[{"_1":2,"_211":-5,"_212":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fa3f791f-027c-4cfd-903f-c85ca44ec3fb","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":197,"_198":199},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_43":15,"_44":45},"correctOptionId","","difficulty","id","fa3f791f-027c-4cfd-903f-c85ca44ec3fb","options",[21,27,31,35,39],{"_17":22,"_23":24,"_25":26},"c7ac59f0-6f2b-45fd-ba91-fbef740caeb7","label","A","text","20 \\, \text{m}",{"_17":28,"_23":29,"_25":30},"9f72f579-4376-4616-9aa3-ab1bdd86363f","B","40 \\, \text{m}",{"_17":32,"_23":33,"_25":34},"b07b6570-7045-45ef-9aa8-9e1ee2e5b690","C","10 \\, \text{m}",{"_17":36,"_23":37,"_25":38},"d717539b-5777-4d68-8d3b-5b4237a92a94","D","30 \\, \text{m}",{"_17":40,"_23":41,"_25":42},"9d616877-d0b9-4050-ab66-e2460679d695","E","50 \\, \text{m}","solution_explanation","statement","

Questão 3: Um objeto é lançado verticalmente para cima com uma velocidade inicial de 20 \\, \text{m/s}. Desprezando a resistência do ar, qual será a altura máxima alcançada pelo objeto?

","relatedVideos",[],"similarQuestions",[50,123,140,157,177],{"_14":15,"_16":15,"_17":51,"_19":52,"_43":15,"_44":68,"_69":70},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_17":54,"_23":24,"_25":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":57,"_23":29,"_25":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":60,"_23":33,"_25":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":63,"_23":37,"_25":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":66,"_23":41,"_25":67},"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",[71,94,102,110,116],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":93},"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",{"_86":87,"_88":89,"_90":91},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_17":95,"_73":96,"_75":97,"_77":78,"_79":72,"_81":98,"_83":98,"_84":99,"_92":101},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_86":87,"_88":89,"_90":100},25741,"mecanica-3",{"_17":103,"_73":104,"_75":105,"_77":78,"_79":-5,"_81":106,"_83":106,"_84":107,"_92":105},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_86":108,"_88":89,"_90":109},18,135489,{"_17":111,"_73":96,"_75":97,"_77":78,"_79":103,"_81":82,"_83":82,"_84":112,"_92":115},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_86":113,"_88":89,"_90":114},10,19948,"mecanica-2",{"_17":80,"_73":117,"_75":118,"_77":78,"_79":-5,"_81":119,"_83":119,"_84":120,"_92":118},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_86":121,"_88":89,"_90":122},29,351586,{"_14":15,"_16":15,"_17":124,"_19":125,"_43":15,"_44":138,"_69":139},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[126,129,132,135],{"_17":127,"_23":24,"_25":128},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":130,"_23":29,"_25":131},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":133,"_23":33,"_25":134},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":136,"_23":37,"_25":137},"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.

",[71,94,102,110,116],{"_14":15,"_16":15,"_17":141,"_19":142,"_43":15,"_44":155,"_69":156},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[143,146,149,152],{"_17":144,"_23":24,"_25":145},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":147,"_23":29,"_25":148},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":150,"_23":33,"_25":151},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":153,"_23":37,"_25":154},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[71,94,102,110,116],{"_14":15,"_16":15,"_17":158,"_19":159,"_43":15,"_44":175,"_69":176},"996628fc-4ac3-4821-86bd-839f86a97a6d",[160,163,166,169,172],{"_17":161,"_23":24,"_25":162},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":164,"_23":29,"_25":165},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":167,"_23":33,"_25":168},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":170,"_23":37,"_25":171},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":173,"_23":41,"_25":174},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[71,94,102,110,116],{"_14":15,"_16":15,"_17":178,"_19":179,"_43":15,"_44":195,"_69":196},"c478a46c-46a8-4942-ae14-2e79def3dda2",[180,183,186,189,192],{"_17":181,"_23":24,"_25":182},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":184,"_23":29,"_25":185},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":187,"_23":33,"_25":188},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":190,"_23":37,"_25":191},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":193,"_23":41,"_25":194},"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????",[71,94,102,110,116],[71,94,102,110,116],"tagsTree",[200,205],{"_17":103,"_73":104,"_75":105,"_77":78,"_79":-5,"_81":106,"_83":106,"_84":107,"_92":105,"_201":202},"children",[203],{"_17":111,"_73":96,"_75":97,"_77":78,"_79":103,"_81":82,"_83":82,"_84":112,"_92":115,"_201":204},[],{"_17":80,"_73":117,"_75":118,"_77":78,"_79":-5,"_81":119,"_83":119,"_84":120,"_92":118,"_201":206},[207],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":93,"_201":208},[209],{"_17":95,"_73":96,"_75":97,"_77":78,"_79":72,"_81":98,"_83":98,"_84":99,"_92":101,"_201":210},[],"actionData","errors"]

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