[{"_1":2,"_348":-5,"_349":-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/99765a12-4fb6-4293-bcbe-641ed0e72e00","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_102":103,"_178":179,"_50":250,"_320":321,"_344":345,"_346":347},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_76":77,"_96":41,"_97":98,"_99":100,"_101":16},"correctOptionId","","difficulty","id","99765a12-4fb6-4293-bcbe-641ed0e72e00","metadata",{"_47":48,"_72":73,"_74":75},"pd",{"_49":-5,"_50":51,"_52":53,"_60":61,"_62":63,"_64":16,"_65":66,"_67":16,"_68":69,"_70":71},"area","tags",[],"subjects",[54],{"_43":55,"_56":57,"_58":59},669639,"name","Termodinâmica","alias","termodinamica","materialId","164696689","answerCount",1,"isIndexable","mainSubject",{"_43":55,"_56":57,"_58":59},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","165058435","options",[78,84,88,92],{"_43":79,"_80":81,"_82":83},"467e9553-16fc-40a0-9e0a-36922c2fefca","label","A","text","

dS = \frac{1}{T} dU

",{"_43":85,"_80":86,"_82":87},"141a05a3-e0b5-416b-b004-e91bd35a6bee","B","

dS = TdU

",{"_43":89,"_80":90,"_82":91},"e18838e3-9fe8-4497-bf9b-982124f0905c","C","

dS = T dU

",{"_43":93,"_80":94,"_82":95},"b62b6c6f-e883-4b93-94ff-cb6a4ceb9338","D","

dS = \frac{U}{T}

","solution_explanation","statement","

Em um sistema termodinâmico, a relação entre entropia S, energia interna U e temperatura T pode ser expressa através da seguinte derivada, que é usada para avaliar a mudança de entropia em relação à energia interna. Qual é essa relação?

","status","pending_classification","hasRelatedVideo","relatedVideos",[104],{"_105":106,"_124":125,"_50":140,"_159":160,"_177":141},"content",{"_43":107,"_56":108,"_109":-5,"_110":111,"_112":113,"_114":-5,"_45":115,"_118":119,"_120":119,"_121":-5,"_122":123},"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",{"_116":117},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_126":127,"_133":134,"_135":136,"_137":138,"_28":139},"provider",{"_43":128,"_129":130,"_131":132},"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",[141],{"_43":142,"_56":143,"_58":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":150,"_122":144,"_157":158},"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",{"_151":152,"_153":154,"_155":156},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":113,"_13":108,"_109":-5,"_161":162,"_163":164,"_28":-5,"_165":-5,"_126":164,"_166":167,"_137":-5,"_168":-5,"_169":-5,"_170":-5,"_171":-5,"_45":172,"_173":154,"_174":-5,"_99":175,"_118":176,"_120":176},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_116":117},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[180,211,229],{"_40":181,"_42":41,"_43":182,"_76":183,"_96":199,"_97":200,"_50":201},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[184,187,190,193,196],{"_43":185,"_80":81,"_82":186},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":188,"_80":86,"_82":189},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":191,"_80":90,"_82":192},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":194,"_80":94,"_82":195},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":181,"_80":197,"_82":198},"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

",[202],{"_43":203,"_56":204,"_58":205,"_145":146,"_147":206,"_118":207,"_120":207,"_45":208,"_122":205},"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",{"_151":209,"_153":154,"_155":210},4,12302,{"_40":212,"_42":41,"_43":213,"_76":214,"_96":226,"_97":227,"_50":228},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[215,218,221,223],{"_43":216,"_80":81,"_82":217},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":219,"_80":86,"_82":220},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":212,"_80":90,"_82":222},"

Verdadeiro, falso, verdadeiro

",{"_43":224,"_80":94,"_82":225},"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?

",[202],{"_40":230,"_42":41,"_43":231,"_76":232,"_96":247,"_97":248,"_50":249},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[233,236,239,241,244],{"_43":234,"_80":81,"_82":235},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":237,"_80":86,"_82":238},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":230,"_80":90,"_82":240},"Indeterminado",{"_43":242,"_80":94,"_82":243},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":245,"_80":197,"_82":246},"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????",[202],[202,251,258,268,275,282,283,291,297,302,308,315],{"_43":252,"_56":57,"_58":59,"_145":146,"_147":253,"_118":149,"_120":149,"_45":254,"_122":257},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_151":255,"_153":154,"_155":256},2,11846,"termodinamica-3",{"_43":259,"_56":260,"_58":261,"_145":146,"_147":262,"_118":263,"_120":263,"_45":264,"_122":267},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_151":265,"_153":154,"_155":266},5,30614,"engenharia-mecatronica-1",{"_43":269,"_56":270,"_58":271,"_145":146,"_147":259,"_118":207,"_120":207,"_45":272,"_122":274},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_151":265,"_153":154,"_155":273},25741,"mecanica-3",{"_43":253,"_56":276,"_58":277,"_145":146,"_147":262,"_118":263,"_120":263,"_45":278,"_122":281},"Engenharia Mecânica","engenharia-mecanica",{"_151":279,"_153":154,"_155":280},11,36318,"engenharia-mecanica-2",{"_43":142,"_56":143,"_58":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":150,"_122":144},{"_43":284,"_56":285,"_58":286,"_145":146,"_147":-5,"_118":287,"_120":287,"_45":288,"_122":286},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_151":289,"_153":154,"_155":290},18,135489,{"_43":292,"_56":57,"_58":59,"_145":146,"_147":203,"_118":293,"_120":293,"_45":294,"_122":296},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_151":154,"_153":154,"_155":295},8597,"termodinamica-5",{"_43":206,"_56":298,"_58":299,"_145":146,"_147":262,"_118":263,"_120":263,"_45":300,"_122":301},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":265,"_153":154,"_155":210},"engenharia-de-petroleo-1",{"_43":148,"_56":303,"_58":304,"_145":146,"_147":284,"_118":263,"_120":263,"_45":305,"_122":307},"Física","fisica",{"_151":279,"_153":154,"_155":306},13777,"fisica-4",{"_43":262,"_56":309,"_58":310,"_145":146,"_147":-5,"_118":311,"_120":311,"_45":312,"_122":310},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":313,"_153":154,"_155":314},29,351586,{"_43":316,"_56":57,"_58":59,"_145":146,"_147":269,"_118":317,"_120":317,"_45":318,"_122":319},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_151":154,"_153":154,"_155":295},"termodinamica-4","tagsTree",[322,326],{"_43":284,"_56":285,"_58":286,"_145":146,"_147":-5,"_118":287,"_120":287,"_45":288,"_122":286,"_157":323},[324],{"_43":148,"_56":303,"_58":304,"_145":146,"_147":284,"_118":263,"_120":263,"_45":305,"_122":307,"_157":325},[141],{"_43":262,"_56":309,"_58":310,"_145":146,"_147":-5,"_118":311,"_120":311,"_45":312,"_122":310,"_157":327},[328,334,338],{"_43":259,"_56":260,"_58":261,"_145":146,"_147":262,"_118":263,"_120":263,"_45":264,"_122":267,"_157":329},[330],{"_43":269,"_56":270,"_58":271,"_145":146,"_147":259,"_118":207,"_120":207,"_45":272,"_122":274,"_157":331},[332],{"_43":316,"_56":57,"_58":59,"_145":146,"_147":269,"_118":317,"_120":317,"_45":318,"_122":319,"_157":333},[],{"_43":253,"_56":276,"_58":277,"_145":146,"_147":262,"_118":263,"_120":263,"_45":278,"_122":281,"_157":335},[336],{"_43":252,"_56":57,"_58":59,"_145":146,"_147":253,"_118":149,"_120":149,"_45":254,"_122":257,"_157":337},[],{"_43":206,"_56":298,"_58":299,"_145":146,"_147":262,"_118":263,"_120":263,"_45":300,"_122":301,"_157":339},[340],{"_43":203,"_56":204,"_58":205,"_145":146,"_147":206,"_118":207,"_120":207,"_45":208,"_122":205,"_157":341},[342],{"_43":292,"_56":57,"_58":59,"_145":146,"_147":203,"_118":293,"_120":293,"_45":294,"_122":296,"_157":343},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários