[{"_1":2,"_194":-5,"_195":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fc5cff8e-4752-4cc9-a2a2-555d673cd161","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":184,"_185":186},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_41":17,"_42":43,"_44":45},"correctOptionId","","difficulty","id","fc5cff8e-4752-4cc9-a2a2-555d673cd161","options",[23,29,33,37],{"_19":24,"_25":26,"_27":28},"ff8a89a5-04ea-46c3-b67d-e05c51082887","label","A","text","\\frac{Mg}{4}",{"_19":30,"_25":31,"_27":32},"9ae391ce-d20a-444f-abda-a340d592f9f4","B","Mg",{"_19":34,"_25":35,"_27":36},"075fe4fa-3d0a-4ea9-bdbb-f01ac8daa2d4","C","\\frac{Mg}{3}",{"_19":38,"_25":39,"_27":40},"1330ca56-ac9e-4c93-bb67-7cdf0802f2a1","D","\\frac{Mg}{2}","solution_explanation","statement","

Um sistema de duas polias ideais (massas desprezíveis e sem atrito) está montado sob um suporte fixo, conforme figura abaixo. Uma massa M está presa ao eixo da polia 2 e o sistema encontra-se sob a ação do campo gravitacional g. Todos os fios possuem massas desprezíveis. O valor da força F que mantém o sistema em equilíbrio estático é

","status","pending_classification","relatedVideos",[],"similarQuestions",[50,110,127,144,164],{"_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],{"_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":81,"_74":104,"_76":105,"_78":79,"_80":-5,"_82":106,"_84":106,"_85":107,"_93":105},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":108,"_89":90,"_91":109},29,351586,{"_16":17,"_18":17,"_19":111,"_21":112,"_41":17,"_42":125,"_70":126},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[113,116,119,122],{"_19":114,"_25":26,"_27":115},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":117,"_25":31,"_27":118},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":120,"_25":35,"_27":121},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":123,"_25":39,"_27":124},"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],{"_16":17,"_18":17,"_19":128,"_21":129,"_41":17,"_42":142,"_70":143},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[130,133,136,139],{"_19":131,"_25":26,"_27":132},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":134,"_25":31,"_27":135},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":137,"_25":35,"_27":138},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":140,"_25":39,"_27":141},"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],{"_16":17,"_18":17,"_19":145,"_21":146,"_41":17,"_42":162,"_70":163},"996628fc-4ac3-4821-86bd-839f86a97a6d",[147,150,153,156,159],{"_19":148,"_25":26,"_27":149},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":151,"_25":31,"_27":152},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":154,"_25":35,"_27":155},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":157,"_25":39,"_27":158},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":160,"_25":67,"_27":161},"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],{"_16":17,"_18":17,"_19":165,"_21":166,"_41":17,"_42":182,"_70":183},"c478a46c-46a8-4942-ae14-2e79def3dda2",[167,170,173,176,179],{"_19":168,"_25":26,"_27":169},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":171,"_25":31,"_27":172},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":174,"_25":35,"_27":175},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":177,"_25":39,"_27":178},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":180,"_25":67,"_27":181},"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],[72,95,103],"tagsTree",[187],{"_19":81,"_74":104,"_76":105,"_78":79,"_80":-5,"_82":106,"_84":106,"_85":107,"_93":105,"_188":189},"children",[190],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94,"_188":191},[192],{"_19":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":102,"_188":193},[],"actionData","errors"]

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