[{"_1":2,"_277":-5,"_278":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/c385f365-af46-43ea-b841-a210a22a6115","user","pages/questions/show/index",{"_10":11,"_12":13,"_42":43,"_44":45,"_66":247,"_248":249},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_39":15,"_40":41},"correctOptionId","","difficulty","id","c385f365-af46-43ea-b841-a210a22a6115","options",[21,27,31,35],{"_17":22,"_23":24,"_25":26},"25105100-4886-4b11-8a98-5c3ffcbbc01c","label","A","text","Galáxias elípticas, espirais e irregulares.",{"_17":28,"_23":29,"_25":30},"89ff35db-d5db-4cc9-9fac-d7fa3be036e4","B","Galáxias anãs, gigantes e supermassivas.",{"_17":32,"_23":33,"_25":34},"51917304-169a-4418-b7f8-185af295f7c7","C","Galáxias ativas, passivas e inativas.",{"_17":36,"_23":37,"_25":38},"a8a15e3a-bebd-441d-8889-8182a06adb46","D","Galáxias azuis, vermelhas e brancas.","solution_explanation","statement","

O estudo das galáxias é fundamental para a compreensão da estrutura do universo. Qual é a classificação básica das galáxias de acordo com sua forma?

","relatedVideos",[],"similarQuestions",[46,173,190,207,227],{"_14":15,"_16":15,"_17":47,"_19":48,"_39":15,"_40":65,"_66":67},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[49,52,55,58,61],{"_17":50,"_23":24,"_25":51},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":53,"_23":29,"_25":54},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":56,"_23":33,"_25":57},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":59,"_23":37,"_25":60},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":62,"_23":63,"_25":64},"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",[68,90,100,109,115,123,129,137,142,150,155,160,166],{"_17":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":73},"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",{"_83":84,"_85":86,"_87":88},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":91,"_70":92,"_72":93,"_74":75,"_76":94,"_78":95,"_80":95,"_81":96,"_89":99},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_83":97,"_85":86,"_87":98},5,30614,"engenharia-mecatronica-1",{"_17":101,"_70":102,"_72":103,"_74":75,"_76":104,"_78":105,"_80":105,"_81":106,"_89":108},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_83":86,"_85":86,"_87":107},3376,"resistencia-dos-materiais-6",{"_17":104,"_70":110,"_72":111,"_74":75,"_76":91,"_78":79,"_80":79,"_81":112,"_89":114},"Mecânica","mecanica",{"_83":97,"_85":86,"_87":113},25741,"mecanica-3",{"_17":116,"_70":117,"_72":118,"_74":75,"_76":-5,"_78":119,"_80":119,"_81":120,"_89":118},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_83":121,"_85":86,"_87":122},18,135489,{"_17":124,"_70":102,"_72":103,"_74":75,"_76":125,"_78":126,"_80":126,"_81":127,"_89":128},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_83":86,"_85":86,"_87":107},"resistencia-dos-materiais-4",{"_17":130,"_70":131,"_72":132,"_74":75,"_76":94,"_78":95,"_80":95,"_81":133,"_89":136},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_83":134,"_85":86,"_87":135},21,45865,"engenharia-civil-3",{"_17":77,"_70":138,"_72":139,"_74":75,"_76":94,"_78":95,"_80":95,"_81":140,"_89":141},"Engenharia de Petróleo","engenharia-de-petroleo",{"_83":97,"_85":86,"_87":88},"engenharia-de-petroleo-1",{"_17":143,"_70":144,"_72":145,"_74":75,"_76":130,"_78":146,"_80":146,"_81":147,"_89":149},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_83":97,"_85":86,"_87":148},8852,"estruturas-1",{"_17":125,"_70":110,"_72":111,"_74":75,"_76":116,"_78":95,"_80":95,"_81":151,"_89":154},{"_83":152,"_85":86,"_87":153},10,19948,"mecanica-2",{"_17":156,"_70":102,"_72":103,"_74":75,"_76":69,"_78":157,"_80":157,"_81":158,"_89":159},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_83":86,"_85":86,"_87":107},"resistencia-dos-materiais-7",{"_17":161,"_70":162,"_72":103,"_74":75,"_76":143,"_78":163,"_80":163,"_81":164,"_89":165},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_83":86,"_85":86,"_87":107},"resistencia-dos-materiais-5",{"_17":94,"_70":167,"_72":168,"_74":75,"_76":-5,"_78":169,"_80":169,"_81":170,"_89":168},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_83":171,"_85":86,"_87":172},29,351586,{"_14":15,"_16":15,"_17":174,"_19":175,"_39":15,"_40":188,"_66":189},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[176,179,182,185],{"_17":177,"_23":24,"_25":178},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":180,"_23":29,"_25":181},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":183,"_23":33,"_25":184},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":186,"_23":37,"_25":187},"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.

",[68,90,100,109,115,123,129,137,142,150,155,160,166],{"_14":15,"_16":15,"_17":191,"_19":192,"_39":15,"_40":205,"_66":206},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,202],{"_17":194,"_23":24,"_25":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":197,"_23":29,"_25":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":200,"_23":33,"_25":201},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":203,"_23":37,"_25":204},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[68,90,100,109,115,123,129,137,142,150,155,160,166],{"_14":15,"_16":15,"_17":208,"_19":209,"_39":15,"_40":225,"_66":226},"996628fc-4ac3-4821-86bd-839f86a97a6d",[210,213,216,219,222],{"_17":211,"_23":24,"_25":212},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":214,"_23":29,"_25":215},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":217,"_23":33,"_25":218},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":220,"_23":37,"_25":221},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":223,"_23":63,"_25":224},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[68,90,100,109,115,123,129,137,142,150,155,160,166],{"_14":15,"_16":15,"_17":228,"_19":229,"_39":15,"_40":245,"_66":246},"c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,239,242],{"_17":231,"_23":24,"_25":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":234,"_23":29,"_25":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":237,"_23":33,"_25":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":240,"_23":37,"_25":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":243,"_23":63,"_25":244},"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????",[68,90,100,109,115,123,129,137,142,150,155,160,166],[68,90,100,109,115,123,129,137,142,150,155,160,166],"tagsTree",[250,257],{"_17":116,"_70":117,"_72":118,"_74":75,"_76":-5,"_78":119,"_80":119,"_81":120,"_89":118,"_251":252},"children",[253],{"_17":125,"_70":110,"_72":111,"_74":75,"_76":116,"_78":95,"_80":95,"_81":151,"_89":154,"_251":254},[255],{"_17":124,"_70":102,"_72":103,"_74":75,"_76":125,"_78":126,"_80":126,"_81":127,"_89":128,"_251":256},[],{"_17":94,"_70":167,"_72":168,"_74":75,"_76":-5,"_78":169,"_80":169,"_81":170,"_89":168,"_251":258},[259,265,271],{"_17":91,"_70":92,"_72":93,"_74":75,"_76":94,"_78":95,"_80":95,"_81":96,"_89":99,"_251":260},[261],{"_17":104,"_70":110,"_72":111,"_74":75,"_76":91,"_78":79,"_80":79,"_81":112,"_89":114,"_251":262},[263],{"_17":101,"_70":102,"_72":103,"_74":75,"_76":104,"_78":105,"_80":105,"_81":106,"_89":108,"_251":264},[],{"_17":130,"_70":131,"_72":132,"_74":75,"_76":94,"_78":95,"_80":95,"_81":133,"_89":136,"_251":266},[267],{"_17":143,"_70":144,"_72":145,"_74":75,"_76":130,"_78":146,"_80":146,"_81":147,"_89":149,"_251":268},[269],{"_17":161,"_70":162,"_72":103,"_74":75,"_76":143,"_78":163,"_80":163,"_81":164,"_89":165,"_251":270},[],{"_17":77,"_70":138,"_72":139,"_74":75,"_76":94,"_78":95,"_80":95,"_81":140,"_89":141,"_251":272},[273],{"_17":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":73,"_251":274},[275],{"_17":156,"_70":102,"_72":103,"_74":75,"_76":69,"_78":157,"_80":157,"_81":158,"_89":159,"_251":276},[],"actionData","errors"]

Aulas em vídeo Em breve

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