[{"_1":2,"_356":-5,"_357":-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/c99c7902-4c71-4283-a3c6-a40236412a46?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_111":112,"_187":188,"_51":258,"_328":329,"_352":353,"_354":355},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_81":82,"_105":41,"_106":107,"_108":109,"_110":16},"correctOptionId","","difficulty","id","c99c7902-4c71-4283-a3c6-a40236412a46","metadata",{"_47":48,"_77":78,"_79":80},"pd",{"_49":50,"_51":52,"_59":60,"_65":66,"_67":68,"_69":16,"_70":71,"_72":16,"_73":74,"_75":76},"area","Outros","tags",[53],{"_43":54,"_55":56,"_57":58},1380935,"name","quimica#fisica","alias","quimica%23fisica","subjects",[61],{"_43":62,"_55":63,"_57":64},669639,"Termodinâmica","termodinamica","materialId","126576575","answerCount",1,"isIndexable","mainSubject",{"_43":62,"_55":63,"_57":64},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","133048472","options",[83,89,93,97,101],{"_43":84,"_85":86,"_87":88},"15255bb5-d247-4785-a630-ad47567d466e","label","A","text","Ondas eletromagnéticas.",{"_43":90,"_85":91,"_87":92},"50a5f2a0-8659-4c63-b096-a4a574e75133","B","Ondas numa superfície líquida.",{"_43":94,"_85":95,"_87":96},"0d34c89c-1bbe-41e1-b872-17801e718fa3","C","Ondas de rádio.",{"_43":98,"_85":99,"_87":100},"92e1cd2d-cc7e-4203-b7d5-df3eec585290","D","Ondas numa corda elástica.",{"_43":102,"_85":103,"_87":104},"6b47201b-f55b-441a-8158-982edd53e8c1","E","Ondas sonoras.","solution_explanation","statement","

Considerando o fragmento de texto, os conteúdos do livro Física II e todos os materiais disponíveis na rota sobre som e audição, assinale a alternativa que corresponde a uma onda longitudinal.

","status","pending_classification","hasRelatedVideo","relatedVideos",[113],{"_114":115,"_133":134,"_51":149,"_168":169,"_186":150},"content",{"_43":116,"_55":117,"_118":-5,"_119":120,"_121":122,"_123":-5,"_45":124,"_127":128,"_129":128,"_130":-5,"_131":132},"162087be-594f-460e-bbdd-a339ac2f10ad","Calor Latente - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f2b62fc2-7079-40e7-a5b5-c4a9769b205d","user_id",{"_125":126},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_135":136,"_142":143,"_144":145,"_146":147,"_28":148},"provider",{"_43":137,"_138":139,"_140":141},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","bf8aacba-3de9-4b10-961c-47ada80dfe8c","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/levels.m3u8",[150],{"_43":151,"_55":152,"_57":153,"_154":155,"_156":157,"_127":158,"_129":158,"_45":159,"_131":153,"_166":167},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9","2025-04-29T03:44:27.560682+00:00",{"_160":161,"_162":163,"_164":165},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":122,"_13":117,"_118":-5,"_170":171,"_172":173,"_28":-5,"_174":-5,"_135":173,"_175":176,"_146":-5,"_177":-5,"_178":-5,"_179":-5,"_180":-5,"_45":181,"_182":163,"_183":-5,"_108":184,"_127":185,"_129":185},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_125":126},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[189,219,237],{"_40":190,"_42":41,"_43":191,"_81":192,"_105":207,"_106":208,"_51":209},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[193,196,199,202,205],{"_43":194,"_85":86,"_87":195},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":197,"_85":91,"_87":198},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":200,"_85":95,"_87":201},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":203,"_85":99,"_87":204},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":190,"_85":103,"_87":206},"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],{"_43":211,"_55":212,"_57":213,"_154":155,"_156":214,"_127":215,"_129":215,"_45":216,"_131":213},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_160":217,"_162":163,"_164":218},4,12302,{"_40":220,"_42":41,"_43":221,"_81":222,"_105":234,"_106":235,"_51":236},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[223,226,229,231],{"_43":224,"_85":86,"_87":225},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":227,"_85":91,"_87":228},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":220,"_85":95,"_87":230},"

Verdadeiro, falso, verdadeiro

",{"_43":232,"_85":99,"_87":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":41,"_43":239,"_81":240,"_105":255,"_106":256,"_51":257},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[241,244,247,249,252],{"_43":242,"_85":86,"_87":243},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":245,"_85":91,"_87":246},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":238,"_85":95,"_87":248},"Indeterminado",{"_43":250,"_85":99,"_87":251},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":253,"_85":103,"_87":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],[210,259,266,276,283,290,291,299,305,310,316,323],{"_43":260,"_55":63,"_57":64,"_154":155,"_156":261,"_127":158,"_129":158,"_45":262,"_131":265},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_160":263,"_162":163,"_164":264},2,11846,"termodinamica-3",{"_43":267,"_55":268,"_57":269,"_154":155,"_156":270,"_127":271,"_129":271,"_45":272,"_131":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_160":273,"_162":163,"_164":274},5,30614,"engenharia-mecatronica-1",{"_43":277,"_55":278,"_57":279,"_154":155,"_156":267,"_127":215,"_129":215,"_45":280,"_131":282},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_160":273,"_162":163,"_164":281},25741,"mecanica-3",{"_43":261,"_55":284,"_57":285,"_154":155,"_156":270,"_127":271,"_129":271,"_45":286,"_131":289},"Engenharia Mecânica","engenharia-mecanica",{"_160":287,"_162":163,"_164":288},11,36318,"engenharia-mecanica-2",{"_43":151,"_55":152,"_57":153,"_154":155,"_156":157,"_127":158,"_129":158,"_45":159,"_131":153},{"_43":292,"_55":293,"_57":294,"_154":155,"_156":-5,"_127":295,"_129":295,"_45":296,"_131":294},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_160":297,"_162":163,"_164":298},18,135489,{"_43":300,"_55":63,"_57":64,"_154":155,"_156":211,"_127":301,"_129":301,"_45":302,"_131":304},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_160":163,"_162":163,"_164":303},8597,"termodinamica-5",{"_43":214,"_55":306,"_57":307,"_154":155,"_156":270,"_127":271,"_129":271,"_45":308,"_131":309},"Engenharia de Petróleo","engenharia-de-petroleo",{"_160":273,"_162":163,"_164":218},"engenharia-de-petroleo-1",{"_43":157,"_55":311,"_57":312,"_154":155,"_156":292,"_127":271,"_129":271,"_45":313,"_131":315},"Física","fisica",{"_160":287,"_162":163,"_164":314},13777,"fisica-4",{"_43":270,"_55":317,"_57":318,"_154":155,"_156":-5,"_127":319,"_129":319,"_45":320,"_131":318},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_160":321,"_162":163,"_164":322},29,351586,{"_43":324,"_55":63,"_57":64,"_154":155,"_156":277,"_127":325,"_129":325,"_45":326,"_131":327},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_160":163,"_162":163,"_164":303},"termodinamica-4","tagsTree",[330,334],{"_43":292,"_55":293,"_57":294,"_154":155,"_156":-5,"_127":295,"_129":295,"_45":296,"_131":294,"_166":331},[332],{"_43":157,"_55":311,"_57":312,"_154":155,"_156":292,"_127":271,"_129":271,"_45":313,"_131":315,"_166":333},[150],{"_43":270,"_55":317,"_57":318,"_154":155,"_156":-5,"_127":319,"_129":319,"_45":320,"_131":318,"_166":335},[336,342,346],{"_43":267,"_55":268,"_57":269,"_154":155,"_156":270,"_127":271,"_129":271,"_45":272,"_131":275,"_166":337},[338],{"_43":277,"_55":278,"_57":279,"_154":155,"_156":267,"_127":215,"_129":215,"_45":280,"_131":282,"_166":339},[340],{"_43":324,"_55":63,"_57":64,"_154":155,"_156":277,"_127":325,"_129":325,"_45":326,"_131":327,"_166":341},[],{"_43":261,"_55":284,"_57":285,"_154":155,"_156":270,"_127":271,"_129":271,"_45":286,"_131":289,"_166":343},[344],{"_43":260,"_55":63,"_57":64,"_154":155,"_156":261,"_127":158,"_129":158,"_45":262,"_131":265,"_166":345},[],{"_43":214,"_55":306,"_57":307,"_154":155,"_156":270,"_127":271,"_129":271,"_45":308,"_131":309,"_166":347},[348],{"_43":211,"_55":212,"_57":213,"_154":155,"_156":214,"_127":215,"_129":215,"_45":216,"_131":213,"_166":349},[350],{"_43":300,"_55":63,"_57":64,"_154":155,"_156":211,"_127":301,"_129":301,"_45":302,"_131":304,"_166":351},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários