[{"_1":2,"_205":-5,"_206":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/fc80964b-ac6c-42d5-8c6d-caea834e4ea4","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_105":106,"_51":186,"_194":195,"_201":202,"_203":204},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_97":41,"_98":99,"_100":101,"_102":36},"correctOptionId","","difficulty","id","fc80964b-ac6c-42d5-8c6d-caea834e4ea4","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},1481802,"name","Engenharia Civil","alias","engenharia-civil","materialId","62951697","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","165050571","options",[79,85,89,93],{"_43":80,"_81":82,"_83":84},"d9cc0ec6-d24b-4eaf-8442-5021cdeaa650","label","A","text","He made many mistakes as he did not study for the test;",{"_43":86,"_81":87,"_83":88},"bda043b5-592e-4e46-8f1a-5a9067e69e29","B","He realized his mistakes as he was checking the answers;",{"_43":90,"_81":91,"_83":92},"ca3fc8d5-cb18-47d6-b407-0b83bb51152a","C","Candidates such as this one should be considered for the job;",{"_43":94,"_81":95,"_83":96},"43200521-866a-4cdb-85eb-d3b52bac85c6","D","As he had already passed the exam, all his worries were gone.","solution_explanation","statement",""as" in "as development proceeds" is used in the same way as in:","status","published","hasRelatedVideo","relatedVideos",[],"similarQuestions",[107,147,165],{"_40":108,"_42":41,"_43":109,"_77":110,"_97":126,"_98":127,"_51":128},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[111,114,117,120,123],{"_43":112,"_81":82,"_83":113},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":115,"_81":87,"_83":116},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":118,"_81":91,"_83":119},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":121,"_81":95,"_83":122},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":108,"_81":124,"_83":125},"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

",[129],{"_43":130,"_57":58,"_59":60,"_131":132,"_133":134,"_135":136,"_137":136,"_45":138,"_145":146},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","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",{"_139":140,"_141":142,"_143":144},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_40":148,"_42":41,"_43":149,"_77":150,"_97":162,"_98":163,"_51":164},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[151,154,157,159],{"_43":152,"_81":82,"_83":153},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":155,"_81":87,"_83":156},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":148,"_81":91,"_83":158},"

Verdadeiro, falso, verdadeiro

",{"_43":160,"_81":95,"_83":161},"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?

",[129],{"_40":166,"_42":41,"_43":167,"_77":168,"_97":183,"_98":184,"_51":185},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[169,172,175,177,180],{"_43":170,"_81":82,"_83":171},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":173,"_81":87,"_83":174},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":166,"_81":91,"_83":176},"Indeterminado",{"_43":178,"_81":95,"_83":179},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":181,"_81":124,"_83":182},"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????",[129],[129,187],{"_43":134,"_57":188,"_59":189,"_131":132,"_133":-5,"_135":190,"_137":190,"_45":191,"_145":189},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_139":192,"_141":142,"_143":193},29,351586,"tagsTree",[196],{"_43":134,"_57":188,"_59":189,"_131":132,"_133":-5,"_135":190,"_137":190,"_45":191,"_145":189,"_197":198},"children",[199],{"_43":130,"_57":58,"_59":60,"_131":132,"_133":134,"_135":136,"_137":136,"_45":138,"_145":146,"_197":200},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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