[{"_1":2,"_207":-5,"_208":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/eb30b570-32b8-41ba-af31-568064332609","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_52":53,"_73":195,"_196":197},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":19,"_20":21,"_22":23,"_45":19,"_46":47,"_48":49},"correctOptionId","b86d9cdd-b441-4291-8799-3376f1e2a031","difficulty","","id","eb30b570-32b8-41ba-af31-568064332609","options",[24,30,34,37,41],{"_20":25,"_26":27,"_28":29},"92796732-ef68-4f15-9c3a-cc16a447149e","label","A","text","R$ 7,50",{"_20":31,"_26":32,"_28":33},"cb6d915f-be3b-49c7-ac57-753166fce683","B","R$ 8,00",{"_20":17,"_26":35,"_28":36},"C","R$ 8,75",{"_20":38,"_26":39,"_28":40},"4ea8cc21-51f7-4d43-a26c-4b867262b2ea","D","R$ 8,25",{"_20":42,"_26":43,"_28":44},"c8da7d72-666b-41a1-9f89-1de9522aa156","E","R$ 8,55","solution_explanation","statement","

Um rapaz consumiu 3 sucos de laranja em um bar. Se cada suco custa R$ 2,50 e a taxa de serviço é de 10\text{%}, qual o valor final da conta?

","status","has_issues","relatedVideos",[],"similarQuestions",[54,121,138,155,175],{"_16":19,"_18":19,"_20":55,"_22":56,"_45":19,"_46":72,"_73":74},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[57,60,63,66,69],{"_20":58,"_26":27,"_28":59},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":61,"_26":32,"_28":62},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":64,"_26":35,"_28":65},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":67,"_26":39,"_28":68},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":70,"_26":43,"_28":71},"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",[75,98,107,114],{"_20":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97},"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",{"_90":91,"_92":93,"_94":95},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_20":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":106},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_90":104,"_92":93,"_94":105},5,8852,"estruturas-1",{"_20":108,"_77":109,"_79":110,"_81":82,"_83":99,"_85":111,"_87":111,"_88":112,"_96":110},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","Análise Estrutural","analise-estrutural","2025-04-29T04:00:06.9766+00:00",{"_90":93,"_92":93,"_94":113},4694,{"_20":84,"_77":115,"_79":116,"_81":82,"_83":-5,"_85":117,"_87":117,"_88":118,"_96":116},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_90":119,"_92":93,"_94":120},29,351586,{"_16":19,"_18":19,"_20":122,"_22":123,"_45":19,"_46":136,"_73":137},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[124,127,130,133],{"_20":125,"_26":27,"_28":126},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":128,"_26":32,"_28":129},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":131,"_26":35,"_28":132},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":134,"_26":39,"_28":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.

",[75,98,107,114],{"_16":19,"_18":19,"_20":139,"_22":140,"_45":19,"_46":153,"_73":154},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[141,144,147,150],{"_20":142,"_26":27,"_28":143},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":145,"_26":32,"_28":146},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":148,"_26":35,"_28":149},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":151,"_26":39,"_28":152},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[75,98,107,114],{"_16":19,"_18":19,"_20":156,"_22":157,"_45":19,"_46":173,"_73":174},"996628fc-4ac3-4821-86bd-839f86a97a6d",[158,161,164,167,170],{"_20":159,"_26":27,"_28":160},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":162,"_26":32,"_28":163},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":165,"_26":35,"_28":166},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":168,"_26":39,"_28":169},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":171,"_26":43,"_28":172},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[75,98,107,114],{"_16":19,"_18":19,"_20":176,"_22":177,"_45":19,"_46":193,"_73":194},"c478a46c-46a8-4942-ae14-2e79def3dda2",[178,181,184,187,190],{"_20":179,"_26":27,"_28":180},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":182,"_26":32,"_28":183},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":185,"_26":35,"_28":186},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":188,"_26":39,"_28":189},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":191,"_26":43,"_28":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????",[75,98,107,114],[75,98,107,114],"tagsTree",[198],{"_20":84,"_77":115,"_79":116,"_81":82,"_83":-5,"_85":117,"_87":117,"_88":118,"_96":116,"_199":200},"children",[201],{"_20":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97,"_199":202},[203],{"_20":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":106,"_199":204},[205],{"_20":108,"_77":109,"_79":110,"_81":82,"_83":99,"_85":111,"_87":111,"_88":112,"_96":110,"_199":206},[],"actionData","errors"]

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