[{"_1":2,"_282":-5,"_283":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ff93f3c2-50b2-4c58-9c04-2f719292d4bc","user","pages/questions/show/index",{"_10":11,"_12":13,"_48":49,"_50":51,"_71":252,"_253":254},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45,"_46":47},"correctOptionId","","difficulty","id","ff93f3c2-50b2-4c58-9c04-2f719292d4bc","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"45a0b6a5-5e9b-4e0e-beab-2f4d7a7abcf9","label","A","text","2, 5\text{√}12",{"_17":28,"_23":29,"_25":30},"2b6bfda2-b0c2-4033-9b51-c7e86c8c9a33","B","7, 5\text{√}12",{"_17":32,"_23":33,"_25":34},"cb6ae676-b548-4c89-9522-2ab1ca2e5271","C","30\text{√}12",{"_17":36,"_23":37,"_25":38},"e598d45e-2eec-4546-9a43-234b3d21c6e5","D","15\text{√}12",{"_17":40,"_23":41,"_25":42},"15f60c10-e492-4a82-a536-46f32b3a420d","E","22, 5\text{√}12","solution_explanation","statement","

TJ – GO / 2014 Um pilar de aço, com 3m de comprimento e extremidades rotuladas, está em equilíbrio e suporta uma carga de compressão. Sua seção transversal é retangular de 200 \text{ mm} \times 400 \text{ mm} de dimensões. O maior índice de esbeltez desse pilar é:

","status","has_issues","relatedVideos",[],"similarQuestions",[52,178,195,212,232],{"_14":15,"_16":15,"_17":53,"_19":54,"_43":15,"_44":70,"_71":72},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[55,58,61,64,67],{"_17":56,"_23":24,"_25":57},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":59,"_23":29,"_25":60},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":62,"_23":33,"_25":63},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":65,"_23":37,"_25":66},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":68,"_23":41,"_25":69},"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",[73,95,105,114,120,128,134,142,147,155,160,165,171],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78},"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",{"_88":89,"_90":91,"_92":93},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":96,"_75":97,"_77":98,"_79":80,"_81":99,"_83":100,"_85":100,"_86":101,"_94":104},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_88":102,"_90":91,"_92":103},5,30614,"engenharia-mecatronica-1",{"_17":106,"_75":107,"_77":108,"_79":80,"_81":109,"_83":110,"_85":110,"_86":111,"_94":113},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_88":91,"_90":91,"_92":112},3376,"resistencia-dos-materiais-6",{"_17":109,"_75":115,"_77":116,"_79":80,"_81":96,"_83":84,"_85":84,"_86":117,"_94":119},"Mecânica","mecanica",{"_88":102,"_90":91,"_92":118},25741,"mecanica-3",{"_17":121,"_75":122,"_77":123,"_79":80,"_81":-5,"_83":124,"_85":124,"_86":125,"_94":123},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_88":126,"_90":91,"_92":127},18,135489,{"_17":129,"_75":107,"_77":108,"_79":80,"_81":130,"_83":131,"_85":131,"_86":132,"_94":133},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_88":91,"_90":91,"_92":112},"resistencia-dos-materiais-4",{"_17":135,"_75":136,"_77":137,"_79":80,"_81":99,"_83":100,"_85":100,"_86":138,"_94":141},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_88":139,"_90":91,"_92":140},21,45865,"engenharia-civil-3",{"_17":82,"_75":143,"_77":144,"_79":80,"_81":99,"_83":100,"_85":100,"_86":145,"_94":146},"Engenharia de Petróleo","engenharia-de-petroleo",{"_88":102,"_90":91,"_92":93},"engenharia-de-petroleo-1",{"_17":148,"_75":149,"_77":150,"_79":80,"_81":135,"_83":151,"_85":151,"_86":152,"_94":154},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_88":102,"_90":91,"_92":153},8852,"estruturas-1",{"_17":130,"_75":115,"_77":116,"_79":80,"_81":121,"_83":100,"_85":100,"_86":156,"_94":159},{"_88":157,"_90":91,"_92":158},10,19948,"mecanica-2",{"_17":161,"_75":107,"_77":108,"_79":80,"_81":74,"_83":162,"_85":162,"_86":163,"_94":164},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_88":91,"_90":91,"_92":112},"resistencia-dos-materiais-7",{"_17":166,"_75":167,"_77":108,"_79":80,"_81":148,"_83":168,"_85":168,"_86":169,"_94":170},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_88":91,"_90":91,"_92":112},"resistencia-dos-materiais-5",{"_17":99,"_75":172,"_77":173,"_79":80,"_81":-5,"_83":174,"_85":174,"_86":175,"_94":173},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_88":176,"_90":91,"_92":177},29,351586,{"_14":15,"_16":15,"_17":179,"_19":180,"_43":15,"_44":193,"_71":194},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[181,184,187,190],{"_17":182,"_23":24,"_25":183},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":185,"_23":29,"_25":186},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":188,"_23":33,"_25":189},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":191,"_23":37,"_25":192},"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.

",[73,95,105,114,120,128,134,142,147,155,160,165,171],{"_14":15,"_16":15,"_17":196,"_19":197,"_43":15,"_44":210,"_71":211},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[198,201,204,207],{"_17":199,"_23":24,"_25":200},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":202,"_23":29,"_25":203},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":205,"_23":33,"_25":206},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":208,"_23":37,"_25":209},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[73,95,105,114,120,128,134,142,147,155,160,165,171],{"_14":15,"_16":15,"_17":213,"_19":214,"_43":15,"_44":230,"_71":231},"996628fc-4ac3-4821-86bd-839f86a97a6d",[215,218,221,224,227],{"_17":216,"_23":24,"_25":217},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":219,"_23":29,"_25":220},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":222,"_23":33,"_25":223},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":225,"_23":37,"_25":226},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":228,"_23":41,"_25":229},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[73,95,105,114,120,128,134,142,147,155,160,165,171],{"_14":15,"_16":15,"_17":233,"_19":234,"_43":15,"_44":250,"_71":251},"c478a46c-46a8-4942-ae14-2e79def3dda2",[235,238,241,244,247],{"_17":236,"_23":24,"_25":237},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":239,"_23":29,"_25":240},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":242,"_23":33,"_25":243},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":245,"_23":37,"_25":246},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":248,"_23":41,"_25":249},"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????",[73,95,105,114,120,128,134,142,147,155,160,165,171],[73,95,105,114,120,128,134,142,147,155,160,165,171],"tagsTree",[255,262],{"_17":121,"_75":122,"_77":123,"_79":80,"_81":-5,"_83":124,"_85":124,"_86":125,"_94":123,"_256":257},"children",[258],{"_17":130,"_75":115,"_77":116,"_79":80,"_81":121,"_83":100,"_85":100,"_86":156,"_94":159,"_256":259},[260],{"_17":129,"_75":107,"_77":108,"_79":80,"_81":130,"_83":131,"_85":131,"_86":132,"_94":133,"_256":261},[],{"_17":99,"_75":172,"_77":173,"_79":80,"_81":-5,"_83":174,"_85":174,"_86":175,"_94":173,"_256":263},[264,270,276],{"_17":96,"_75":97,"_77":98,"_79":80,"_81":99,"_83":100,"_85":100,"_86":101,"_94":104,"_256":265},[266],{"_17":109,"_75":115,"_77":116,"_79":80,"_81":96,"_83":84,"_85":84,"_86":117,"_94":119,"_256":267},[268],{"_17":106,"_75":107,"_77":108,"_79":80,"_81":109,"_83":110,"_85":110,"_86":111,"_94":113,"_256":269},[],{"_17":135,"_75":136,"_77":137,"_79":80,"_81":99,"_83":100,"_85":100,"_86":138,"_94":141,"_256":271},[272],{"_17":148,"_75":149,"_77":150,"_79":80,"_81":135,"_83":151,"_85":151,"_86":152,"_94":154,"_256":273},[274],{"_17":166,"_75":167,"_77":108,"_79":80,"_81":148,"_83":168,"_85":168,"_86":169,"_94":170,"_256":275},[],{"_17":82,"_75":143,"_77":144,"_79":80,"_81":99,"_83":100,"_85":100,"_86":145,"_94":146,"_256":277},[278],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78,"_256":279},[280],{"_17":161,"_75":107,"_77":108,"_79":80,"_81":74,"_83":162,"_85":162,"_86":163,"_94":164,"_256":281},[],"actionData","errors"]

Aulas em vídeo Em breve

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