[{"_1":2,"_189":-5,"_190":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fb699432-be07-4b0c-ab5b-e3659da2cddb","user","pages/questions/show/index",{"_10":11,"_12":13,"_41":42,"_43":44,"_65":179,"_180":181},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_38":15,"_39":40},"correctOptionId","","difficulty","id","fb699432-be07-4b0c-ab5b-e3659da2cddb","options",[21,27,31,35],{"_17":22,"_23":24,"_25":26},"69f2eb83-1907-447b-bab9-39e0ace9a446","label","A","text","4=2a; \\frac{4}{2}=a; 2=a",{"_17":28,"_23":29,"_25":30},"01a7f136-2e3b-4395-ab9e-c4d0dcefd34c","B","3+4=2a; 7=2a; 3,5=a",{"_17":32,"_23":33,"_25":34},"30951960-538f-465c-b857-fceb0957e5fc","C","-3+4=2a; \\frac{1}{2}=a",{"_17":36,"_23":37,"_25":30},"e7b1944e-f912-4019-896e-fb97b21c07e7","D","solution_explanation","statement","

Nas figuras abaixo, representamos as forças que agem nos blocos (todos de massa igual a 2kg). Determine, em cada caso, o módulo da aceleração que esses blocos adquirem:

","relatedVideos",[],"similarQuestions",[45,105,122,139,159],{"_14":15,"_16":15,"_17":46,"_19":47,"_38":15,"_39":64,"_65":66},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[48,51,54,57,60],{"_17":49,"_23":24,"_25":50},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":52,"_23":29,"_25":53},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":55,"_23":33,"_25":56},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":58,"_23":37,"_25":59},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":61,"_23":62,"_25":63},"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",[67,90,98],{"_17":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":78,"_80":81,"_88":89},"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",{"_82":83,"_84":85,"_86":87},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_17":91,"_69":92,"_71":93,"_73":74,"_75":68,"_77":94,"_79":94,"_80":95,"_88":97},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_82":83,"_84":85,"_86":96},25741,"mecanica-3",{"_17":76,"_69":99,"_71":100,"_73":74,"_75":-5,"_77":101,"_79":101,"_80":102,"_88":100},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_82":103,"_84":85,"_86":104},29,351586,{"_14":15,"_16":15,"_17":106,"_19":107,"_38":15,"_39":120,"_65":121},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[108,111,114,117],{"_17":109,"_23":24,"_25":110},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":112,"_23":29,"_25":113},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":115,"_23":33,"_25":116},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":118,"_23":37,"_25":119},"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.

",[67,90,98],{"_14":15,"_16":15,"_17":123,"_19":124,"_38":15,"_39":137,"_65":138},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[125,128,131,134],{"_17":126,"_23":24,"_25":127},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":129,"_23":29,"_25":130},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":132,"_23":33,"_25":133},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":135,"_23":37,"_25":136},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[67,90,98],{"_14":15,"_16":15,"_17":140,"_19":141,"_38":15,"_39":157,"_65":158},"996628fc-4ac3-4821-86bd-839f86a97a6d",[142,145,148,151,154],{"_17":143,"_23":24,"_25":144},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":146,"_23":29,"_25":147},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":149,"_23":33,"_25":150},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":152,"_23":37,"_25":153},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":155,"_23":62,"_25":156},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[67,90,98],{"_14":15,"_16":15,"_17":160,"_19":161,"_38":15,"_39":177,"_65":178},"c478a46c-46a8-4942-ae14-2e79def3dda2",[162,165,168,171,174],{"_17":163,"_23":24,"_25":164},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":166,"_23":29,"_25":167},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":169,"_23":33,"_25":170},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":172,"_23":37,"_25":173},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":175,"_23":62,"_25":176},"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????",[67,90,98],[67,90,98],"tagsTree",[182],{"_17":76,"_69":99,"_71":100,"_73":74,"_75":-5,"_77":101,"_79":101,"_80":102,"_88":100,"_183":184},"children",[185],{"_17":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":78,"_80":81,"_88":89,"_183":186},[187],{"_17":91,"_69":92,"_71":93,"_73":74,"_75":68,"_77":94,"_79":94,"_80":95,"_88":97,"_183":188},[],"actionData","errors"]

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