",{"_12":13,"_14":13,"_15":16,"_17":18,"_41":13,"_42":43},"correctOptionId","","difficulty","id","fd11ee5d-bffd-4be5-a6eb-61511431a354","options",[19,25,29,33,37],{"_15":20,"_21":22,"_23":24},"c2c295aa-47c3-4fa7-915e-6781e247eb1b","label","A","text","5 minutos",{"_15":26,"_21":27,"_23":28},"6c066bc7-63dd-4a62-a24d-2ee28b309715","B","8,4 minutos",{"_15":30,"_21":31,"_23":32},"13343d18-f6cb-4d97-8431-8af6ad16ca87","C","1 hora",{"_15":34,"_21":35,"_23":36},"3481f4cf-7ce1-4152-811b-42eed0ef56fa","D","25 minutos",{"_15":38,"_21":39,"_23":40},"f7c161cd-bd9c-4874-aa7d-bd0d1fbffb64","E","45 minutos","solution_explanation","statement","

Um motor de carro consome um combustível que tem 30.000 \\, \text{kJ/kg}. Se o motor tem uma potência de 120 \\, \text{HP} e um rendimento de 30\\\\%, em quanto tempo o motor estará funcionando à plena carga, se é alimentado com 5 \\, \text{kg} de combustível?

","relatedVideos",[],"similarQuestions",[48,170,187,204,224],{"_12":13,"_14":13,"_15":49,"_17":50,"_41":13,"_42":66,"_67":68},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[51,54,57,60,63],{"_15":52,"_21":22,"_23":53},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_15":55,"_21":27,"_23":56},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_15":58,"_21":31,"_23":59},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_15":61,"_21":35,"_23":62},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_15":64,"_21":39,"_23":65},"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",[69,91,101,111,118,125,133,141,147,152,158,165],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":74},"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",{"_84":85,"_86":87,"_88":89},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_15":92,"_71":93,"_73":94,"_75":76,"_77":95,"_79":96,"_81":96,"_82":97,"_90":100},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_84":98,"_86":87,"_88":99},2,11846,"termodinamica-3",{"_15":102,"_71":103,"_73":104,"_75":76,"_77":105,"_79":106,"_81":106,"_82":107,"_90":110},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_84":108,"_86":87,"_88":109},5,30614,"engenharia-mecatronica-1",{"_15":112,"_71":113,"_73":114,"_75":76,"_77":102,"_79":80,"_81":80,"_82":115,"_90":117},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_84":108,"_86":87,"_88":116},25741,"mecanica-3",{"_15":95,"_71":119,"_73":120,"_75":76,"_77":105,"_79":106,"_81":106,"_82":121,"_90":124},"Engenharia Mecânica","engenharia-mecanica",{"_84":122,"_86":87,"_88":123},11,36318,"engenharia-mecanica-2",{"_15":126,"_71":127,"_73":128,"_75":76,"_77":129,"_79":96,"_81":96,"_82":130,"_90":128},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_84":131,"_86":87,"_88":132},10,8575,{"_15":134,"_71":135,"_73":136,"_75":76,"_77":-5,"_79":137,"_81":137,"_82":138,"_90":136},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_84":139,"_86":87,"_88":140},18,135489,{"_15":142,"_71":93,"_73":94,"_75":76,"_77":70,"_79":143,"_81":143,"_82":144,"_90":146},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_84":87,"_86":87,"_88":145},8597,"termodinamica-5",{"_15":78,"_71":148,"_73":149,"_75":76,"_77":105,"_79":106,"_81":106,"_82":150,"_90":151},"Engenharia de Petróleo","engenharia-de-petroleo",{"_84":108,"_86":87,"_88":89},"engenharia-de-petroleo-1",{"_15":129,"_71":153,"_73":154,"_75":76,"_77":134,"_79":106,"_81":106,"_82":155,"_90":157},"Física","fisica",{"_84":122,"_86":87,"_88":156},13777,"fisica-4",{"_15":105,"_71":159,"_73":160,"_75":76,"_77":-5,"_79":161,"_81":161,"_82":162,"_90":160},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_84":163,"_86":87,"_88":164},29,351586,{"_15":166,"_71":93,"_73":94,"_75":76,"_77":112,"_79":167,"_81":167,"_82":168,"_90":169},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_84":87,"_86":87,"_88":145},"termodinamica-4",{"_12":13,"_14":13,"_15":171,"_17":172,"_41":13,"_42":185,"_67":186},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[173,176,179,182],{"_15":174,"_21":22,"_23":175},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_15":177,"_21":27,"_23":178},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_15":180,"_21":31,"_23":181},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_15":183,"_21":35,"_23":184},"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.

",[69,91,101,111,118,125,133,141,147,152,158,165],{"_12":13,"_14":13,"_15":188,"_17":189,"_41":13,"_42":202,"_67":203},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[190,193,196,199],{"_15":191,"_21":22,"_23":192},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_15":194,"_21":27,"_23":195},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_15":197,"_21":31,"_23":198},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_15":200,"_21":35,"_23":201},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[69,91,101,111,118,125,133,141,147,152,158,165],{"_12":13,"_14":13,"_15":205,"_17":206,"_41":13,"_42":222,"_67":223},"996628fc-4ac3-4821-86bd-839f86a97a6d",[207,210,213,216,219],{"_15":208,"_21":22,"_23":209},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_15":211,"_21":27,"_23":212},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_15":214,"_21":31,"_23":215},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_15":217,"_21":35,"_23":218},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_15":220,"_21":39,"_23":221},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[69,91,101,111,118,125,133,141,147,152,158,165],{"_12":13,"_14":13,"_15":225,"_17":226,"_41":13,"_42":242,"_67":243},"c478a46c-46a8-4942-ae14-2e79def3dda2",[227,230,233,236,239],{"_15":228,"_21":22,"_23":229},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_15":231,"_21":27,"_23":232},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_15":234,"_21":31,"_23":235},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_15":237,"_21":35,"_23":238},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_15":240,"_21":39,"_23":241},"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????",[69,91,101,111,118,125,133,141,147,152,158,165],[69,91,101,111,118,125,133,141,147,152,158,165],"tagsTree",[247,254],{"_15":134,"_71":135,"_73":136,"_75":76,"_77":-5,"_79":137,"_81":137,"_82":138,"_90":136,"_248":249},"children",[250],{"_15":129,"_71":153,"_73":154,"_75":76,"_77":134,"_79":106,"_81":106,"_82":155,"_90":157,"_248":251},[252],{"_15":126,"_71":127,"_73":128,"_75":76,"_77":129,"_79":96,"_81":96,"_82":130,"_90":128,"_248":253},[],{"_15":105,"_71":159,"_73":160,"_75":76,"_77":-5,"_79":161,"_81":161,"_82":162,"_90":160,"_248":255},[256,262,266],{"_15":102,"_71":103,"_73":104,"_75":76,"_77":105,"_79":106,"_81":106,"_82":107,"_90":110,"_248":257},[258],{"_15":112,"_71":113,"_73":114,"_75":76,"_77":102,"_79":80,"_81":80,"_82":115,"_90":117,"_248":259},[260],{"_15":166,"_71":93,"_73":94,"_75":76,"_77":112,"_79":167,"_81":167,"_82":168,"_90":169,"_248":261},[],{"_15":95,"_71":119,"_73":120,"_75":76,"_77":105,"_79":106,"_81":106,"_82":121,"_90":124,"_248":263},[264],{"_15":92,"_71":93,"_73":94,"_75":76,"_77":95,"_79":96,"_81":96,"_82":97,"_90":100,"_248":265},[],{"_15":78,"_71":148,"_73":149,"_75":76,"_77":105,"_79":106,"_81":106,"_82":150,"_90":151,"_248":267},[268],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":74,"_248":269},[270],{"_15":142,"_71":93,"_73":94,"_75":76,"_77":70,"_79":143,"_81":143,"_82":144,"_90":146,"_248":271},[],"actionData","errors"]

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