[{"_1":2,"_275":-5,"_276":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f102c6b0-142b-4f09-9626-1ea5dc061207","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":247,"_248":249},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":19,"_20":21,"_22":23,"_41":19,"_42":43,"_44":45},"correctOptionId","ea5cec4c-0a2b-4ad6-b2c8-a416fa486f0e","difficulty","","id","f102c6b0-142b-4f09-9626-1ea5dc061207","options",[24,30,34,37],{"_20":25,"_26":27,"_28":29},"6b4f3c8d-1a12-4a3e-b0de-661d7340c493","label","A","text","

1200 J

",{"_20":31,"_26":32,"_28":33},"9c54924a-e488-4772-b646-7f0bf39d8370","B","

1400 J

",{"_20":17,"_26":35,"_28":36},"C","

1600 J

",{"_20":38,"_26":39,"_28":40},"25794047-3ba7-4120-8303-4a2092f084bc","D","

1800 J

","solution_explanation","statement","

Um sistema termodinâmico opera em um ciclo de Carnot entre duas fontes térmicas a 600 \text{ K} e 400 \text{ K}. Se o sistema realiza um trabalho de 800 \text{ J}, qual é a quantidade de calor absorvida da fonte quente?

","status","pending_classification","relatedVideos",[],"similarQuestions",[50,173,190,207,227],{"_16":19,"_18":19,"_20":51,"_22":52,"_41":19,"_42":69,"_70":71},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_20":54,"_26":27,"_28":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":57,"_26":32,"_28":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":60,"_26":35,"_28":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":63,"_26":39,"_28":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":66,"_26":67,"_28":68},"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",[72,94,104,114,121,128,136,144,150,155,161,168],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":77},"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",{"_87":88,"_89":90,"_91":92},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_20":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_87":101,"_89":90,"_91":102},2,11846,"termodinamica-3",{"_20":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":113},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_87":111,"_89":90,"_91":112},5,30614,"engenharia-mecatronica-1",{"_20":115,"_74":116,"_76":117,"_78":79,"_80":105,"_82":83,"_84":83,"_85":118,"_93":120},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_87":111,"_89":90,"_91":119},25741,"mecanica-3",{"_20":98,"_74":122,"_76":123,"_78":79,"_80":108,"_82":109,"_84":109,"_85":124,"_93":127},"Engenharia Mecânica","engenharia-mecanica",{"_87":125,"_89":90,"_91":126},11,36318,"engenharia-mecanica-2",{"_20":129,"_74":130,"_76":131,"_78":79,"_80":132,"_82":99,"_84":99,"_85":133,"_93":131},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_87":134,"_89":90,"_91":135},10,8575,{"_20":137,"_74":138,"_76":139,"_78":79,"_80":-5,"_82":140,"_84":140,"_85":141,"_93":139},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_87":142,"_89":90,"_91":143},18,135489,{"_20":145,"_74":96,"_76":97,"_78":79,"_80":73,"_82":146,"_84":146,"_85":147,"_93":149},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_87":90,"_89":90,"_91":148},8597,"termodinamica-5",{"_20":81,"_74":151,"_76":152,"_78":79,"_80":108,"_82":109,"_84":109,"_85":153,"_93":154},"Engenharia de Petróleo","engenharia-de-petroleo",{"_87":111,"_89":90,"_91":92},"engenharia-de-petroleo-1",{"_20":132,"_74":156,"_76":157,"_78":79,"_80":137,"_82":109,"_84":109,"_85":158,"_93":160},"Física","fisica",{"_87":125,"_89":90,"_91":159},13777,"fisica-4",{"_20":108,"_74":162,"_76":163,"_78":79,"_80":-5,"_82":164,"_84":164,"_85":165,"_93":163},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":166,"_89":90,"_91":167},29,351586,{"_20":169,"_74":96,"_76":97,"_78":79,"_80":115,"_82":170,"_84":170,"_85":171,"_93":172},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_87":90,"_89":90,"_91":148},"termodinamica-4",{"_16":19,"_18":19,"_20":174,"_22":175,"_41":19,"_42":188,"_70":189},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[176,179,182,185],{"_20":177,"_26":27,"_28":178},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":180,"_26":32,"_28":181},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":183,"_26":35,"_28":184},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":186,"_26":39,"_28":187},"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.

",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":19,"_18":19,"_20":191,"_22":192,"_41":19,"_42":205,"_70":206},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,202],{"_20":194,"_26":27,"_28":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":197,"_26":32,"_28":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":200,"_26":35,"_28":201},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":203,"_26":39,"_28":204},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":19,"_18":19,"_20":208,"_22":209,"_41":19,"_42":225,"_70":226},"996628fc-4ac3-4821-86bd-839f86a97a6d",[210,213,216,219,222],{"_20":211,"_26":27,"_28":212},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":214,"_26":32,"_28":215},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":217,"_26":35,"_28":218},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":220,"_26":39,"_28":221},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":223,"_26":67,"_28":224},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":19,"_18":19,"_20":228,"_22":229,"_41":19,"_42":245,"_70":246},"c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,239,242],{"_20":231,"_26":27,"_28":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":234,"_26":32,"_28":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":237,"_26":35,"_28":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":240,"_26":39,"_28":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":243,"_26":67,"_28":244},"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????",[72,94,104,114,121,128,136,144,150,155,161,168],[72,94,104,114,121,128,136,144,150,155,161,168],"tagsTree",[250,257],{"_20":137,"_74":138,"_76":139,"_78":79,"_80":-5,"_82":140,"_84":140,"_85":141,"_93":139,"_251":252},"children",[253],{"_20":132,"_74":156,"_76":157,"_78":79,"_80":137,"_82":109,"_84":109,"_85":158,"_93":160,"_251":254},[255],{"_20":129,"_74":130,"_76":131,"_78":79,"_80":132,"_82":99,"_84":99,"_85":133,"_93":131,"_251":256},[],{"_20":108,"_74":162,"_76":163,"_78":79,"_80":-5,"_82":164,"_84":164,"_85":165,"_93":163,"_251":258},[259,265,269],{"_20":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":113,"_251":260},[261],{"_20":115,"_74":116,"_76":117,"_78":79,"_80":105,"_82":83,"_84":83,"_85":118,"_93":120,"_251":262},[263],{"_20":169,"_74":96,"_76":97,"_78":79,"_80":115,"_82":170,"_84":170,"_85":171,"_93":172,"_251":264},[],{"_20":98,"_74":122,"_76":123,"_78":79,"_80":108,"_82":109,"_84":109,"_85":124,"_93":127,"_251":266},[267],{"_20":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103,"_251":268},[],{"_20":81,"_74":151,"_76":152,"_78":79,"_80":108,"_82":109,"_84":109,"_85":153,"_93":154,"_251":270},[271],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":77,"_251":272},[273],{"_20":145,"_74":96,"_76":97,"_78":79,"_80":73,"_82":146,"_84":146,"_85":147,"_93":149,"_251":274},[],"actionData","errors"]

Comentários