[{"_1":2,"_374":-5,"_375":-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/c4e24319-45a8-429c-aa54-25ff167a196f?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_185":186,"_51":260,"_332":333,"_370":371,"_372":373},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_100":41,"_101":102,"_103":104,"_105":16},"correctOptionId","","difficulty","id","c4e24319-45a8-429c-aa54-25ff167a196f","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},669639,"name","Termodinâmica","alias","termodinamica","materialId","133378404","answerCount",2,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","133453012","options",[79,85,89,93,97],{"_43":80,"_81":82,"_83":84},"d037ea90-524a-4c3c-b5bf-63c5a49113cc","label","A","text","F, F",{"_43":86,"_81":87,"_83":88},"073acc8e-3662-4a93-abae-a0dffe1b1080","B","V, F",{"_43":90,"_81":91,"_83":92},"8aec062c-641c-4eb9-8152-a5f89a853276","C","V, V",{"_43":94,"_81":95,"_83":96},"34b7db63-0c4b-498b-baba-97d50d828bd5","D","F, V",{"_43":98,"_81":99,"_83":84},"bca0e265-1257-4025-aa10-546e12674a9a","E","solution_explanation","statement","Para uma expansão livre de um gás ideal, a temperatura inicial é igual a temperatura final. Portanto, a variação de entropia \\Delta S para uma expansão livre de 1 \\text{mol} de um gás ideal de V_1 até V_2 é igual a 0 num processo isotérmico de T.","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_51":144,"_163":164,"_181":182},"content",{"_43":111,"_57":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_130":131,"_137":138,"_139":140,"_141":142,"_28":143},"provider",{"_43":132,"_133":134,"_135":136},"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",[145],{"_43":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":154,"_126":148,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":117,"_13":112,"_113":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_130":168,"_170":171,"_141":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_45":176,"_177":158,"_178":-5,"_103":179,"_122":180,"_124":180},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_43":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":183,"_126":148,"_161":184},{"_155":156,"_157":158,"_159":160},[],"similarQuestions",[187,217,237],{"_40":188,"_42":41,"_43":189,"_77":190,"_100":205,"_101":206,"_51":207},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[191,194,197,200,203],{"_43":192,"_81":82,"_83":193},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":195,"_81":87,"_83":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":198,"_81":91,"_83":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":201,"_81":95,"_83":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":188,"_81":99,"_83":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],{"_43":209,"_57":210,"_59":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":214,"_126":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",{"_155":215,"_157":158,"_159":216},4,12302,{"_40":218,"_42":41,"_43":219,"_77":220,"_100":232,"_101":233,"_51":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_43":222,"_81":82,"_83":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":225,"_81":87,"_83":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":218,"_81":91,"_83":228},"

Verdadeiro, falso, verdadeiro

",{"_43":230,"_81":95,"_83":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?

",[235],{"_43":209,"_57":210,"_59":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":236,"_126":211},{"_155":215,"_157":158,"_159":216},{"_40":238,"_42":41,"_43":239,"_77":240,"_100":255,"_101":256,"_51":257},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[241,244,247,249,252],{"_43":242,"_81":82,"_83":243},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":245,"_81":87,"_83":246},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":238,"_81":91,"_83":248},"Indeterminado",{"_43":250,"_81":95,"_83":251},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":253,"_81":99,"_83":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????",[258],{"_43":209,"_57":210,"_59":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":259,"_126":211},{"_155":215,"_157":158,"_159":216},[261,263,269,279,286,293,295,303,309,314,320,327],{"_43":209,"_57":210,"_59":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":262,"_126":211},{"_155":215,"_157":158,"_159":216},{"_43":264,"_57":58,"_59":60,"_149":150,"_151":265,"_122":153,"_124":153,"_45":266,"_126":268},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":64,"_157":158,"_159":267},11846,"termodinamica-3",{"_43":270,"_57":271,"_59":272,"_149":150,"_151":273,"_122":274,"_124":274,"_45":275,"_126":278},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":276,"_157":158,"_159":277},5,30614,"engenharia-mecatronica-1",{"_43":280,"_57":281,"_59":282,"_149":150,"_151":270,"_122":213,"_124":213,"_45":283,"_126":285},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":276,"_157":158,"_159":284},25741,"mecanica-3",{"_43":265,"_57":287,"_59":288,"_149":150,"_151":273,"_122":274,"_124":274,"_45":289,"_126":292},"Engenharia Mecânica","engenharia-mecanica",{"_155":290,"_157":158,"_159":291},11,36318,"engenharia-mecanica-2",{"_43":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":294,"_126":148},{"_155":156,"_157":158,"_159":160},{"_43":296,"_57":297,"_59":298,"_149":150,"_151":-5,"_122":299,"_124":299,"_45":300,"_126":298},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":301,"_157":158,"_159":302},18,135489,{"_43":304,"_57":58,"_59":60,"_149":150,"_151":209,"_122":305,"_124":305,"_45":306,"_126":308},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":307},8597,"termodinamica-5",{"_43":212,"_57":310,"_59":311,"_149":150,"_151":273,"_122":274,"_124":274,"_45":312,"_126":313},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":276,"_157":158,"_159":216},"engenharia-de-petroleo-1",{"_43":152,"_57":315,"_59":316,"_149":150,"_151":296,"_122":274,"_124":274,"_45":317,"_126":319},"Física","fisica",{"_155":290,"_157":158,"_159":318},13777,"fisica-4",{"_43":273,"_57":321,"_59":322,"_149":150,"_151":-5,"_122":323,"_124":323,"_45":324,"_126":322},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":325,"_157":158,"_159":326},29,351586,{"_43":328,"_57":58,"_59":60,"_149":150,"_151":280,"_122":329,"_124":329,"_45":330,"_126":331},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":307},"termodinamica-4","tagsTree",[334,343],{"_43":296,"_57":297,"_59":298,"_149":150,"_151":-5,"_122":299,"_124":299,"_45":335,"_126":298,"_161":336},{"_155":301,"_157":158,"_159":302},[337],{"_43":152,"_57":315,"_59":316,"_149":150,"_151":296,"_122":274,"_124":274,"_45":338,"_126":319,"_161":339},{"_155":290,"_157":158,"_159":318},[340],{"_43":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":341,"_126":148,"_161":342},{"_155":156,"_157":158,"_159":160},[],{"_43":273,"_57":321,"_59":322,"_149":150,"_151":-5,"_122":323,"_124":323,"_45":344,"_126":322,"_161":345},{"_155":325,"_157":158,"_159":326},[346,355,361],{"_43":270,"_57":271,"_59":272,"_149":150,"_151":273,"_122":274,"_124":274,"_45":347,"_126":278,"_161":348},{"_155":276,"_157":158,"_159":277},[349],{"_43":280,"_57":281,"_59":282,"_149":150,"_151":270,"_122":213,"_124":213,"_45":350,"_126":285,"_161":351},{"_155":276,"_157":158,"_159":284},[352],{"_43":328,"_57":58,"_59":60,"_149":150,"_151":280,"_122":329,"_124":329,"_45":353,"_126":331,"_161":354},{"_155":158,"_157":158,"_159":307},[],{"_43":265,"_57":287,"_59":288,"_149":150,"_151":273,"_122":274,"_124":274,"_45":356,"_126":292,"_161":357},{"_155":290,"_157":158,"_159":291},[358],{"_43":264,"_57":58,"_59":60,"_149":150,"_151":265,"_122":153,"_124":153,"_45":359,"_126":268,"_161":360},{"_155":64,"_157":158,"_159":267},[],{"_43":212,"_57":310,"_59":311,"_149":150,"_151":273,"_122":274,"_124":274,"_45":362,"_126":313,"_161":363},{"_155":276,"_157":158,"_159":216},[364],{"_43":209,"_57":210,"_59":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":365,"_126":211,"_161":366},{"_155":215,"_157":158,"_159":216},[367],{"_43":304,"_57":58,"_59":60,"_149":150,"_151":209,"_122":305,"_124":305,"_45":368,"_126":308,"_161":369},{"_155":158,"_157":158,"_159":307},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários