[{"_1":2,"_354":-5,"_355":-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/983ea48b-4d04-4b40-9b1c-9c12e38c4530?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_109":110,"_185":186,"_51":256,"_326":327,"_350":351,"_352":353},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_80":81,"_103":43,"_104":105,"_106":107,"_108":16},"correctOptionId","d09a7c82-5aa3-427a-8102-e99aea63c55b","difficulty","","id","983ea48b-4d04-4b40-9b1c-9c12e38c4530","metadata",{"_48":49,"_76":77,"_78":79},"pd",{"_50":-5,"_51":52,"_58":59,"_64":65,"_66":67,"_68":16,"_69":70,"_71":16,"_72":73,"_74":75},"area","tags",[53],{"_44":54,"_55":56,"_57":56},32,"name","prova","alias","subjects",[60],{"_44":61,"_55":62,"_57":63},669639,"Termodinâmica","termodinamica","materialId","122665615","answerCount",1,"isIndexable","mainSubject",{"_44":61,"_55":62,"_57":63},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122665671","options",[82,88,91,95,99],{"_44":83,"_84":85,"_86":87},"a7475a4d-747c-45cf-a634-0acd7ef29669","label","A","text","

Turbina a vapor

",{"_44":41,"_84":89,"_86":90},"B","

Turbina quântica

",{"_44":92,"_84":93,"_86":94},"aaa7ea9f-efae-4d39-beb7-66dbb52c21c4","C","

Motor elétrico

",{"_44":96,"_84":97,"_86":98},"a5ed0cf5-98c9-4551-b465-d0c3ae2f2ee8","D","

Turbina hidráulica

",{"_44":100,"_84":101,"_86":102},"68840a2f-2b40-469a-9f96-fba2404a7280","E","

Turbina eólica

","solution_explanation","statement","

Assinale a alternativa que NÃO apresenta um exemplo de máquina motriz

","status","pending_classification","hasRelatedVideo","relatedVideos",[111],{"_112":113,"_131":132,"_51":147,"_166":167,"_184":148},"content",{"_44":114,"_55":115,"_116":-5,"_117":118,"_119":120,"_121":-5,"_46":122,"_125":126,"_127":126,"_128":-5,"_129":130},"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",{"_123":124},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_133":134,"_140":141,"_142":143,"_144":145,"_28":146},"provider",{"_44":135,"_136":137,"_138":139},"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",[148],{"_44":149,"_55":150,"_57":151,"_152":153,"_154":155,"_125":156,"_127":156,"_46":157,"_129":151,"_164":165},"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",{"_158":159,"_160":161,"_162":163},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":120,"_13":115,"_116":-5,"_168":169,"_170":171,"_28":-5,"_172":-5,"_133":171,"_173":174,"_144":-5,"_175":-5,"_176":-5,"_177":-5,"_178":-5,"_46":179,"_180":161,"_181":-5,"_106":182,"_125":183,"_127":183},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_123":124},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[187,217,235],{"_40":188,"_42":43,"_44":189,"_80":190,"_103":205,"_104":206,"_51":207},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[191,194,197,200,203],{"_44":192,"_84":85,"_86":193},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":195,"_84":89,"_86":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":198,"_84":93,"_86":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":201,"_84":97,"_86":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":188,"_84":101,"_86":204},"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

",[208],{"_44":209,"_55":210,"_57":211,"_152":153,"_154":212,"_125":213,"_127":213,"_46":214,"_129":211},"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",{"_158":215,"_160":161,"_162":216},4,12302,{"_40":218,"_42":43,"_44":219,"_80":220,"_103":232,"_104":233,"_51":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_44":222,"_84":85,"_86":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":225,"_84":89,"_86":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":218,"_84":93,"_86":228},"

Verdadeiro, falso, verdadeiro

",{"_44":230,"_84":97,"_86":231},"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?

",[208],{"_40":236,"_42":43,"_44":237,"_80":238,"_103":253,"_104":254,"_51":255},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[239,242,245,247,250],{"_44":240,"_84":85,"_86":241},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":243,"_84":89,"_86":244},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":236,"_84":93,"_86":246},"Indeterminado",{"_44":248,"_84":97,"_86":249},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":251,"_84":101,"_86":252},"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????",[208],[208,257,264,274,281,288,289,297,303,308,314,321],{"_44":258,"_55":62,"_57":63,"_152":153,"_154":259,"_125":156,"_127":156,"_46":260,"_129":263},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_158":261,"_160":161,"_162":262},2,11846,"termodinamica-3",{"_44":265,"_55":266,"_57":267,"_152":153,"_154":268,"_125":269,"_127":269,"_46":270,"_129":273},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_158":271,"_160":161,"_162":272},5,30614,"engenharia-mecatronica-1",{"_44":275,"_55":276,"_57":277,"_152":153,"_154":265,"_125":213,"_127":213,"_46":278,"_129":280},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_158":271,"_160":161,"_162":279},25741,"mecanica-3",{"_44":259,"_55":282,"_57":283,"_152":153,"_154":268,"_125":269,"_127":269,"_46":284,"_129":287},"Engenharia Mecânica","engenharia-mecanica",{"_158":285,"_160":161,"_162":286},11,36318,"engenharia-mecanica-2",{"_44":149,"_55":150,"_57":151,"_152":153,"_154":155,"_125":156,"_127":156,"_46":157,"_129":151},{"_44":290,"_55":291,"_57":292,"_152":153,"_154":-5,"_125":293,"_127":293,"_46":294,"_129":292},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_158":295,"_160":161,"_162":296},18,135489,{"_44":298,"_55":62,"_57":63,"_152":153,"_154":209,"_125":299,"_127":299,"_46":300,"_129":302},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_158":161,"_160":161,"_162":301},8597,"termodinamica-5",{"_44":212,"_55":304,"_57":305,"_152":153,"_154":268,"_125":269,"_127":269,"_46":306,"_129":307},"Engenharia de Petróleo","engenharia-de-petroleo",{"_158":271,"_160":161,"_162":216},"engenharia-de-petroleo-1",{"_44":155,"_55":309,"_57":310,"_152":153,"_154":290,"_125":269,"_127":269,"_46":311,"_129":313},"Física","fisica",{"_158":285,"_160":161,"_162":312},13777,"fisica-4",{"_44":268,"_55":315,"_57":316,"_152":153,"_154":-5,"_125":317,"_127":317,"_46":318,"_129":316},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_158":319,"_160":161,"_162":320},29,351586,{"_44":322,"_55":62,"_57":63,"_152":153,"_154":275,"_125":323,"_127":323,"_46":324,"_129":325},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_158":161,"_160":161,"_162":301},"termodinamica-4","tagsTree",[328,332],{"_44":290,"_55":291,"_57":292,"_152":153,"_154":-5,"_125":293,"_127":293,"_46":294,"_129":292,"_164":329},[330],{"_44":155,"_55":309,"_57":310,"_152":153,"_154":290,"_125":269,"_127":269,"_46":311,"_129":313,"_164":331},[148],{"_44":268,"_55":315,"_57":316,"_152":153,"_154":-5,"_125":317,"_127":317,"_46":318,"_129":316,"_164":333},[334,340,344],{"_44":265,"_55":266,"_57":267,"_152":153,"_154":268,"_125":269,"_127":269,"_46":270,"_129":273,"_164":335},[336],{"_44":275,"_55":276,"_57":277,"_152":153,"_154":265,"_125":213,"_127":213,"_46":278,"_129":280,"_164":337},[338],{"_44":322,"_55":62,"_57":63,"_152":153,"_154":275,"_125":323,"_127":323,"_46":324,"_129":325,"_164":339},[],{"_44":259,"_55":282,"_57":283,"_152":153,"_154":268,"_125":269,"_127":269,"_46":284,"_129":287,"_164":341},[342],{"_44":258,"_55":62,"_57":63,"_152":153,"_154":259,"_125":156,"_127":156,"_46":260,"_129":263,"_164":343},[],{"_44":212,"_55":304,"_57":305,"_152":153,"_154":268,"_125":269,"_127":269,"_46":306,"_129":307,"_164":345},[346],{"_44":209,"_55":210,"_57":211,"_152":153,"_154":212,"_125":213,"_127":213,"_46":214,"_129":211,"_164":347},[348],{"_44":298,"_55":62,"_57":63,"_152":153,"_154":209,"_125":299,"_127":299,"_46":300,"_129":302,"_164":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários