[{"_1":2,"_269":-5,"_270":-5},"loaderData",{"_3":4,"_6":7},"root",{"_5":-5},"user","pages/questions/show/index",{"_8":9,"_10":11,"_40":41,"_42":43,"_64":241,"_242":243},"comments",[],"question",{"_12":13,"_14":13,"_15":16,"_17":18,"_37":13,"_38":39},"correctOptionId","","difficulty","id","f61de1e8-3bb4-4a77-813f-068789f86de7","options",[19,25,29,33],{"_15":20,"_21":22,"_23":24},"d2016247-cf19-45cd-8490-757eb7900665","label","A","text","

1500 J

",{"_15":26,"_21":27,"_23":28},"1438a70b-b50e-4eb6-8eab-505abc9ceddf","B","

2000 J

",{"_15":30,"_21":31,"_23":32},"9b6f7888-fcac-476a-8ab5-db1725ec14bc","C","

2500 J

",{"_15":34,"_21":35,"_23":36},"500a7f57-db85-47ac-b762-62c308de13f0","D","

3000 J

","solution_explanation","statement","

Um sistema termodinâmico opera em um ciclo de Carnot entre duas fontes térmicas a 500 \text{ K} e 300 \text{ K}. Se o sistema realiza um trabalho de 1000 \text{ J}, qual é a quantidade de calor absorvida da fonte quente?

","relatedVideos",[],"similarQuestions",[44,167,184,201,221],{"_12":13,"_14":13,"_15":45,"_17":46,"_37":13,"_38":63,"_64":65},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[47,50,53,56,59],{"_15":48,"_21":22,"_23":49},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_15":51,"_21":27,"_23":52},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_15":54,"_21":31,"_23":55},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_15":57,"_21":35,"_23":58},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_15":60,"_21":61,"_23":62},"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",[66,88,98,108,115,122,130,138,144,149,155,162],{"_15":67,"_68":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":77,"_79":80,"_87":71},"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",{"_81":82,"_83":84,"_85":86},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_15":89,"_68":90,"_70":91,"_72":73,"_74":92,"_76":93,"_78":93,"_79":94,"_87":97},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_81":95,"_83":84,"_85":96},2,11846,"termodinamica-3",{"_15":99,"_68":100,"_70":101,"_72":73,"_74":102,"_76":103,"_78":103,"_79":104,"_87":107},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_81":105,"_83":84,"_85":106},5,30614,"engenharia-mecatronica-1",{"_15":109,"_68":110,"_70":111,"_72":73,"_74":99,"_76":77,"_78":77,"_79":112,"_87":114},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_81":105,"_83":84,"_85":113},25741,"mecanica-3",{"_15":92,"_68":116,"_70":117,"_72":73,"_74":102,"_76":103,"_78":103,"_79":118,"_87":121},"Engenharia Mecânica","engenharia-mecanica",{"_81":119,"_83":84,"_85":120},11,36318,"engenharia-mecanica-2",{"_15":123,"_68":124,"_70":125,"_72":73,"_74":126,"_76":93,"_78":93,"_79":127,"_87":125},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_81":128,"_83":84,"_85":129},10,8575,{"_15":131,"_68":132,"_70":133,"_72":73,"_74":-5,"_76":134,"_78":134,"_79":135,"_87":133},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_81":136,"_83":84,"_85":137},18,135489,{"_15":139,"_68":90,"_70":91,"_72":73,"_74":67,"_76":140,"_78":140,"_79":141,"_87":143},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_81":84,"_83":84,"_85":142},8597,"termodinamica-5",{"_15":75,"_68":145,"_70":146,"_72":73,"_74":102,"_76":103,"_78":103,"_79":147,"_87":148},"Engenharia de Petróleo","engenharia-de-petroleo",{"_81":105,"_83":84,"_85":86},"engenharia-de-petroleo-1",{"_15":126,"_68":150,"_70":151,"_72":73,"_74":131,"_76":103,"_78":103,"_79":152,"_87":154},"Física","fisica",{"_81":119,"_83":84,"_85":153},13777,"fisica-4",{"_15":102,"_68":156,"_70":157,"_72":73,"_74":-5,"_76":158,"_78":158,"_79":159,"_87":157},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_81":160,"_83":84,"_85":161},29,351586,{"_15":163,"_68":90,"_70":91,"_72":73,"_74":109,"_76":164,"_78":164,"_79":165,"_87":166},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_81":84,"_83":84,"_85":142},"termodinamica-4",{"_12":13,"_14":13,"_15":168,"_17":169,"_37":13,"_38":182,"_64":183},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[170,173,176,179],{"_15":171,"_21":22,"_23":172},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_15":174,"_21":27,"_23":175},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_15":177,"_21":31,"_23":178},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_15":180,"_21":35,"_23":181},"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.

",[66,88,98,108,115,122,130,138,144,149,155,162],{"_12":13,"_14":13,"_15":185,"_17":186,"_37":13,"_38":199,"_64":200},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[187,190,193,196],{"_15":188,"_21":22,"_23":189},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_15":191,"_21":27,"_23":192},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_15":194,"_21":31,"_23":195},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_15":197,"_21":35,"_23":198},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[66,88,98,108,115,122,130,138,144,149,155,162],{"_12":13,"_14":13,"_15":202,"_17":203,"_37":13,"_38":219,"_64":220},"996628fc-4ac3-4821-86bd-839f86a97a6d",[204,207,210,213,216],{"_15":205,"_21":22,"_23":206},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_15":208,"_21":27,"_23":209},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_15":211,"_21":31,"_23":212},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_15":214,"_21":35,"_23":215},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_15":217,"_21":61,"_23":218},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[66,88,98,108,115,122,130,138,144,149,155,162],{"_12":13,"_14":13,"_15":222,"_17":223,"_37":13,"_38":239,"_64":240},"c478a46c-46a8-4942-ae14-2e79def3dda2",[224,227,230,233,236],{"_15":225,"_21":22,"_23":226},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_15":228,"_21":27,"_23":229},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_15":231,"_21":31,"_23":232},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_15":234,"_21":35,"_23":235},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_15":237,"_21":61,"_23":238},"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????",[66,88,98,108,115,122,130,138,144,149,155,162],[66,88,98,108,115,122,130,138,144,149,155,162],"tagsTree",[244,251],{"_15":131,"_68":132,"_70":133,"_72":73,"_74":-5,"_76":134,"_78":134,"_79":135,"_87":133,"_245":246},"children",[247],{"_15":126,"_68":150,"_70":151,"_72":73,"_74":131,"_76":103,"_78":103,"_79":152,"_87":154,"_245":248},[249],{"_15":123,"_68":124,"_70":125,"_72":73,"_74":126,"_76":93,"_78":93,"_79":127,"_87":125,"_245":250},[],{"_15":102,"_68":156,"_70":157,"_72":73,"_74":-5,"_76":158,"_78":158,"_79":159,"_87":157,"_245":252},[253,259,263],{"_15":99,"_68":100,"_70":101,"_72":73,"_74":102,"_76":103,"_78":103,"_79":104,"_87":107,"_245":254},[255],{"_15":109,"_68":110,"_70":111,"_72":73,"_74":99,"_76":77,"_78":77,"_79":112,"_87":114,"_245":256},[257],{"_15":163,"_68":90,"_70":91,"_72":73,"_74":109,"_76":164,"_78":164,"_79":165,"_87":166,"_245":258},[],{"_15":92,"_68":116,"_70":117,"_72":73,"_74":102,"_76":103,"_78":103,"_79":118,"_87":121,"_245":260},[261],{"_15":89,"_68":90,"_70":91,"_72":73,"_74":92,"_76":93,"_78":93,"_79":94,"_87":97,"_245":262},[],{"_15":75,"_68":145,"_70":146,"_72":73,"_74":102,"_76":103,"_78":103,"_79":147,"_87":148,"_245":264},[265],{"_15":67,"_68":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":77,"_79":80,"_87":71,"_245":266},[267],{"_15":139,"_68":90,"_70":91,"_72":73,"_74":67,"_76":140,"_78":140,"_79":141,"_87":143,"_245":268},[],"actionData","errors"]

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