[{"_1":2,"_274":-5,"_275":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e5f6433d-94dd-4fab-8703-d66f9529402d","user","pages/questions/show/index",{"_10":11,"_12":13,"_38":39,"_40":41,"_63":244,"_245":246},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_35":15,"_36":37},"correctOptionId","","difficulty","id","e5f6433d-94dd-4fab-8703-d66f9529402d","options",[21,27,31],{"_17":22,"_23":24,"_25":26},"781eda9c-0c16-48aa-89a3-b9fd0e439762","label","A","text","1600 MPa.",{"_17":28,"_23":29,"_25":30},"2c5bbda6-d217-4c92-ae61-77aa9e8e76fd","B","200 MPa.",{"_17":32,"_23":33,"_25":34},"c0116a8d-9c98-4afd-bdcc-453a74cdcbdc","C","800 MPa.","solution_explanation","statement","

Um vaso de pressão cilíndrico tem diâmetro interno de 4 \text{ m} e comprimento de 6 \text{ m}. Sabe-se que esse reservatório foi construído com uma espessura de 5 \text{ mm} e que deve suportar uma pressão de 2,0 \text{ MPa}. Qual a tensão tangencial atuante nas paredes desse vaso de pressão?

","relatedVideos",[],"similarQuestions",[42,170,187,204,224],{"_14":15,"_16":15,"_17":43,"_19":44,"_35":15,"_36":62,"_63":64},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[45,48,51,54,58],{"_17":46,"_23":24,"_25":47},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":49,"_23":29,"_25":50},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":52,"_23":33,"_25":53},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":55,"_23":56,"_25":57},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_17":59,"_23":60,"_25":61},"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",[65,87,97,106,112,120,126,134,139,147,152,157,163],{"_17":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":76,"_78":79,"_86":70},"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",{"_80":81,"_82":83,"_84":85},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":88,"_67":89,"_69":90,"_71":72,"_73":91,"_75":92,"_77":92,"_78":93,"_86":96},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_80":94,"_82":83,"_84":95},5,30614,"engenharia-mecatronica-1",{"_17":98,"_67":99,"_69":100,"_71":72,"_73":101,"_75":102,"_77":102,"_78":103,"_86":105},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_80":83,"_82":83,"_84":104},3376,"resistencia-dos-materiais-6",{"_17":101,"_67":107,"_69":108,"_71":72,"_73":88,"_75":76,"_77":76,"_78":109,"_86":111},"Mecânica","mecanica",{"_80":94,"_82":83,"_84":110},25741,"mecanica-3",{"_17":113,"_67":114,"_69":115,"_71":72,"_73":-5,"_75":116,"_77":116,"_78":117,"_86":115},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_80":118,"_82":83,"_84":119},18,135489,{"_17":121,"_67":99,"_69":100,"_71":72,"_73":122,"_75":123,"_77":123,"_78":124,"_86":125},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_80":83,"_82":83,"_84":104},"resistencia-dos-materiais-4",{"_17":127,"_67":128,"_69":129,"_71":72,"_73":91,"_75":92,"_77":92,"_78":130,"_86":133},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_80":131,"_82":83,"_84":132},21,45865,"engenharia-civil-3",{"_17":74,"_67":135,"_69":136,"_71":72,"_73":91,"_75":92,"_77":92,"_78":137,"_86":138},"Engenharia de Petróleo","engenharia-de-petroleo",{"_80":94,"_82":83,"_84":85},"engenharia-de-petroleo-1",{"_17":140,"_67":141,"_69":142,"_71":72,"_73":127,"_75":143,"_77":143,"_78":144,"_86":146},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_80":94,"_82":83,"_84":145},8852,"estruturas-1",{"_17":122,"_67":107,"_69":108,"_71":72,"_73":113,"_75":92,"_77":92,"_78":148,"_86":151},{"_80":149,"_82":83,"_84":150},10,19948,"mecanica-2",{"_17":153,"_67":99,"_69":100,"_71":72,"_73":66,"_75":154,"_77":154,"_78":155,"_86":156},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_80":83,"_82":83,"_84":104},"resistencia-dos-materiais-7",{"_17":158,"_67":159,"_69":100,"_71":72,"_73":140,"_75":160,"_77":160,"_78":161,"_86":162},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_80":83,"_82":83,"_84":104},"resistencia-dos-materiais-5",{"_17":91,"_67":164,"_69":165,"_71":72,"_73":-5,"_75":166,"_77":166,"_78":167,"_86":165},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_80":168,"_82":83,"_84":169},29,351586,{"_14":15,"_16":15,"_17":171,"_19":172,"_35":15,"_36":185,"_63":186},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[173,176,179,182],{"_17":174,"_23":24,"_25":175},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":177,"_23":29,"_25":178},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":180,"_23":33,"_25":181},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":183,"_23":56,"_25":184},"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.

",[65,87,97,106,112,120,126,134,139,147,152,157,163],{"_14":15,"_16":15,"_17":188,"_19":189,"_35":15,"_36":202,"_63":203},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[190,193,196,199],{"_17":191,"_23":24,"_25":192},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":194,"_23":29,"_25":195},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":197,"_23":33,"_25":198},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":200,"_23":56,"_25":201},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[65,87,97,106,112,120,126,134,139,147,152,157,163],{"_14":15,"_16":15,"_17":205,"_19":206,"_35":15,"_36":222,"_63":223},"996628fc-4ac3-4821-86bd-839f86a97a6d",[207,210,213,216,219],{"_17":208,"_23":24,"_25":209},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":211,"_23":29,"_25":212},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":214,"_23":33,"_25":215},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":217,"_23":56,"_25":218},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":220,"_23":60,"_25":221},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[65,87,97,106,112,120,126,134,139,147,152,157,163],{"_14":15,"_16":15,"_17":225,"_19":226,"_35":15,"_36":242,"_63":243},"c478a46c-46a8-4942-ae14-2e79def3dda2",[227,230,233,236,239],{"_17":228,"_23":24,"_25":229},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":231,"_23":29,"_25":232},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":234,"_23":33,"_25":235},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":237,"_23":56,"_25":238},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":240,"_23":60,"_25":241},"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????",[65,87,97,106,112,120,126,134,139,147,152,157,163],[65,87,97,106,112,120,126,134,139,147,152,157,163],"tagsTree",[247,254],{"_17":113,"_67":114,"_69":115,"_71":72,"_73":-5,"_75":116,"_77":116,"_78":117,"_86":115,"_248":249},"children",[250],{"_17":122,"_67":107,"_69":108,"_71":72,"_73":113,"_75":92,"_77":92,"_78":148,"_86":151,"_248":251},[252],{"_17":121,"_67":99,"_69":100,"_71":72,"_73":122,"_75":123,"_77":123,"_78":124,"_86":125,"_248":253},[],{"_17":91,"_67":164,"_69":165,"_71":72,"_73":-5,"_75":166,"_77":166,"_78":167,"_86":165,"_248":255},[256,262,268],{"_17":88,"_67":89,"_69":90,"_71":72,"_73":91,"_75":92,"_77":92,"_78":93,"_86":96,"_248":257},[258],{"_17":101,"_67":107,"_69":108,"_71":72,"_73":88,"_75":76,"_77":76,"_78":109,"_86":111,"_248":259},[260],{"_17":98,"_67":99,"_69":100,"_71":72,"_73":101,"_75":102,"_77":102,"_78":103,"_86":105,"_248":261},[],{"_17":127,"_67":128,"_69":129,"_71":72,"_73":91,"_75":92,"_77":92,"_78":130,"_86":133,"_248":263},[264],{"_17":140,"_67":141,"_69":142,"_71":72,"_73":127,"_75":143,"_77":143,"_78":144,"_86":146,"_248":265},[266],{"_17":158,"_67":159,"_69":100,"_71":72,"_73":140,"_75":160,"_77":160,"_78":161,"_86":162,"_248":267},[],{"_17":74,"_67":135,"_69":136,"_71":72,"_73":91,"_75":92,"_77":92,"_78":137,"_86":138,"_248":269},[270],{"_17":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":76,"_78":79,"_86":70,"_248":271},[272],{"_17":153,"_67":99,"_69":100,"_71":72,"_73":66,"_75":154,"_77":154,"_78":155,"_86":156,"_248":273},[],"actionData","errors"]

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