[{"_1":2,"_271":-5,"_272":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e2297ad7-9c65-4836-b0e4-f14ec43c6978","user","pages/questions/show/index",{"_10":11,"_12":13,"_42":43,"_44":45,"_66":243,"_244":245},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_39":15,"_40":41},"correctOptionId","","difficulty","id","e2297ad7-9c65-4836-b0e4-f14ec43c6978","options",[21,27,31,35],{"_17":22,"_23":24,"_25":26},"9684b3ce-3da0-4535-a4c6-1994de0c2ad3","label","A","text","

dS = \frac{1}{T} dU

",{"_17":28,"_23":29,"_25":30},"57580129-27da-479b-a9e5-d799035f5b8f","B","

dS = TdU

",{"_17":32,"_23":33,"_25":34},"001b842a-6c81-48e8-a210-32da4ae3c0bc","C","

dS = T dU

",{"_17":36,"_23":37,"_25":38},"1655ff99-033e-4d19-8920-030ce9478c7a","D","

dS = \frac{U}{T}

","solution_explanation","statement","

Em um sistema termodinâmico, a relação entre entropia S, energia interna U e temperatura T pode ser expressa através da seguinte derivada, que é usada para avaliar a mudança de entropia em relação à energia interna. Qual é essa relação?

","relatedVideos",[],"similarQuestions",[46,169,186,203,223],{"_14":15,"_16":15,"_17":47,"_19":48,"_39":15,"_40":65,"_66":67},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[49,52,55,58,61],{"_17":50,"_23":24,"_25":51},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":53,"_23":29,"_25":54},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":56,"_23":33,"_25":57},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":59,"_23":37,"_25":60},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":62,"_23":63,"_25":64},"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",[68,90,100,110,117,124,132,140,146,151,157,164],{"_17":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":73},"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",{"_83":84,"_85":86,"_87":88},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":91,"_70":92,"_72":93,"_74":75,"_76":94,"_78":95,"_80":95,"_81":96,"_89":99},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_83":97,"_85":86,"_87":98},2,11846,"termodinamica-3",{"_17":101,"_70":102,"_72":103,"_74":75,"_76":104,"_78":105,"_80":105,"_81":106,"_89":109},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_83":107,"_85":86,"_87":108},5,30614,"engenharia-mecatronica-1",{"_17":111,"_70":112,"_72":113,"_74":75,"_76":101,"_78":79,"_80":79,"_81":114,"_89":116},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_83":107,"_85":86,"_87":115},25741,"mecanica-3",{"_17":94,"_70":118,"_72":119,"_74":75,"_76":104,"_78":105,"_80":105,"_81":120,"_89":123},"Engenharia Mecânica","engenharia-mecanica",{"_83":121,"_85":86,"_87":122},11,36318,"engenharia-mecanica-2",{"_17":125,"_70":126,"_72":127,"_74":75,"_76":128,"_78":95,"_80":95,"_81":129,"_89":127},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_83":130,"_85":86,"_87":131},10,8575,{"_17":133,"_70":134,"_72":135,"_74":75,"_76":-5,"_78":136,"_80":136,"_81":137,"_89":135},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_83":138,"_85":86,"_87":139},18,135489,{"_17":141,"_70":92,"_72":93,"_74":75,"_76":69,"_78":142,"_80":142,"_81":143,"_89":145},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_83":86,"_85":86,"_87":144},8597,"termodinamica-5",{"_17":77,"_70":147,"_72":148,"_74":75,"_76":104,"_78":105,"_80":105,"_81":149,"_89":150},"Engenharia de Petróleo","engenharia-de-petroleo",{"_83":107,"_85":86,"_87":88},"engenharia-de-petroleo-1",{"_17":128,"_70":152,"_72":153,"_74":75,"_76":133,"_78":105,"_80":105,"_81":154,"_89":156},"Física","fisica",{"_83":121,"_85":86,"_87":155},13777,"fisica-4",{"_17":104,"_70":158,"_72":159,"_74":75,"_76":-5,"_78":160,"_80":160,"_81":161,"_89":159},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_83":162,"_85":86,"_87":163},29,351586,{"_17":165,"_70":92,"_72":93,"_74":75,"_76":111,"_78":166,"_80":166,"_81":167,"_89":168},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_83":86,"_85":86,"_87":144},"termodinamica-4",{"_14":15,"_16":15,"_17":170,"_19":171,"_39":15,"_40":184,"_66":185},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[172,175,178,181],{"_17":173,"_23":24,"_25":174},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":176,"_23":29,"_25":177},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":179,"_23":33,"_25":180},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":182,"_23":37,"_25":183},"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.

",[68,90,100,110,117,124,132,140,146,151,157,164],{"_14":15,"_16":15,"_17":187,"_19":188,"_39":15,"_40":201,"_66":202},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[189,192,195,198],{"_17":190,"_23":24,"_25":191},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":193,"_23":29,"_25":194},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":196,"_23":33,"_25":197},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":199,"_23":37,"_25":200},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[68,90,100,110,117,124,132,140,146,151,157,164],{"_14":15,"_16":15,"_17":204,"_19":205,"_39":15,"_40":221,"_66":222},"996628fc-4ac3-4821-86bd-839f86a97a6d",[206,209,212,215,218],{"_17":207,"_23":24,"_25":208},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":210,"_23":29,"_25":211},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":213,"_23":33,"_25":214},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":216,"_23":37,"_25":217},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":219,"_23":63,"_25":220},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[68,90,100,110,117,124,132,140,146,151,157,164],{"_14":15,"_16":15,"_17":224,"_19":225,"_39":15,"_40":241,"_66":242},"c478a46c-46a8-4942-ae14-2e79def3dda2",[226,229,232,235,238],{"_17":227,"_23":24,"_25":228},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":230,"_23":29,"_25":231},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":233,"_23":33,"_25":234},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":236,"_23":37,"_25":237},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":239,"_23":63,"_25":240},"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????",[68,90,100,110,117,124,132,140,146,151,157,164],[68,90,100,110,117,124,132,140,146,151,157,164],"tagsTree",[246,253],{"_17":133,"_70":134,"_72":135,"_74":75,"_76":-5,"_78":136,"_80":136,"_81":137,"_89":135,"_247":248},"children",[249],{"_17":128,"_70":152,"_72":153,"_74":75,"_76":133,"_78":105,"_80":105,"_81":154,"_89":156,"_247":250},[251],{"_17":125,"_70":126,"_72":127,"_74":75,"_76":128,"_78":95,"_80":95,"_81":129,"_89":127,"_247":252},[],{"_17":104,"_70":158,"_72":159,"_74":75,"_76":-5,"_78":160,"_80":160,"_81":161,"_89":159,"_247":254},[255,261,265],{"_17":101,"_70":102,"_72":103,"_74":75,"_76":104,"_78":105,"_80":105,"_81":106,"_89":109,"_247":256},[257],{"_17":111,"_70":112,"_72":113,"_74":75,"_76":101,"_78":79,"_80":79,"_81":114,"_89":116,"_247":258},[259],{"_17":165,"_70":92,"_72":93,"_74":75,"_76":111,"_78":166,"_80":166,"_81":167,"_89":168,"_247":260},[],{"_17":94,"_70":118,"_72":119,"_74":75,"_76":104,"_78":105,"_80":105,"_81":120,"_89":123,"_247":262},[263],{"_17":91,"_70":92,"_72":93,"_74":75,"_76":94,"_78":95,"_80":95,"_81":96,"_89":99,"_247":264},[],{"_17":77,"_70":147,"_72":148,"_74":75,"_76":104,"_78":105,"_80":105,"_81":149,"_89":150,"_247":266},[267],{"_17":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":73,"_247":268},[269],{"_17":141,"_70":92,"_72":93,"_74":75,"_76":69,"_78":142,"_80":142,"_81":143,"_89":145,"_247":270},[],"actionData","errors"]

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