[{"_1":2,"_278":-5,"_279":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f1d69095-5e14-4dc7-aafd-63988d55734b","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_52":53,"_73":250,"_251":252},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","f1d69095-5e14-4dc7-aafd-63988d55734b","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"44809c3d-17e2-4614-887e-1759345e6f91","label","A","text","–1000J",{"_19":30,"_25":31,"_27":32},"a052368a-85f4-428a-9ad8-a5d7f4def60a","B","+2000J",{"_19":34,"_25":35,"_27":36},"e62449e5-2ed7-43e8-95ff-877b4d0720bb","C","–4000J",{"_19":38,"_25":39,"_27":40},"14e00d82-1a09-4247-9711-ad457c4ab050","D","+4000J",{"_19":42,"_25":43,"_27":44},"a72c42c3-0eb5-46db-a559-59c1dac44118","E","+7000J","solution_explanation","statement","

7 - Sobre um sistema, realiza-se um trabalho de 3000 \text{ J} e, em resposta, ele fornece 1000 \text{ cal} de calor durante o mesmo intervalo de tempo. A variação de energia interna do sistema, durante esse processo, é, aproximadamente: (considere 1,0 \text{ cal} = 4,0 \text{ J})

","status","has_issues","relatedVideos",[],"similarQuestions",[54,176,193,210,230],{"_16":17,"_18":17,"_19":55,"_21":56,"_45":17,"_46":72,"_73":74},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[57,60,63,66,69],{"_19":58,"_25":26,"_27":59},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":61,"_25":31,"_27":62},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":64,"_25":35,"_27":65},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":67,"_25":39,"_27":68},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":70,"_25":43,"_27":71},"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",[75,97,107,117,124,131,139,147,153,158,164,171],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":80},"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",{"_90":91,"_92":93,"_94":95},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_19":98,"_77":99,"_79":100,"_81":82,"_83":101,"_85":102,"_87":102,"_88":103,"_96":106},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_90":104,"_92":93,"_94":105},2,11846,"termodinamica-3",{"_19":108,"_77":109,"_79":110,"_81":82,"_83":111,"_85":112,"_87":112,"_88":113,"_96":116},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_90":114,"_92":93,"_94":115},5,30614,"engenharia-mecatronica-1",{"_19":118,"_77":119,"_79":120,"_81":82,"_83":108,"_85":86,"_87":86,"_88":121,"_96":123},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_90":114,"_92":93,"_94":122},25741,"mecanica-3",{"_19":101,"_77":125,"_79":126,"_81":82,"_83":111,"_85":112,"_87":112,"_88":127,"_96":130},"Engenharia Mecânica","engenharia-mecanica",{"_90":128,"_92":93,"_94":129},11,36318,"engenharia-mecanica-2",{"_19":132,"_77":133,"_79":134,"_81":82,"_83":135,"_85":102,"_87":102,"_88":136,"_96":134},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_90":137,"_92":93,"_94":138},10,8575,{"_19":140,"_77":141,"_79":142,"_81":82,"_83":-5,"_85":143,"_87":143,"_88":144,"_96":142},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_90":145,"_92":93,"_94":146},18,135489,{"_19":148,"_77":99,"_79":100,"_81":82,"_83":76,"_85":149,"_87":149,"_88":150,"_96":152},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_90":93,"_92":93,"_94":151},8597,"termodinamica-5",{"_19":84,"_77":154,"_79":155,"_81":82,"_83":111,"_85":112,"_87":112,"_88":156,"_96":157},"Engenharia de Petróleo","engenharia-de-petroleo",{"_90":114,"_92":93,"_94":95},"engenharia-de-petroleo-1",{"_19":135,"_77":159,"_79":160,"_81":82,"_83":140,"_85":112,"_87":112,"_88":161,"_96":163},"Física","fisica",{"_90":128,"_92":93,"_94":162},13777,"fisica-4",{"_19":111,"_77":165,"_79":166,"_81":82,"_83":-5,"_85":167,"_87":167,"_88":168,"_96":166},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_90":169,"_92":93,"_94":170},29,351586,{"_19":172,"_77":99,"_79":100,"_81":82,"_83":118,"_85":173,"_87":173,"_88":174,"_96":175},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_90":93,"_92":93,"_94":151},"termodinamica-4",{"_16":17,"_18":17,"_19":177,"_21":178,"_45":17,"_46":191,"_73":192},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[179,182,185,188],{"_19":180,"_25":26,"_27":181},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":183,"_25":31,"_27":184},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":186,"_25":35,"_27":187},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":189,"_25":39,"_27":190},"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.

",[75,97,107,117,124,131,139,147,153,158,164,171],{"_16":17,"_18":17,"_19":194,"_21":195,"_45":17,"_46":208,"_73":209},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[196,199,202,205],{"_19":197,"_25":26,"_27":198},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":200,"_25":31,"_27":201},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":203,"_25":35,"_27":204},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":206,"_25":39,"_27":207},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[75,97,107,117,124,131,139,147,153,158,164,171],{"_16":17,"_18":17,"_19":211,"_21":212,"_45":17,"_46":228,"_73":229},"996628fc-4ac3-4821-86bd-839f86a97a6d",[213,216,219,222,225],{"_19":214,"_25":26,"_27":215},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":217,"_25":31,"_27":218},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":220,"_25":35,"_27":221},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":223,"_25":39,"_27":224},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":226,"_25":43,"_27":227},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[75,97,107,117,124,131,139,147,153,158,164,171],{"_16":17,"_18":17,"_19":231,"_21":232,"_45":17,"_46":248,"_73":249},"c478a46c-46a8-4942-ae14-2e79def3dda2",[233,236,239,242,245],{"_19":234,"_25":26,"_27":235},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":237,"_25":31,"_27":238},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":240,"_25":35,"_27":241},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":243,"_25":39,"_27":244},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":246,"_25":43,"_27":247},"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????",[75,97,107,117,124,131,139,147,153,158,164,171],[75,97,107,117,124,131,139,147,153,158,164,171],"tagsTree",[253,260],{"_19":140,"_77":141,"_79":142,"_81":82,"_83":-5,"_85":143,"_87":143,"_88":144,"_96":142,"_254":255},"children",[256],{"_19":135,"_77":159,"_79":160,"_81":82,"_83":140,"_85":112,"_87":112,"_88":161,"_96":163,"_254":257},[258],{"_19":132,"_77":133,"_79":134,"_81":82,"_83":135,"_85":102,"_87":102,"_88":136,"_96":134,"_254":259},[],{"_19":111,"_77":165,"_79":166,"_81":82,"_83":-5,"_85":167,"_87":167,"_88":168,"_96":166,"_254":261},[262,268,272],{"_19":108,"_77":109,"_79":110,"_81":82,"_83":111,"_85":112,"_87":112,"_88":113,"_96":116,"_254":263},[264],{"_19":118,"_77":119,"_79":120,"_81":82,"_83":108,"_85":86,"_87":86,"_88":121,"_96":123,"_254":265},[266],{"_19":172,"_77":99,"_79":100,"_81":82,"_83":118,"_85":173,"_87":173,"_88":174,"_96":175,"_254":267},[],{"_19":101,"_77":125,"_79":126,"_81":82,"_83":111,"_85":112,"_87":112,"_88":127,"_96":130,"_254":269},[270],{"_19":98,"_77":99,"_79":100,"_81":82,"_83":101,"_85":102,"_87":102,"_88":103,"_96":106,"_254":271},[],{"_19":84,"_77":154,"_79":155,"_81":82,"_83":111,"_85":112,"_87":112,"_88":156,"_96":157,"_254":273},[274],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":80,"_254":275},[276],{"_19":148,"_77":99,"_79":100,"_81":82,"_83":76,"_85":149,"_87":149,"_88":150,"_96":152,"_254":277},[],"actionData","errors"]

Comentários