[{"_1":2,"_193":-5,"_194":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f992e62e-5406-4d79-88f4-064a85fa2701","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":183,"_184":185},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45},"correctOptionId","","difficulty","id","f992e62e-5406-4d79-88f4-064a85fa2701","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"b9a0cb0f-6ab0-41df-93f1-d7eec8f44d1f","label","A","text","\\frac{1}{4}",{"_17":28,"_23":29,"_25":30},"af9a3461-03e4-4dd3-bab0-deed897b71a4","B","\\frac{1}{2}",{"_17":32,"_23":33,"_25":34},"e16a8c2c-29d1-49d5-8b6b-895e2d8fec0e","C","1",{"_17":36,"_23":37,"_25":38},"917c3c1e-c926-4084-a45c-6870834ff9bb","D","2",{"_17":40,"_23":41,"_25":42},"5c615552-0c7a-45b3-b058-1f69ad86e018","E","4","solution_explanation","statement","

9-Duas partículas (1) e (2) estão situadas na mesma vertical a alturas respectivamente iguais a h_1 e h_2 do solo, sendo h_1 = 4 h_2. As partículas são então lançadas horizontalmente de forma a atingirem o solo num mesmo ponto P. Qual a razão \\frac{v_1}{v_2} entre os módulos das velocidades de lançamento das partículas (1) e (2)?

","relatedVideos",[],"similarQuestions",[50,109,126,143,163],{"_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",[71,94,102],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":93},"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",{"_86":87,"_88":89,"_90":91},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_17":95,"_73":96,"_75":97,"_77":78,"_79":72,"_81":98,"_83":98,"_84":99,"_92":101},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_86":87,"_88":89,"_90":100},25741,"mecanica-3",{"_17":80,"_73":103,"_75":104,"_77":78,"_79":-5,"_81":105,"_83":105,"_84":106,"_92":104},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_86":107,"_88":89,"_90":108},29,351586,{"_14":15,"_16":15,"_17":110,"_19":111,"_43":15,"_44":124,"_69":125},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[112,115,118,121],{"_17":113,"_23":24,"_25":114},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":116,"_23":29,"_25":117},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":119,"_23":33,"_25":120},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":122,"_23":37,"_25":123},"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.

",[71,94,102],{"_14":15,"_16":15,"_17":127,"_19":128,"_43":15,"_44":141,"_69":142},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[129,132,135,138],{"_17":130,"_23":24,"_25":131},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":133,"_23":29,"_25":134},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":136,"_23":33,"_25":137},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":139,"_23":37,"_25":140},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[71,94,102],{"_14":15,"_16":15,"_17":144,"_19":145,"_43":15,"_44":161,"_69":162},"996628fc-4ac3-4821-86bd-839f86a97a6d",[146,149,152,155,158],{"_17":147,"_23":24,"_25":148},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":150,"_23":29,"_25":151},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":153,"_23":33,"_25":154},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":156,"_23":37,"_25":157},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":159,"_23":41,"_25":160},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[71,94,102],{"_14":15,"_16":15,"_17":164,"_19":165,"_43":15,"_44":181,"_69":182},"c478a46c-46a8-4942-ae14-2e79def3dda2",[166,169,172,175,178],{"_17":167,"_23":24,"_25":168},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":170,"_23":29,"_25":171},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":173,"_23":33,"_25":174},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":176,"_23":37,"_25":177},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":179,"_23":41,"_25":180},"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????",[71,94,102],[71,94,102],"tagsTree",[186],{"_17":80,"_73":103,"_75":104,"_77":78,"_79":-5,"_81":105,"_83":105,"_84":106,"_92":104,"_187":188},"children",[189],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":93,"_187":190},[191],{"_17":95,"_73":96,"_75":97,"_77":78,"_79":72,"_81":98,"_83":98,"_84":99,"_92":101,"_187":192},[],"actionData","errors"]

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