[{"_1":2,"_378":-5,"_379":-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","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_109":110,"_188":189,"_51":263,"_336":337,"_374":375,"_376":377},"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":185},"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",{"_44":149,"_55":150,"_57":151,"_152":153,"_154":155,"_125":156,"_127":156,"_46":186,"_129":151,"_164":187},{"_158":159,"_160":161,"_162":163},[],"similarQuestions",[190,220,240],{"_40":191,"_42":43,"_44":192,"_80":193,"_103":208,"_104":209,"_51":210},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[194,197,200,203,206],{"_44":195,"_84":85,"_86":196},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":198,"_84":89,"_86":199},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":201,"_84":93,"_86":202},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":204,"_84":97,"_86":205},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":191,"_84":101,"_86":207},"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

",[211],{"_44":212,"_55":213,"_57":214,"_152":153,"_154":215,"_125":216,"_127":216,"_46":217,"_129":214},"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":218,"_160":161,"_162":219},4,12302,{"_40":221,"_42":43,"_44":222,"_80":223,"_103":235,"_104":236,"_51":237},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[224,227,230,232],{"_44":225,"_84":85,"_86":226},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":228,"_84":89,"_86":229},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":221,"_84":93,"_86":231},"

Verdadeiro, falso, verdadeiro

",{"_44":233,"_84":97,"_86":234},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[261],{"_44":212,"_55":213,"_57":214,"_152":153,"_154":215,"_125":216,"_127":216,"_46":262,"_129":214},{"_158":218,"_160":161,"_162":219},[264,266,273,283,290,297,299,307,313,318,324,331],{"_44":212,"_55":213,"_57":214,"_152":153,"_154":215,"_125":216,"_127":216,"_46":265,"_129":214},{"_158":218,"_160":161,"_162":219},{"_44":267,"_55":62,"_57":63,"_152":153,"_154":268,"_125":156,"_127":156,"_46":269,"_129":272},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_158":270,"_160":161,"_162":271},2,11846,"termodinamica-3",{"_44":274,"_55":275,"_57":276,"_152":153,"_154":277,"_125":278,"_127":278,"_46":279,"_129":282},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_158":280,"_160":161,"_162":281},5,30614,"engenharia-mecatronica-1",{"_44":284,"_55":285,"_57":286,"_152":153,"_154":274,"_125":216,"_127":216,"_46":287,"_129":289},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_158":280,"_160":161,"_162":288},25741,"mecanica-3",{"_44":268,"_55":291,"_57":292,"_152":153,"_154":277,"_125":278,"_127":278,"_46":293,"_129":296},"Engenharia Mecânica","engenharia-mecanica",{"_158":294,"_160":161,"_162":295},11,36318,"engenharia-mecanica-2",{"_44":149,"_55":150,"_57":151,"_152":153,"_154":155,"_125":156,"_127":156,"_46":298,"_129":151},{"_158":159,"_160":161,"_162":163},{"_44":300,"_55":301,"_57":302,"_152":153,"_154":-5,"_125":303,"_127":303,"_46":304,"_129":302},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_158":305,"_160":161,"_162":306},18,135489,{"_44":308,"_55":62,"_57":63,"_152":153,"_154":212,"_125":309,"_127":309,"_46":310,"_129":312},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_158":161,"_160":161,"_162":311},8597,"termodinamica-5",{"_44":215,"_55":314,"_57":315,"_152":153,"_154":277,"_125":278,"_127":278,"_46":316,"_129":317},"Engenharia de Petróleo","engenharia-de-petroleo",{"_158":280,"_160":161,"_162":219},"engenharia-de-petroleo-1",{"_44":155,"_55":319,"_57":320,"_152":153,"_154":300,"_125":278,"_127":278,"_46":321,"_129":323},"Física","fisica",{"_158":294,"_160":161,"_162":322},13777,"fisica-4",{"_44":277,"_55":325,"_57":326,"_152":153,"_154":-5,"_125":327,"_127":327,"_46":328,"_129":326},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_158":329,"_160":161,"_162":330},29,351586,{"_44":332,"_55":62,"_57":63,"_152":153,"_154":284,"_125":333,"_127":333,"_46":334,"_129":335},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_158":161,"_160":161,"_162":311},"termodinamica-4","tagsTree",[338,347],{"_44":300,"_55":301,"_57":302,"_152":153,"_154":-5,"_125":303,"_127":303,"_46":339,"_129":302,"_164":340},{"_158":305,"_160":161,"_162":306},[341],{"_44":155,"_55":319,"_57":320,"_152":153,"_154":300,"_125":278,"_127":278,"_46":342,"_129":323,"_164":343},{"_158":294,"_160":161,"_162":322},[344],{"_44":149,"_55":150,"_57":151,"_152":153,"_154":155,"_125":156,"_127":156,"_46":345,"_129":151,"_164":346},{"_158":159,"_160":161,"_162":163},[],{"_44":277,"_55":325,"_57":326,"_152":153,"_154":-5,"_125":327,"_127":327,"_46":348,"_129":326,"_164":349},{"_158":329,"_160":161,"_162":330},[350,359,365],{"_44":274,"_55":275,"_57":276,"_152":153,"_154":277,"_125":278,"_127":278,"_46":351,"_129":282,"_164":352},{"_158":280,"_160":161,"_162":281},[353],{"_44":284,"_55":285,"_57":286,"_152":153,"_154":274,"_125":216,"_127":216,"_46":354,"_129":289,"_164":355},{"_158":280,"_160":161,"_162":288},[356],{"_44":332,"_55":62,"_57":63,"_152":153,"_154":284,"_125":333,"_127":333,"_46":357,"_129":335,"_164":358},{"_158":161,"_160":161,"_162":311},[],{"_44":268,"_55":291,"_57":292,"_152":153,"_154":277,"_125":278,"_127":278,"_46":360,"_129":296,"_164":361},{"_158":294,"_160":161,"_162":295},[362],{"_44":267,"_55":62,"_57":63,"_152":153,"_154":268,"_125":156,"_127":156,"_46":363,"_129":272,"_164":364},{"_158":270,"_160":161,"_162":271},[],{"_44":215,"_55":314,"_57":315,"_152":153,"_154":277,"_125":278,"_127":278,"_46":366,"_129":317,"_164":367},{"_158":280,"_160":161,"_162":219},[368],{"_44":212,"_55":213,"_57":214,"_152":153,"_154":215,"_125":216,"_127":216,"_46":369,"_129":214,"_164":370},{"_158":218,"_160":161,"_162":219},[371],{"_44":308,"_55":62,"_57":63,"_152":153,"_154":212,"_125":309,"_127":309,"_46":372,"_129":312,"_164":373},{"_158":161,"_160":161,"_162":311},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários