[{"_1":2,"_209":-5,"_210":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fb2d9666-d980-440a-a0ee-4ee0112ecb8a","user","pages/questions/show/index",{"_10":11,"_12":13,"_44":45,"_46":47,"_67":195,"_196":197},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_41":15,"_42":43},"correctOptionId","","difficulty","id","fb2d9666-d980-440a-a0ee-4ee0112ecb8a","options",[21,27,31,35,38],{"_17":22,"_23":24,"_25":26},"2afb0d64-17ec-4f77-9ffb-eada56456cce","label","A","text","2 \\, s ; rad/s.",{"_17":28,"_23":29,"_25":30},"2d2dc191-e68b-43ca-adc8-d3e9f4351917","B","3 \\, s ; rad/s.",{"_17":32,"_23":33,"_25":34},"c3edefb5-68ec-4696-a20d-7e5de62b98af","C","4 \\, s ; rad/s.",{"_17":36,"_23":37,"_25":26},"6ece28c8-2e61-4220-adc4-f7bc029ba8c5","D",{"_17":39,"_23":40,"_25":30},"baa2ef1a-6662-4a6e-9b7f-822bff87f1c6","E","solution_explanation","statement","Marque a alternativa que apresenta, respectivamente, o período e a velocidade angular do movimento.","relatedVideos",[],"similarQuestions",[48,121,138,155,175],{"_14":15,"_16":15,"_17":49,"_19":50,"_41":15,"_42":66,"_67":68},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[51,54,57,60,63],{"_17":52,"_23":24,"_25":53},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":55,"_23":29,"_25":56},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":58,"_23":33,"_25":59},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":61,"_23":37,"_25":62},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":64,"_23":40,"_25":65},"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",[69,92,100,108,114],{"_17":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":91},"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",{"_84":85,"_86":87,"_88":89},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_17":93,"_71":94,"_73":95,"_75":76,"_77":70,"_79":96,"_81":96,"_82":97,"_90":99},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_84":85,"_86":87,"_88":98},25741,"mecanica-3",{"_17":101,"_71":102,"_73":103,"_75":76,"_77":-5,"_79":104,"_81":104,"_82":105,"_90":103},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_84":106,"_86":87,"_88":107},18,135489,{"_17":109,"_71":94,"_73":95,"_75":76,"_77":101,"_79":80,"_81":80,"_82":110,"_90":113},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_84":111,"_86":87,"_88":112},10,19948,"mecanica-2",{"_17":78,"_71":115,"_73":116,"_75":76,"_77":-5,"_79":117,"_81":117,"_82":118,"_90":116},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_84":119,"_86":87,"_88":120},29,351586,{"_14":15,"_16":15,"_17":122,"_19":123,"_41":15,"_42":136,"_67":137},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[124,127,130,133],{"_17":125,"_23":24,"_25":126},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":128,"_23":29,"_25":129},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":131,"_23":33,"_25":132},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":134,"_23":37,"_25":135},"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.

",[69,92,100,108,114],{"_14":15,"_16":15,"_17":139,"_19":140,"_41":15,"_42":153,"_67":154},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[141,144,147,150],{"_17":142,"_23":24,"_25":143},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":145,"_23":29,"_25":146},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":148,"_23":33,"_25":149},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":151,"_23":37,"_25":152},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[69,92,100,108,114],{"_14":15,"_16":15,"_17":156,"_19":157,"_41":15,"_42":173,"_67":174},"996628fc-4ac3-4821-86bd-839f86a97a6d",[158,161,164,167,170],{"_17":159,"_23":24,"_25":160},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":162,"_23":29,"_25":163},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":165,"_23":33,"_25":166},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":168,"_23":37,"_25":169},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":171,"_23":40,"_25":172},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[69,92,100,108,114],{"_14":15,"_16":15,"_17":176,"_19":177,"_41":15,"_42":193,"_67":194},"c478a46c-46a8-4942-ae14-2e79def3dda2",[178,181,184,187,190],{"_17":179,"_23":24,"_25":180},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":182,"_23":29,"_25":183},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":185,"_23":33,"_25":186},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":188,"_23":37,"_25":189},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":191,"_23":40,"_25":192},"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????",[69,92,100,108,114],[69,92,100,108,114],"tagsTree",[198,203],{"_17":101,"_71":102,"_73":103,"_75":76,"_77":-5,"_79":104,"_81":104,"_82":105,"_90":103,"_199":200},"children",[201],{"_17":109,"_71":94,"_73":95,"_75":76,"_77":101,"_79":80,"_81":80,"_82":110,"_90":113,"_199":202},[],{"_17":78,"_71":115,"_73":116,"_75":76,"_77":-5,"_79":117,"_81":117,"_82":118,"_90":116,"_199":204},[205],{"_17":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":91,"_199":206},[207],{"_17":93,"_71":94,"_73":95,"_75":76,"_77":70,"_79":96,"_81":96,"_82":97,"_90":99,"_199":208},[],"actionData","errors"]

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