[{"_1":2,"_280":-5,"_281":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/d76adaf4-b075-4cda-b563-e6e0cc5675aa","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":250,"_251":252},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45},"correctOptionId","","difficulty","id","d76adaf4-b075-4cda-b563-e6e0cc5675aa","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"39309030-e614-4f13-a3ac-6fdd70909341","label","A","text","10,7 mm",{"_17":28,"_23":29,"_25":30},"0edfa578-9404-4545-b7f1-1ce795ea7080","B","0,87 mm",{"_17":32,"_23":33,"_25":34},"ca841101-ba68-40b2-8164-12622aa290d4","C","107 mm",{"_17":36,"_23":37,"_25":38},"9b1083cd-0bbb-4458-b38e-09c908a2a923","D","1,07 mm",{"_17":40,"_23":41,"_25":42},"d09f6231-8611-4214-9eed-632d6b1e774b","E","8,7 mm","solution_explanation","statement","Uma força de tração de 9 \\, kN vai ser aplicada a um fio de aço de 50 \\, m de comprimento. Determine o menor diâmetro a ser adotado para o fio, se a tensão normal não pode exceder a 150 \\, MPa e a deformação do fio deve ser no máximo de 25 \\, mm. Considerar E = 200 \\, GPa.","relatedVideos",[],"similarQuestions",[50,176,193,210,230],{"_14":15,"_16":15,"_17":51,"_19":52,"_43":15,"_44":68,"_69":70},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_17":54,"_23":24,"_25":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":57,"_23":29,"_25":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":60,"_23":33,"_25":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":63,"_23":37,"_25":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":66,"_23":41,"_25":67},"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",[71,93,103,112,118,126,132,140,145,153,158,163,169],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76},"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",{"_86":87,"_88":89,"_90":91},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":94,"_73":95,"_75":96,"_77":78,"_79":97,"_81":98,"_83":98,"_84":99,"_92":102},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_86":100,"_88":89,"_90":101},5,30614,"engenharia-mecatronica-1",{"_17":104,"_73":105,"_75":106,"_77":78,"_79":107,"_81":108,"_83":108,"_84":109,"_92":111},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_86":89,"_88":89,"_90":110},3376,"resistencia-dos-materiais-6",{"_17":107,"_73":113,"_75":114,"_77":78,"_79":94,"_81":82,"_83":82,"_84":115,"_92":117},"Mecânica","mecanica",{"_86":100,"_88":89,"_90":116},25741,"mecanica-3",{"_17":119,"_73":120,"_75":121,"_77":78,"_79":-5,"_81":122,"_83":122,"_84":123,"_92":121},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_86":124,"_88":89,"_90":125},18,135489,{"_17":127,"_73":105,"_75":106,"_77":78,"_79":128,"_81":129,"_83":129,"_84":130,"_92":131},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_86":89,"_88":89,"_90":110},"resistencia-dos-materiais-4",{"_17":133,"_73":134,"_75":135,"_77":78,"_79":97,"_81":98,"_83":98,"_84":136,"_92":139},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_86":137,"_88":89,"_90":138},21,45865,"engenharia-civil-3",{"_17":80,"_73":141,"_75":142,"_77":78,"_79":97,"_81":98,"_83":98,"_84":143,"_92":144},"Engenharia de Petróleo","engenharia-de-petroleo",{"_86":100,"_88":89,"_90":91},"engenharia-de-petroleo-1",{"_17":146,"_73":147,"_75":148,"_77":78,"_79":133,"_81":149,"_83":149,"_84":150,"_92":152},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_86":100,"_88":89,"_90":151},8852,"estruturas-1",{"_17":128,"_73":113,"_75":114,"_77":78,"_79":119,"_81":98,"_83":98,"_84":154,"_92":157},{"_86":155,"_88":89,"_90":156},10,19948,"mecanica-2",{"_17":159,"_73":105,"_75":106,"_77":78,"_79":72,"_81":160,"_83":160,"_84":161,"_92":162},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_86":89,"_88":89,"_90":110},"resistencia-dos-materiais-7",{"_17":164,"_73":165,"_75":106,"_77":78,"_79":146,"_81":166,"_83":166,"_84":167,"_92":168},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_86":89,"_88":89,"_90":110},"resistencia-dos-materiais-5",{"_17":97,"_73":170,"_75":171,"_77":78,"_79":-5,"_81":172,"_83":172,"_84":173,"_92":171},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_86":174,"_88":89,"_90":175},29,351586,{"_14":15,"_16":15,"_17":177,"_19":178,"_43":15,"_44":191,"_69":192},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[179,182,185,188],{"_17":180,"_23":24,"_25":181},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":183,"_23":29,"_25":184},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":186,"_23":33,"_25":187},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":189,"_23":37,"_25":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.

",[71,93,103,112,118,126,132,140,145,153,158,163,169],{"_14":15,"_16":15,"_17":194,"_19":195,"_43":15,"_44":208,"_69":209},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[196,199,202,205],{"_17":197,"_23":24,"_25":198},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":200,"_23":29,"_25":201},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":203,"_23":33,"_25":204},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":206,"_23":37,"_25":207},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[71,93,103,112,118,126,132,140,145,153,158,163,169],{"_14":15,"_16":15,"_17":211,"_19":212,"_43":15,"_44":228,"_69":229},"996628fc-4ac3-4821-86bd-839f86a97a6d",[213,216,219,222,225],{"_17":214,"_23":24,"_25":215},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":217,"_23":29,"_25":218},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":220,"_23":33,"_25":221},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":223,"_23":37,"_25":224},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":226,"_23":41,"_25":227},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[71,93,103,112,118,126,132,140,145,153,158,163,169],{"_14":15,"_16":15,"_17":231,"_19":232,"_43":15,"_44":248,"_69":249},"c478a46c-46a8-4942-ae14-2e79def3dda2",[233,236,239,242,245],{"_17":234,"_23":24,"_25":235},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":237,"_23":29,"_25":238},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":240,"_23":33,"_25":241},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":243,"_23":37,"_25":244},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":246,"_23":41,"_25":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????",[71,93,103,112,118,126,132,140,145,153,158,163,169],[71,93,103,112,118,126,132,140,145,153,158,163,169],"tagsTree",[253,260],{"_17":119,"_73":120,"_75":121,"_77":78,"_79":-5,"_81":122,"_83":122,"_84":123,"_92":121,"_254":255},"children",[256],{"_17":128,"_73":113,"_75":114,"_77":78,"_79":119,"_81":98,"_83":98,"_84":154,"_92":157,"_254":257},[258],{"_17":127,"_73":105,"_75":106,"_77":78,"_79":128,"_81":129,"_83":129,"_84":130,"_92":131,"_254":259},[],{"_17":97,"_73":170,"_75":171,"_77":78,"_79":-5,"_81":172,"_83":172,"_84":173,"_92":171,"_254":261},[262,268,274],{"_17":94,"_73":95,"_75":96,"_77":78,"_79":97,"_81":98,"_83":98,"_84":99,"_92":102,"_254":263},[264],{"_17":107,"_73":113,"_75":114,"_77":78,"_79":94,"_81":82,"_83":82,"_84":115,"_92":117,"_254":265},[266],{"_17":104,"_73":105,"_75":106,"_77":78,"_79":107,"_81":108,"_83":108,"_84":109,"_92":111,"_254":267},[],{"_17":133,"_73":134,"_75":135,"_77":78,"_79":97,"_81":98,"_83":98,"_84":136,"_92":139,"_254":269},[270],{"_17":146,"_73":147,"_75":148,"_77":78,"_79":133,"_81":149,"_83":149,"_84":150,"_92":152,"_254":271},[272],{"_17":164,"_73":165,"_75":106,"_77":78,"_79":146,"_81":166,"_83":166,"_84":167,"_92":168,"_254":273},[],{"_17":80,"_73":141,"_75":142,"_77":78,"_79":97,"_81":98,"_83":98,"_84":143,"_92":144,"_254":275},[276],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76,"_254":277},[278],{"_17":159,"_73":105,"_75":106,"_77":78,"_79":72,"_81":160,"_83":160,"_84":161,"_92":162,"_254":279},[],"actionData","errors"]

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