[{"_1":2,"_284":-5,"_285":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/dbf829a6-5dbe-45e9-a83d-9d26e3db4340","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_52":53,"_73":254,"_255":256},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","dbf829a6-5dbe-45e9-a83d-9d26e3db4340","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"a443d795-aead-413b-ab5d-46dffab6ab28","label","A","text","\\frac{N1}{N2} = 15; \\ V = 15",{"_19":30,"_25":31,"_27":32},"9d01b8c6-8c07-424a-a579-abce1c9e1dd1","B","\\frac{N1}{N2} = 5; \\ V = 9",{"_19":34,"_25":35,"_27":36},"0b9ad151-36de-4808-be75-377ff1b589d0","C","\\frac{N1}{N2} = 10; \\ V = 11",{"_19":38,"_25":39,"_27":40},"d7284cc0-7900-4137-866f-f6ec7d729314","D","\\frac{N1}{N2} = 25; \\ V = 22",{"_19":42,"_25":43,"_27":44},"996e95c1-4d4f-4a3d-841e-4c4c57da990d","E","\\frac{N1}{N2} = 20; \\ V = 20","solution_explanation","statement","

Questão 9

Escolha uma opção:

","status","has_issues","relatedVideos",[],"similarQuestions",[54,180,197,214,234],{"_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",[75,97,107,116,122,130,136,144,149,157,162,167,173],{"_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},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_90":104,"_92":93,"_94":105},5,30614,"engenharia-mecatronica-1",{"_19":108,"_77":109,"_79":110,"_81":82,"_83":111,"_85":112,"_87":112,"_88":113,"_96":115},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_90":93,"_92":93,"_94":114},3376,"resistencia-dos-materiais-6",{"_19":111,"_77":117,"_79":118,"_81":82,"_83":98,"_85":86,"_87":86,"_88":119,"_96":121},"Mecânica","mecanica",{"_90":104,"_92":93,"_94":120},25741,"mecanica-3",{"_19":123,"_77":124,"_79":125,"_81":82,"_83":-5,"_85":126,"_87":126,"_88":127,"_96":125},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_90":128,"_92":93,"_94":129},18,135489,{"_19":131,"_77":109,"_79":110,"_81":82,"_83":132,"_85":133,"_87":133,"_88":134,"_96":135},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_90":93,"_92":93,"_94":114},"resistencia-dos-materiais-4",{"_19":137,"_77":138,"_79":139,"_81":82,"_83":101,"_85":102,"_87":102,"_88":140,"_96":143},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_90":141,"_92":93,"_94":142},21,45865,"engenharia-civil-3",{"_19":84,"_77":145,"_79":146,"_81":82,"_83":101,"_85":102,"_87":102,"_88":147,"_96":148},"Engenharia de Petróleo","engenharia-de-petroleo",{"_90":104,"_92":93,"_94":95},"engenharia-de-petroleo-1",{"_19":150,"_77":151,"_79":152,"_81":82,"_83":137,"_85":153,"_87":153,"_88":154,"_96":156},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_90":104,"_92":93,"_94":155},8852,"estruturas-1",{"_19":132,"_77":117,"_79":118,"_81":82,"_83":123,"_85":102,"_87":102,"_88":158,"_96":161},{"_90":159,"_92":93,"_94":160},10,19948,"mecanica-2",{"_19":163,"_77":109,"_79":110,"_81":82,"_83":76,"_85":164,"_87":164,"_88":165,"_96":166},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_90":93,"_92":93,"_94":114},"resistencia-dos-materiais-7",{"_19":168,"_77":169,"_79":110,"_81":82,"_83":150,"_85":170,"_87":170,"_88":171,"_96":172},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_90":93,"_92":93,"_94":114},"resistencia-dos-materiais-5",{"_19":101,"_77":174,"_79":175,"_81":82,"_83":-5,"_85":176,"_87":176,"_88":177,"_96":175},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_90":178,"_92":93,"_94":179},29,351586,{"_16":17,"_18":17,"_19":181,"_21":182,"_45":17,"_46":195,"_73":196},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[183,186,189,192],{"_19":184,"_25":26,"_27":185},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":187,"_25":31,"_27":188},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":190,"_25":35,"_27":191},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":193,"_25":39,"_27":194},"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.

",[75,97,107,116,122,130,136,144,149,157,162,167,173],{"_16":17,"_18":17,"_19":198,"_21":199,"_45":17,"_46":212,"_73":213},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[200,203,206,209],{"_19":201,"_25":26,"_27":202},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":204,"_25":31,"_27":205},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":207,"_25":35,"_27":208},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":210,"_25":39,"_27":211},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[75,97,107,116,122,130,136,144,149,157,162,167,173],{"_16":17,"_18":17,"_19":215,"_21":216,"_45":17,"_46":232,"_73":233},"996628fc-4ac3-4821-86bd-839f86a97a6d",[217,220,223,226,229],{"_19":218,"_25":26,"_27":219},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":221,"_25":31,"_27":222},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":224,"_25":35,"_27":225},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":227,"_25":39,"_27":228},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":230,"_25":43,"_27":231},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[75,97,107,116,122,130,136,144,149,157,162,167,173],{"_16":17,"_18":17,"_19":235,"_21":236,"_45":17,"_46":252,"_73":253},"c478a46c-46a8-4942-ae14-2e79def3dda2",[237,240,243,246,249],{"_19":238,"_25":26,"_27":239},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":241,"_25":31,"_27":242},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":244,"_25":35,"_27":245},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":247,"_25":39,"_27":248},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":250,"_25":43,"_27":251},"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????",[75,97,107,116,122,130,136,144,149,157,162,167,173],[75,97,107,116,122,130,136,144,149,157,162,167,173],"tagsTree",[257,264],{"_19":123,"_77":124,"_79":125,"_81":82,"_83":-5,"_85":126,"_87":126,"_88":127,"_96":125,"_258":259},"children",[260],{"_19":132,"_77":117,"_79":118,"_81":82,"_83":123,"_85":102,"_87":102,"_88":158,"_96":161,"_258":261},[262],{"_19":131,"_77":109,"_79":110,"_81":82,"_83":132,"_85":133,"_87":133,"_88":134,"_96":135,"_258":263},[],{"_19":101,"_77":174,"_79":175,"_81":82,"_83":-5,"_85":176,"_87":176,"_88":177,"_96":175,"_258":265},[266,272,278],{"_19":98,"_77":99,"_79":100,"_81":82,"_83":101,"_85":102,"_87":102,"_88":103,"_96":106,"_258":267},[268],{"_19":111,"_77":117,"_79":118,"_81":82,"_83":98,"_85":86,"_87":86,"_88":119,"_96":121,"_258":269},[270],{"_19":108,"_77":109,"_79":110,"_81":82,"_83":111,"_85":112,"_87":112,"_88":113,"_96":115,"_258":271},[],{"_19":137,"_77":138,"_79":139,"_81":82,"_83":101,"_85":102,"_87":102,"_88":140,"_96":143,"_258":273},[274],{"_19":150,"_77":151,"_79":152,"_81":82,"_83":137,"_85":153,"_87":153,"_88":154,"_96":156,"_258":275},[276],{"_19":168,"_77":169,"_79":110,"_81":82,"_83":150,"_85":170,"_87":170,"_88":171,"_96":172,"_258":277},[],{"_19":84,"_77":145,"_79":146,"_81":82,"_83":101,"_85":102,"_87":102,"_88":147,"_96":148,"_258":279},[280],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":80,"_258":281},[282],{"_19":163,"_77":109,"_79":110,"_81":82,"_83":76,"_85":164,"_87":164,"_88":165,"_96":166,"_258":283},[],"actionData","errors"]

Comentários