[{"_1":2,"_204":-5,"_205":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/dff2b21e-529a-41a5-9db7-c2aa158ccbf7","user","pages/questions/show/index",{"_10":11,"_12":13,"_48":49,"_50":51,"_71":192,"_193":194},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45,"_46":47},"correctOptionId","","difficulty","id","dff2b21e-529a-41a5-9db7-c2aa158ccbf7","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"8d79d4d0-5994-4ec9-bb7b-97403a66221b","label","A","text","V=40-4t",{"_17":28,"_23":29,"_25":30},"e42cf02e-5f03-4f43-b796-fc10c05a1ae6","B","V=40+4t",{"_17":32,"_23":33,"_25":34},"8a645e94-c7c8-4bed-bb00-70c63a657e34","C","V=40t-4",{"_17":36,"_23":37,"_25":38},"e1d64f76-15e2-42b6-a894-6192098934cc","D","V=40t+4",{"_17":40,"_23":41,"_25":42},"d4f1267d-f257-4c5c-8b94-74a9586cc5b8","E","V=44t","solution_explanation","statement","

Um tanque contém, inicialmente, 40 litros de água e é esvaziado à taxa constante de 4 litros por hora. A equação que relaciona o volume V (em litros) de água no interior do tanque em função do tempo t (em horas) é dada por:

","status","has_issues","relatedVideos",[],"similarQuestions",[52,118,135,152,172],{"_14":15,"_16":15,"_17":53,"_19":54,"_43":15,"_44":70,"_71":72},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[55,58,61,64,67],{"_17":56,"_23":24,"_25":57},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":59,"_23":29,"_25":60},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":62,"_23":33,"_25":63},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":65,"_23":37,"_25":66},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":68,"_23":41,"_25":69},"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",[73,95,103,111],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78},"6516bbbd-f2a3-4710-8382-702240b17836","name","Mecânica na Engenharia de Petróleo","alias","mecanica-na-engenharia-de-petroleo","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","b787e438-0ab3-454c-ab43-5d3d14c2720d","created_at","2025-04-29T03:44:35.328997+00:00","updated_at","metadata",{"_88":89,"_90":91,"_92":93},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":96,"_75":97,"_77":98,"_79":80,"_81":74,"_83":99,"_85":99,"_86":100,"_94":102},"8c444991-e4be-4bd9-bc90-7d0f27eb9a2f","Mecânica dos Fluidos na Engenharia de Petróleo","mecanica-dos-fluidos-na-engenharia-de-petroleo","2025-04-29T04:00:14.680867+00:00",{"_88":91,"_90":91,"_92":101},329,"mecanica-dos-fluidos-na-engenharia-de-petroleo-1",{"_17":82,"_75":104,"_77":105,"_79":80,"_81":106,"_83":107,"_85":107,"_86":108,"_94":110},"Engenharia de Petróleo","engenharia-de-petroleo","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_88":109,"_90":91,"_92":93},5,"engenharia-de-petroleo-1",{"_17":106,"_75":112,"_77":113,"_79":80,"_81":-5,"_83":114,"_85":114,"_86":115,"_94":113},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_88":116,"_90":91,"_92":117},29,351586,{"_14":15,"_16":15,"_17":119,"_19":120,"_43":15,"_44":133,"_71":134},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[121,124,127,130],{"_17":122,"_23":24,"_25":123},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":125,"_23":29,"_25":126},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":128,"_23":33,"_25":129},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":131,"_23":37,"_25":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.

",[73,95,103,111],{"_14":15,"_16":15,"_17":136,"_19":137,"_43":15,"_44":150,"_71":151},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[138,141,144,147],{"_17":139,"_23":24,"_25":140},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":142,"_23":29,"_25":143},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":145,"_23":33,"_25":146},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":148,"_23":37,"_25":149},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[73,95,103,111],{"_14":15,"_16":15,"_17":153,"_19":154,"_43":15,"_44":170,"_71":171},"996628fc-4ac3-4821-86bd-839f86a97a6d",[155,158,161,164,167],{"_17":156,"_23":24,"_25":157},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":159,"_23":29,"_25":160},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":162,"_23":33,"_25":163},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":165,"_23":37,"_25":166},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":168,"_23":41,"_25":169},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[73,95,103,111],{"_14":15,"_16":15,"_17":173,"_19":174,"_43":15,"_44":190,"_71":191},"c478a46c-46a8-4942-ae14-2e79def3dda2",[175,178,181,184,187],{"_17":176,"_23":24,"_25":177},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":179,"_23":29,"_25":180},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":182,"_23":33,"_25":183},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":185,"_23":37,"_25":186},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":188,"_23":41,"_25":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????",[73,95,103,111],[73,95,103,111],"tagsTree",[195],{"_17":106,"_75":112,"_77":113,"_79":80,"_81":-5,"_83":114,"_85":114,"_86":115,"_94":113,"_196":197},"children",[198],{"_17":82,"_75":104,"_77":105,"_79":80,"_81":106,"_83":107,"_85":107,"_86":108,"_94":110,"_196":199},[200],{"_17":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":84,"_86":87,"_94":78,"_196":201},[202],{"_17":96,"_75":97,"_77":98,"_79":80,"_81":74,"_83":99,"_85":99,"_86":100,"_94":102,"_196":203},[],"actionData","errors"]

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