[{"_1":2,"_204":-5,"_205":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/f57ba443-5387-4659-83f7-2cbedd23aa14","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_89":90,"_91":92,"_28":175,"_191":192,"_200":201,"_202":203},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_67":68,"_83":19,"_84":85,"_86":87,"_88":14},"correctOptionId","","difficulty","id","f57ba443-5387-4659-83f7-2cbedd23aa14","metadata",{"_25":26,"_63":64,"_65":66},"pd",{"_27":-5,"_28":29,"_44":45,"_50":51,"_52":53,"_54":55,"_56":57,"_58":55,"_59":60,"_61":62},"area","tags",[30,36,40],{"_21":31,"_32":33,"_34":35},3545,"name","Aritmética","alias","aritmetica",{"_21":37,"_32":38,"_34":39},85912,"matemáticas","matematicas",{"_21":41,"_32":42,"_34":43},1304147,"EJERCICIOS RESUELTOS","ejercicios-resueltos","subjects",[46],{"_21":47,"_32":48,"_34":49},685549,"Mecânica Clássica","mecanica-classica","materialId","122503206","answerCount",1,"isIndexable",true,"mainSubject",{"_21":47,"_32":48,"_34":49},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122567304","options",[69,75,79],{"_21":70,"_71":72,"_73":74},"007c8829-e14d-4689-821a-19ffeb605f03","label","A","text","49, 14, 33, 83, 4067, 462, 1162, 4529, 1162, 647, 166",{"_21":76,"_71":77,"_73":78},"ce03bb0b-bfe5-46d3-9341-7f2cdf26aaf6","B","71, 57, 41, 86, 6106, 2337, 4902, 8443, 4902",{"_21":80,"_71":81,"_73":82},"be2bf299-5a3c-4327-987b-df0edca04ff2","C","25, 96, 52, 56, 1400, 4992, 5376, 6392, 5376, 799, 672","solution_explanation","statement","

Qual é a sequência correta de obras literárias brasileiras do período colonial?

","status","pending_classification","hasRelatedVideo","relatedVideos",[],"similarQuestions",[93,136,154],{"_18":94,"_20":19,"_21":95,"_67":96,"_83":113,"_84":114,"_28":115},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[97,100,103,106,110],{"_21":98,"_71":72,"_73":99},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":101,"_71":77,"_73":102},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":104,"_71":81,"_73":105},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":107,"_71":108,"_73":109},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":94,"_71":111,"_73":112},"E","y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

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

",[116],{"_21":117,"_32":118,"_34":119,"_120":121,"_122":123,"_124":125,"_126":125,"_23":127,"_134":135},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","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",{"_128":129,"_130":131,"_132":133},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_18":137,"_20":19,"_21":138,"_67":139,"_83":151,"_84":152,"_28":153},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[140,143,146,148],{"_21":141,"_71":72,"_73":142},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":144,"_71":77,"_73":145},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":137,"_71":81,"_73":147},"

Verdadeiro, falso, verdadeiro

",{"_21":149,"_71":108,"_73":150},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

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

",[116],{"_18":155,"_20":19,"_21":156,"_67":157,"_83":172,"_84":173,"_28":174},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[158,161,164,166,169],{"_21":159,"_71":72,"_73":160},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":162,"_71":77,"_73":163},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":155,"_71":81,"_73":165},"Indeterminado",{"_21":167,"_71":108,"_73":168},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":170,"_71":111,"_73":171},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","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????",[116],[116,176,184],{"_21":177,"_32":178,"_34":179,"_120":121,"_122":117,"_124":180,"_126":180,"_23":181,"_134":183},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_128":129,"_130":131,"_132":182},25741,"mecanica-3",{"_21":123,"_32":185,"_34":186,"_120":121,"_122":-5,"_124":187,"_126":187,"_23":188,"_134":186},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_128":189,"_130":131,"_132":190},29,351586,"tagsTree",[193],{"_21":123,"_32":185,"_34":186,"_120":121,"_122":-5,"_124":187,"_126":187,"_23":188,"_134":186,"_194":195},"children",[196],{"_21":117,"_32":118,"_34":119,"_120":121,"_122":123,"_124":125,"_126":125,"_23":127,"_134":135,"_194":197},[198],{"_21":177,"_32":178,"_34":179,"_120":121,"_122":117,"_124":180,"_126":180,"_23":181,"_134":183,"_194":199},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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