[{"_1":2,"_190":-5,"_191":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f9e6cb3d-10e2-423b-a9dc-046143189b70","user","pages/questions/show/index",{"_10":11,"_12":13,"_42":43,"_44":45,"_66":180,"_181":182},"comments",[],"question",{"_14":15,"_16":17,"_18":19,"_20":21,"_39":17,"_40":41},"correctOptionId","efde6145-4e88-432e-95ea-8aad0c2d0d02","difficulty","","id","f9e6cb3d-10e2-423b-a9dc-046143189b70","options",[22,28,32,35],{"_18":23,"_24":25,"_26":27},"67ad51e2-b48b-4f48-a7a4-be5065e2f16e","label","A","text","25 \\, \\text{J}",{"_18":29,"_24":30,"_26":31},"29d703f7-5326-4243-adae-e7d7b8721d05","B","50 \\, \\text{J}",{"_18":15,"_24":33,"_26":34},"C","75 \\, \\text{J}",{"_18":36,"_24":37,"_26":38},"b5b26163-dc3b-4ced-9270-d739a2b952d6","D","100 \\, \\text{J}","solution_explanation","statement","Um corpo de 2 \\, \\text{kg} é lançado verticalmente para cima com uma velocidade de 15 \\, \\text{m/s}. Qual é a energia cinética inicial do corpo?","relatedVideos",[],"similarQuestions",[46,106,123,140,160],{"_14":17,"_16":17,"_18":47,"_20":48,"_39":17,"_40":65,"_66":67},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[49,52,55,58,61],{"_18":50,"_24":25,"_26":51},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_18":53,"_24":30,"_26":54},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_18":56,"_24":33,"_26":57},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_18":59,"_24":37,"_26":60},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_18":62,"_24":63,"_26":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",[68,91,99],{"_18":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":90},"861ad829-750d-4a44-9569-2f18b430b4df","name","Engenharia Mecatrônica","alias","engenharia-mecatronica","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at","metadata",{"_83":84,"_85":86,"_87":88},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_18":92,"_70":93,"_72":94,"_74":75,"_76":69,"_78":95,"_80":95,"_81":96,"_89":98},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_83":84,"_85":86,"_87":97},25741,"mecanica-3",{"_18":77,"_70":100,"_72":101,"_74":75,"_76":-5,"_78":102,"_80":102,"_81":103,"_89":101},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_83":104,"_85":86,"_87":105},29,351586,{"_14":17,"_16":17,"_18":107,"_20":108,"_39":17,"_40":121,"_66":122},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[109,112,115,118],{"_18":110,"_24":25,"_26":111},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_18":113,"_24":30,"_26":114},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_18":116,"_24":33,"_26":117},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_18":119,"_24":37,"_26":120},"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.

",[68,91,99],{"_14":17,"_16":17,"_18":124,"_20":125,"_39":17,"_40":138,"_66":139},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[126,129,132,135],{"_18":127,"_24":25,"_26":128},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_18":130,"_24":30,"_26":131},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_18":133,"_24":33,"_26":134},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_18":136,"_24":37,"_26":137},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[68,91,99],{"_14":17,"_16":17,"_18":141,"_20":142,"_39":17,"_40":158,"_66":159},"996628fc-4ac3-4821-86bd-839f86a97a6d",[143,146,149,152,155],{"_18":144,"_24":25,"_26":145},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_18":147,"_24":30,"_26":148},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_18":150,"_24":33,"_26":151},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_18":153,"_24":37,"_26":154},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_18":156,"_24":63,"_26":157},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[68,91,99],{"_14":17,"_16":17,"_18":161,"_20":162,"_39":17,"_40":178,"_66":179},"c478a46c-46a8-4942-ae14-2e79def3dda2",[163,166,169,172,175],{"_18":164,"_24":25,"_26":165},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_18":167,"_24":30,"_26":168},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_18":170,"_24":33,"_26":171},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_18":173,"_24":37,"_26":174},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_18":176,"_24":63,"_26":177},"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????",[68,91,99],[68,91,99],"tagsTree",[183],{"_18":77,"_70":100,"_72":101,"_74":75,"_76":-5,"_78":102,"_80":102,"_81":103,"_89":101,"_184":185},"children",[186],{"_18":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":79,"_80":79,"_81":82,"_89":90,"_184":187},[188],{"_18":92,"_70":93,"_72":94,"_74":75,"_76":69,"_78":95,"_80":95,"_81":96,"_89":98,"_184":189},[],"actionData","errors"]

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