[{"_1":2,"_204":-5,"_205":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/e845b5e9-083a-4261-b3cc-3f65b2966061","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":192,"_193":194},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_41":17,"_42":43,"_44":45},"correctOptionId","","difficulty","id","e845b5e9-083a-4261-b3cc-3f65b2966061","options",[23,29,33,37],{"_19":24,"_25":26,"_27":28},"f542186f-f85b-4dc3-99f5-abd2b5fb7e35","label","A","text","16",{"_19":30,"_25":31,"_27":32},"9d429057-2e08-4b95-9b55-d4393c4f65ed","B","24",{"_19":34,"_25":35,"_27":36},"a38f1ec9-13de-4bb9-9cd9-b5f93f518286","C","18",{"_19":38,"_25":39,"_27":40},"72c90ed5-915e-4499-a3c7-b6de769f0eb5","D","12","solution_explanation","statement","En la siguiente estructura, ¿cuántas rutas distintas hay desde el punto P hasta el punto R pasando siempre por el punto Q, si solo se puede ir por las direcciones frente, izquierdo o abajo?","status","pending_classification","relatedVideos",[],"similarQuestions",[50,118,135,152,172],{"_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",[72,95,104,111],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","name","Engenharia Civil","alias","engenharia-civil","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",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_19":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":103},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_87":101,"_89":90,"_91":102},5,8852,"estruturas-1",{"_19":105,"_74":106,"_76":107,"_78":79,"_80":96,"_82":108,"_84":108,"_85":109,"_93":107},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","Análise Estrutural","analise-estrutural","2025-04-29T04:00:06.9766+00:00",{"_87":90,"_89":90,"_91":110},4694,{"_19":81,"_74":112,"_76":113,"_78":79,"_80":-5,"_82":114,"_84":114,"_85":115,"_93":113},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":116,"_89":90,"_91":117},29,351586,{"_16":17,"_18":17,"_19":119,"_21":120,"_41":17,"_42":133,"_70":134},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[121,124,127,130],{"_19":122,"_25":26,"_27":123},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":125,"_25":31,"_27":126},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":128,"_25":35,"_27":129},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":131,"_25":39,"_27":132},"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.

",[72,95,104,111],{"_16":17,"_18":17,"_19":136,"_21":137,"_41":17,"_42":150,"_70":151},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[138,141,144,147],{"_19":139,"_25":26,"_27":140},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":142,"_25":31,"_27":143},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":145,"_25":35,"_27":146},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":148,"_25":39,"_27":149},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[72,95,104,111],{"_16":17,"_18":17,"_19":153,"_21":154,"_41":17,"_42":170,"_70":171},"996628fc-4ac3-4821-86bd-839f86a97a6d",[155,158,161,164,167],{"_19":156,"_25":26,"_27":157},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":159,"_25":31,"_27":160},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":162,"_25":35,"_27":163},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":165,"_25":39,"_27":166},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":168,"_25":67,"_27":169},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,95,104,111],{"_16":17,"_18":17,"_19":173,"_21":174,"_41":17,"_42":190,"_70":191},"c478a46c-46a8-4942-ae14-2e79def3dda2",[175,178,181,184,187],{"_19":176,"_25":26,"_27":177},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":179,"_25":31,"_27":180},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":182,"_25":35,"_27":183},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":185,"_25":39,"_27":186},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":188,"_25":67,"_27":189},"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????",[72,95,104,111],[72,95,104,111],"tagsTree",[195],{"_19":81,"_74":112,"_76":113,"_78":79,"_80":-5,"_82":114,"_84":114,"_85":115,"_93":113,"_196":197},"children",[198],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":94,"_196":199},[200],{"_19":96,"_74":97,"_76":98,"_78":79,"_80":73,"_82":99,"_84":99,"_85":100,"_93":103,"_196":201},[202],{"_19":105,"_74":106,"_76":107,"_78":79,"_80":96,"_82":108,"_84":108,"_85":109,"_93":107,"_196":203},[],"actionData","errors"]

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