[{"_1":2,"_273":-5,"_274":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f39fd63f-7ac8-4e7b-8075-55f686eab67a","user","pages/questions/show/index",{"_10":11,"_12":13,"_44":45,"_46":47,"_68":245,"_246":247},"comments",[],"question",{"_14":15,"_16":17,"_18":19,"_20":21,"_39":17,"_40":41,"_42":43},"correctOptionId","b5a8257f-afb1-4ad5-a9e0-9cf60a5ea400","difficulty","","id","f39fd63f-7ac8-4e7b-8075-55f686eab67a","options",[22,28,31,35],{"_18":23,"_24":25,"_26":27},"b23650f0-5120-445a-bff4-299df7c15f23","label","A","text","

Energia potencial

",{"_18":15,"_24":29,"_26":30},"B","

Energia cinética

",{"_18":32,"_24":33,"_26":34},"814f84ff-feab-49cc-b77b-e5e7d1517658","C","

Energia térmica

",{"_18":36,"_24":37,"_26":38},"920b6319-3967-437f-97b2-5c24c6fd5a9b","D","

Energia elétrica

","solution_explanation","statement","

A energia é um conceito central na química. Qual é a forma de energia associada à movimentação e interação das partículas em um sistema?

","status","pending_classification","relatedVideos",[],"similarQuestions",[48,171,188,205,225],{"_14":17,"_16":17,"_18":49,"_20":50,"_39":17,"_40":67,"_68":69},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[51,54,57,60,63],{"_18":52,"_24":25,"_26":53},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_18":55,"_24":29,"_26":56},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_18":58,"_24":33,"_26":59},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_18":61,"_24":37,"_26":62},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_18":64,"_24":65,"_26":66},"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",[70,92,102,112,119,126,134,142,148,153,159,166],{"_18":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":81,"_83":84,"_91":75},"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",{"_85":86,"_87":88,"_89":90},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_18":93,"_72":94,"_74":95,"_76":77,"_78":96,"_80":97,"_82":97,"_83":98,"_91":101},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_85":99,"_87":88,"_89":100},2,11846,"termodinamica-3",{"_18":103,"_72":104,"_74":105,"_76":77,"_78":106,"_80":107,"_82":107,"_83":108,"_91":111},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_85":109,"_87":88,"_89":110},5,30614,"engenharia-mecatronica-1",{"_18":113,"_72":114,"_74":115,"_76":77,"_78":103,"_80":81,"_82":81,"_83":116,"_91":118},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_85":109,"_87":88,"_89":117},25741,"mecanica-3",{"_18":96,"_72":120,"_74":121,"_76":77,"_78":106,"_80":107,"_82":107,"_83":122,"_91":125},"Engenharia Mecânica","engenharia-mecanica",{"_85":123,"_87":88,"_89":124},11,36318,"engenharia-mecanica-2",{"_18":127,"_72":128,"_74":129,"_76":77,"_78":130,"_80":97,"_82":97,"_83":131,"_91":129},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_85":132,"_87":88,"_89":133},10,8575,{"_18":135,"_72":136,"_74":137,"_76":77,"_78":-5,"_80":138,"_82":138,"_83":139,"_91":137},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_85":140,"_87":88,"_89":141},18,135489,{"_18":143,"_72":94,"_74":95,"_76":77,"_78":71,"_80":144,"_82":144,"_83":145,"_91":147},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_85":88,"_87":88,"_89":146},8597,"termodinamica-5",{"_18":79,"_72":149,"_74":150,"_76":77,"_78":106,"_80":107,"_82":107,"_83":151,"_91":152},"Engenharia de Petróleo","engenharia-de-petroleo",{"_85":109,"_87":88,"_89":90},"engenharia-de-petroleo-1",{"_18":130,"_72":154,"_74":155,"_76":77,"_78":135,"_80":107,"_82":107,"_83":156,"_91":158},"Física","fisica",{"_85":123,"_87":88,"_89":157},13777,"fisica-4",{"_18":106,"_72":160,"_74":161,"_76":77,"_78":-5,"_80":162,"_82":162,"_83":163,"_91":161},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_85":164,"_87":88,"_89":165},29,351586,{"_18":167,"_72":94,"_74":95,"_76":77,"_78":113,"_80":168,"_82":168,"_83":169,"_91":170},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_85":88,"_87":88,"_89":146},"termodinamica-4",{"_14":17,"_16":17,"_18":172,"_20":173,"_39":17,"_40":186,"_68":187},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[174,177,180,183],{"_18":175,"_24":25,"_26":176},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_18":178,"_24":29,"_26":179},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_18":181,"_24":33,"_26":182},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_18":184,"_24":37,"_26":185},"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.

",[70,92,102,112,119,126,134,142,148,153,159,166],{"_14":17,"_16":17,"_18":189,"_20":190,"_39":17,"_40":203,"_68":204},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[191,194,197,200],{"_18":192,"_24":25,"_26":193},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_18":195,"_24":29,"_26":196},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_18":198,"_24":33,"_26":199},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_18":201,"_24":37,"_26":202},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[70,92,102,112,119,126,134,142,148,153,159,166],{"_14":17,"_16":17,"_18":206,"_20":207,"_39":17,"_40":223,"_68":224},"996628fc-4ac3-4821-86bd-839f86a97a6d",[208,211,214,217,220],{"_18":209,"_24":25,"_26":210},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_18":212,"_24":29,"_26":213},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_18":215,"_24":33,"_26":216},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_18":218,"_24":37,"_26":219},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_18":221,"_24":65,"_26":222},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[70,92,102,112,119,126,134,142,148,153,159,166],{"_14":17,"_16":17,"_18":226,"_20":227,"_39":17,"_40":243,"_68":244},"c478a46c-46a8-4942-ae14-2e79def3dda2",[228,231,234,237,240],{"_18":229,"_24":25,"_26":230},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_18":232,"_24":29,"_26":233},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_18":235,"_24":33,"_26":236},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_18":238,"_24":37,"_26":239},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_18":241,"_24":65,"_26":242},"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????",[70,92,102,112,119,126,134,142,148,153,159,166],[70,92,102,112,119,126,134,142,148,153,159,166],"tagsTree",[248,255],{"_18":135,"_72":136,"_74":137,"_76":77,"_78":-5,"_80":138,"_82":138,"_83":139,"_91":137,"_249":250},"children",[251],{"_18":130,"_72":154,"_74":155,"_76":77,"_78":135,"_80":107,"_82":107,"_83":156,"_91":158,"_249":252},[253],{"_18":127,"_72":128,"_74":129,"_76":77,"_78":130,"_80":97,"_82":97,"_83":131,"_91":129,"_249":254},[],{"_18":106,"_72":160,"_74":161,"_76":77,"_78":-5,"_80":162,"_82":162,"_83":163,"_91":161,"_249":256},[257,263,267],{"_18":103,"_72":104,"_74":105,"_76":77,"_78":106,"_80":107,"_82":107,"_83":108,"_91":111,"_249":258},[259],{"_18":113,"_72":114,"_74":115,"_76":77,"_78":103,"_80":81,"_82":81,"_83":116,"_91":118,"_249":260},[261],{"_18":167,"_72":94,"_74":95,"_76":77,"_78":113,"_80":168,"_82":168,"_83":169,"_91":170,"_249":262},[],{"_18":96,"_72":120,"_74":121,"_76":77,"_78":106,"_80":107,"_82":107,"_83":122,"_91":125,"_249":264},[265],{"_18":93,"_72":94,"_74":95,"_76":77,"_78":96,"_80":97,"_82":97,"_83":98,"_91":101,"_249":266},[],{"_18":79,"_72":149,"_74":150,"_76":77,"_78":106,"_80":107,"_82":107,"_83":151,"_91":152,"_249":268},[269],{"_18":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":81,"_83":84,"_91":75,"_249":270},[271],{"_18":143,"_72":94,"_74":95,"_76":77,"_78":71,"_80":144,"_82":144,"_83":145,"_91":147,"_249":272},[],"actionData","errors"]

Comentários