[{"_1":2,"_212":-5,"_213":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fbee26e3-022f-4a47-b679-bc7426a6aa78","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":198,"_199":200},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_41":17,"_42":43,"_44":45},"correctOptionId","","difficulty","id","fbee26e3-022f-4a47-b679-bc7426a6aa78","options",[23,29,33,37],{"_19":24,"_25":26,"_27":28},"79c6fd54-9aec-48ff-b5be-f7a87357eb4f","label","A","text","70 N/m.",{"_19":30,"_25":31,"_27":32},"f55d14ad-6885-46be-a083-bc33d7550385","B","7,5 N/m.",{"_19":34,"_25":35,"_27":36},"abe0d3c5-de7e-4c32-bbd4-6a63dc3f1475","C","40 N/m.",{"_19":38,"_25":39,"_27":40},"77866a42-81ac-4b26-b779-8608bd039409","D","46,67 N/m.","solution_explanation","statement","

A figura em anexo mostra uma massa conectada a quatro molas. Se o valor de k for igual a 10 \\, \text{N/m}, determine a constante de mola equivalente desse sistema e assinale a alternativa:

","status","has_issues","relatedVideos",[],"similarQuestions",[50,124,141,158,178],{"_16":17,"_18":17,"_19":51,"_21":52,"_41":17,"_42":69,"_70":71},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_19":54,"_25":26,"_27":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":57,"_25":31,"_27":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":60,"_25":35,"_27":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":63,"_25":39,"_27":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":66,"_25":67,"_27":68},"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",[72,95,103,111,117],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94},"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",{"_87":88,"_89":90,"_91":92},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_19":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":102},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_87":88,"_89":90,"_91":101},25741,"mecanica-3",{"_19":104,"_74":105,"_76":106,"_78":79,"_80":-5,"_82":107,"_84":107,"_85":108,"_93":106},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_87":109,"_89":90,"_91":110},18,135489,{"_19":112,"_74":97,"_76":98,"_78":79,"_80":104,"_82":83,"_84":83,"_85":113,"_93":116},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_87":114,"_89":90,"_91":115},10,19948,"mecanica-2",{"_19":81,"_74":118,"_76":119,"_78":79,"_80":-5,"_82":120,"_84":120,"_85":121,"_93":119},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":122,"_89":90,"_91":123},29,351586,{"_16":17,"_18":17,"_19":125,"_21":126,"_41":17,"_42":139,"_70":140},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[127,130,133,136],{"_19":128,"_25":26,"_27":129},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":131,"_25":31,"_27":132},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":134,"_25":35,"_27":135},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":137,"_25":39,"_27":138},"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.

",[72,95,103,111,117],{"_16":17,"_18":17,"_19":142,"_21":143,"_41":17,"_42":156,"_70":157},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[144,147,150,153],{"_19":145,"_25":26,"_27":146},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":148,"_25":31,"_27":149},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":151,"_25":35,"_27":152},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":154,"_25":39,"_27":155},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[72,95,103,111,117],{"_16":17,"_18":17,"_19":159,"_21":160,"_41":17,"_42":176,"_70":177},"996628fc-4ac3-4821-86bd-839f86a97a6d",[161,164,167,170,173],{"_19":162,"_25":26,"_27":163},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":165,"_25":31,"_27":166},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":168,"_25":35,"_27":169},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":171,"_25":39,"_27":172},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":174,"_25":67,"_27":175},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,95,103,111,117],{"_16":17,"_18":17,"_19":179,"_21":180,"_41":17,"_42":196,"_70":197},"c478a46c-46a8-4942-ae14-2e79def3dda2",[181,184,187,190,193],{"_19":182,"_25":26,"_27":183},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":185,"_25":31,"_27":186},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":188,"_25":35,"_27":189},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":191,"_25":39,"_27":192},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":194,"_25":67,"_27":195},"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????",[72,95,103,111,117],[72,95,103,111,117],"tagsTree",[201,206],{"_19":104,"_74":105,"_76":106,"_78":79,"_80":-5,"_82":107,"_84":107,"_85":108,"_93":106,"_202":203},"children",[204],{"_19":112,"_74":97,"_76":98,"_78":79,"_80":104,"_82":83,"_84":83,"_85":113,"_93":116,"_202":205},[],{"_19":81,"_74":118,"_76":119,"_78":79,"_80":-5,"_82":120,"_84":120,"_85":121,"_93":119,"_202":207},[208],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94,"_202":209},[210],{"_19":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":102,"_202":211},[],"actionData","errors"]

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