[{"_1":2,"_286":-5,"_287":-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/dee4da5f-03d9-4846-a377-9403ca0deea6","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_186":187,"_52":258,"_274":275,"_282":283,"_284":285},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_97":43,"_98":99,"_100":101,"_102":16},"correctOptionId","e3f3f0ec-d876-4107-9917-8a90d9f1a0df","difficulty","","id","dee4da5f-03d9-4846-a377-9403ca0deea6","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},672071,"name","Mecânica","alias","mecanica","materialId","136201762","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","136201773","options",[80,86,90,93],{"_44":81,"_82":83,"_84":85},"0062031c-3628-42b6-a7f9-56d50bf303ad","label","A","text","Varia conforme velocidade inicial do objeto.",{"_44":87,"_82":88,"_84":89},"12766d4e-7f76-4f01-a142-a4fda840b10b","B","Diminui.",{"_44":41,"_82":91,"_84":92},"C","Permanece constante.",{"_44":94,"_82":95,"_84":96},"3a0e470d-21ce-4390-9794-e5326bd310b5","D","Aumenta.","solution_explanation","statement","Com base no exposto e no experimento realizado, fica evidenciada que a aceleração de um objeto em queda livre:","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_52":141,"_167":168,"_185":142},"content",{"_44":108,"_58":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_46":116,"_119":120,"_121":120,"_122":-5,"_123":124},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - 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3y = 0",{"_44":196,"_82":88,"_84":197},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":199,"_82":91,"_84":200},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":202,"_82":95,"_84":203},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":189,"_82":205,"_84":206},"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

",[210],{"_44":211,"_58":212,"_60":213,"_146":147,"_148":214,"_119":161,"_121":161,"_46":215,"_123":218},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":216,"_153":154,"_155":217},5,30614,"engenharia-mecatronica-1",{"_40":220,"_42":43,"_44":221,"_78":222,"_97":234,"_98":235,"_52":236},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[223,226,229,231],{"_44":224,"_82":83,"_84":225},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":227,"_82":88,"_84":228},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":220,"_82":91,"_84":230},"

Verdadeiro, falso, verdadeiro

",{"_44":232,"_82":95,"_84":233},"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?

",[210],{"_40":238,"_42":43,"_44":239,"_78":240,"_97":255,"_98":256,"_52":257},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[241,244,247,249,252],{"_44":242,"_82":83,"_84":243},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":245,"_82":88,"_84":246},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":238,"_82":91,"_84":248},"Indeterminado",{"_44":250,"_82":95,"_84":251},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":253,"_82":205,"_84":254},"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????",[210],[210,259,265,266,267],{"_44":260,"_58":59,"_60":61,"_146":147,"_148":211,"_119":261,"_121":261,"_46":262,"_123":264},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_151":216,"_153":154,"_155":263},25741,"mecanica-3",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_46":150,"_123":145},{"_44":160,"_58":59,"_60":61,"_146":147,"_148":143,"_119":161,"_121":161,"_46":162,"_123":165},{"_44":214,"_58":268,"_60":269,"_146":147,"_148":-5,"_119":270,"_121":270,"_46":271,"_123":269},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":272,"_153":154,"_155":273},29,351586,"tagsTree",[142,276],{"_44":214,"_58":268,"_60":269,"_146":147,"_148":-5,"_119":270,"_121":270,"_46":271,"_123":269,"_157":277},[278],{"_44":211,"_58":212,"_60":213,"_146":147,"_148":214,"_119":161,"_121":161,"_46":215,"_123":218,"_157":279},[280],{"_44":260,"_58":59,"_60":61,"_146":147,"_148":211,"_119":261,"_121":261,"_46":262,"_123":264,"_157":281},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários