[{"_1":2,"_598":-5,"_599":-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/5a386df1-d627-4572-90ea-2802ce0e900b","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_314":315,"_413":414,"_51":488,"_553":554,"_594":595,"_596":597},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_284":285,"_308":41,"_309":310,"_311":312,"_313":16},"correctOptionId","","difficulty","id","5a386df1-d627-4572-90ea-2802ce0e900b","metadata",{"_47":48,"_280":281,"_282":283},"pd",{"_49":50,"_51":52,"_229":230,"_268":269,"_270":271,"_272":16,"_273":274,"_275":16,"_276":277,"_278":279},"area","Outros","tags",[53,58,61,65,69,72,75,79,83,87,91,95,99,103,107,111,115,118,122,126,130,134,138,141,145,149,153,157,161,165,169,173,177,181,185,188,192,196,200,204,207,211,214,218,222,225],{"_43":54,"_55":56,"_57":56},32,"name","prova","alias",{"_43":59,"_55":60,"_57":60},43,"basico",{"_43":62,"_55":63,"_57":64},88,"PROVAS","provas",{"_43":66,"_55":67,"_57":68},98,"Exercício","exercicio",{"_43":70,"_55":71,"_57":71},117,"calculo",{"_43":73,"_55":74,"_57":74},293,"respostas",{"_43":76,"_55":77,"_57":78},415,"Mecânica","mecanica",{"_43":80,"_55":81,"_57":82},417,"Cinemática","cinematica",{"_43":84,"_55":85,"_57":86},418,"Dinâmica","dinamica",{"_43":88,"_55":89,"_57":90},466,"Fluídos","fluidos",{"_43":92,"_55":93,"_57":94},564,"Cônicas","conicas",{"_43":96,"_55":97,"_57":98},845,"Engenharia","engenharia",{"_43":100,"_55":101,"_57":102},1066,"Geometria","geometria",{"_43":104,"_55":105,"_57":106},1515,"Termodinâmica","termodinamica",{"_43":108,"_55":109,"_57":110},3375,"Reta","reta",{"_43":112,"_55":113,"_57":114},3433,"Resistência dos materiais","resistencia-dos-materiais",{"_43":116,"_55":117,"_57":117},3747,"dp",{"_43":119,"_55":120,"_57":121},4348,"cálculos","calculos",{"_43":123,"_55":124,"_57":125},5354,"Resultados","resultados",{"_43":127,"_55":128,"_57":129},16596,"CGA","cga",{"_43":131,"_55":132,"_57":133},19021,"NP2","np-2",{"_43":135,"_55":136,"_57":137},19509,"Dependência","dependencia",{"_43":139,"_55":140,"_57":140},26128,"todas",{"_43":142,"_55":143,"_57":144},28393,"NP1","np-1",{"_43":146,"_55":147,"_57":148},31415,"DPS","dps",{"_43":150,"_55":151,"_57":152},32317,"CFVV","cfvv",{"_43":154,"_55":155,"_57":156},55542,"Dinamica-dos-Solidos","dinamica-dos-solidos",{"_43":158,"_55":159,"_57":160},79681,"Cálculo-Geometria","calculo-geometria",{"_43":162,"_55":163,"_57":164},128726,"Cálculo-com-Geom.-Analítica","calculo-com-geom-analitica",{"_43":166,"_55":167,"_57":168},215590,"CALC-COM-GEOMETRIA-ANALITICA","calc-com-geometria-analitica",{"_43":170,"_55":171,"_57":172},223665,"Calcuco","calcuco",{"_43":174,"_55":175,"_57":176},245124,"COLAS","colas",{"_43":178,"_55":179,"_57":180},277097,"DP-ONLINE-DP-UNIP","dp-online-dp-unip",{"_43":182,"_55":183,"_57":184},278103,"DP-cinemática-dos-sólidos","dp-cinematica-dos-solidos",{"_43":186,"_55":187,"_57":187},329424,"dpunip",{"_43":189,"_55":190,"_57":191},353439,"Mecanica-dos-fluidos-aplicada-","mecanica-dos-fluidos-aplicada",{"_43":193,"_55":194,"_57":195},359514,"p1-p2-exame","p-1-p-2-exame",{"_43":197,"_55":198,"_57":199},410007,"tem-varias-resposta-de-dps-","tem-varias-resposta-de-dps",{"_43":201,"_55":202,"_57":203},416265,"Termodinâmica-AplicadaUNIP","termodinamica-aplicada-unip",{"_43":205,"_55":206,"_57":206},434996,"prov",{"_43":208,"_55":209,"_57":210},441068,"DP-ONLINE--UNIP--respostas","dp-online-unip-respostas",{"_43":212,"_55":213,"_57":213},515253,"equilibrio-de-corpos-rigidos-t",{"_43":215,"_55":216,"_57":217},515342,"vigas-isostaticas-centroide-e-","vigas-isostaticas-centroide-e",{"_43":219,"_55":220,"_57":221},515477,"equilibrio-de-particulas-2d-e-","equilibrio-de-particulas-2-d-e",{"_43":223,"_55":224,"_57":224},607199,"provasdps",{"_43":226,"_55":227,"_57":228},635558,"provas unip","provas-unip","subjects",[231,233,237,241,245,249,253,257,260,264],{"_43":232,"_55":105,"_57":106},669639,{"_43":234,"_55":235,"_57":236},669662,"Geometria Analítica","geometria-analitica",{"_43":238,"_55":239,"_57":240},669867,"Cálculo Numérico","calculo-numerico",{"_43":242,"_55":243,"_57":244},670600,"Fenômenos de Transporte","fenomenos-de-transporte",{"_43":246,"_55":247,"_57":248},670683,"Mecânica dos Fluidos","mecanica-dos-fluidos",{"_43":250,"_55":251,"_57":252},732075,"Topografia","topografia",{"_43":254,"_55":255,"_57":256},1497408,"Engenharia de Produção","engenharia-de-producao",{"_43":258,"_55":259,"_57":114},1663620,"Resistência dos Materiais",{"_43":261,"_55":262,"_57":263},1725643,"Concreto","concreto",{"_43":265,"_55":266,"_57":267},1925624,"Engenharia Mecânica","engenharia-mecanica","materialId","33782103","answerCount",1,"isIndexable","mainSubject",{"_43":258,"_55":259,"_57":114},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","132501693","options",[286,292,296,300,304],{"_43":287,"_288":289,"_290":291},"99aa4c16-aaa4-4ec3-85fc-c2bd0c878515","label","A","text","728,2 m/s.",{"_43":293,"_288":294,"_290":295},"5ed74c18-f344-4cf4-82c7-0c388d07f3e9","B","613,4 m/s.",{"_43":297,"_288":298,"_290":299},"7b1ea7f7-27a1-4547-927b-e3cc2de724a5","C","527,3 m/s.",{"_43":301,"_288":302,"_290":303},"f9c04a1b-3fa9-4145-a582-811859ef06e7","D","412,9 m/s.",{"_43":305,"_288":306,"_290":307},"46b80d0d-6e15-402c-bdbb-e9f82b612a0d","E","0 m/s.","solution_explanation","statement","Gases de combustão quentes entram na boca de um motor turbojato a 260 \\, \\text{kPa}, 747 \\, ^\\circ C e 80 \\, \\text{m/s} e saem a uma pressão de 85 \\, \\text{kPa}. Assumindo uma eficiência isentrópica de 92\\% e tratando os gases de combustão como ar, determine a velocidade de saída.","status","pending_classification","hasRelatedVideo","relatedVideos",[316],{"_317":318,"_336":337,"_51":352,"_385":386,"_403":404},"content",{"_43":319,"_55":320,"_321":-5,"_322":323,"_324":325,"_326":-5,"_45":327,"_330":331,"_332":331,"_333":-5,"_334":335},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_328":329},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_338":339,"_345":346,"_347":348,"_349":350,"_28":351},"provider",{"_43":340,"_341":342,"_343":344},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[353],{"_43":354,"_55":355,"_57":356,"_357":358,"_359":-5,"_330":360,"_332":360,"_45":361,"_334":356,"_368":369},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_362":363,"_364":365,"_366":367},"childrenCount",18,"content_count",0,"question_count",135489,"children",[370],{"_43":371,"_55":77,"_57":78,"_357":358,"_359":354,"_330":372,"_332":372,"_45":373,"_334":376,"_368":377},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_362":374,"_364":365,"_366":375},10,19948,"mecanica-2",[378],{"_43":379,"_55":259,"_57":114,"_357":358,"_359":371,"_330":380,"_332":380,"_45":381,"_334":383,"_368":384},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_362":365,"_364":365,"_366":382},3376,"resistencia-dos-materiais-4",[],"video",{"_43":325,"_13":320,"_321":-5,"_387":388,"_389":390,"_28":-5,"_391":-5,"_338":390,"_392":393,"_349":-5,"_394":-5,"_395":-5,"_396":-5,"_397":-5,"_45":398,"_399":365,"_400":-5,"_311":401,"_330":402,"_332":402},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_328":329},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":354,"_55":355,"_57":356,"_357":358,"_359":-5,"_330":360,"_332":360,"_45":405,"_334":356,"_368":406},{"_362":363,"_364":365,"_366":367},[407],{"_43":371,"_55":77,"_57":78,"_357":358,"_359":354,"_330":372,"_332":372,"_45":408,"_334":376,"_368":409},{"_362":374,"_364":365,"_366":375},[410],{"_43":379,"_55":259,"_57":114,"_357":358,"_359":371,"_330":380,"_332":380,"_45":411,"_334":383,"_368":412},{"_362":365,"_364":365,"_366":382},[],"similarQuestions",[415,445,465],{"_40":416,"_42":41,"_43":417,"_284":418,"_308":433,"_309":434,"_51":435},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[419,422,425,428,431],{"_43":420,"_288":289,"_290":421},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":423,"_288":294,"_290":424},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":426,"_288":298,"_290":427},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":429,"_288":302,"_290":430},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":416,"_288":306,"_290":432},"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

",[436],{"_43":437,"_55":438,"_57":439,"_357":358,"_359":440,"_330":441,"_332":441,"_45":442,"_334":439},"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",{"_362":443,"_364":365,"_366":444},4,12302,{"_40":446,"_42":41,"_43":447,"_284":448,"_308":460,"_309":461,"_51":462},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[449,452,455,457],{"_43":450,"_288":289,"_290":451},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":453,"_288":294,"_290":454},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":446,"_288":298,"_290":456},"

Verdadeiro, falso, verdadeiro

",{"_43":458,"_288":302,"_290":459},"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?

",[463],{"_43":437,"_55":438,"_57":439,"_357":358,"_359":440,"_330":441,"_332":441,"_45":464,"_334":439},{"_362":443,"_364":365,"_366":444},{"_40":466,"_42":41,"_43":467,"_284":468,"_308":483,"_309":484,"_51":485},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[469,472,475,477,480],{"_43":470,"_288":289,"_290":471},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":473,"_288":294,"_290":474},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":466,"_288":298,"_290":476},"Indeterminado",{"_43":478,"_288":302,"_290":479},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":481,"_288":306,"_290":482},"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????",[486],{"_43":437,"_55":438,"_57":439,"_357":358,"_359":440,"_330":441,"_332":441,"_45":487,"_334":439},{"_362":443,"_364":365,"_366":444},[489,491,500,506,510,512,514,522,527,535,537,542,548],{"_43":437,"_55":438,"_57":439,"_357":358,"_359":440,"_330":441,"_332":441,"_45":490,"_334":439},{"_362":443,"_364":365,"_366":444},{"_43":492,"_55":493,"_57":494,"_357":358,"_359":495,"_330":372,"_332":372,"_45":496,"_334":499},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_362":497,"_364":365,"_366":498},5,30614,"engenharia-mecatronica-1",{"_43":501,"_55":259,"_57":114,"_357":358,"_359":502,"_330":503,"_332":503,"_45":504,"_334":505},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_362":365,"_364":365,"_366":382},"resistencia-dos-materiais-6",{"_43":502,"_55":77,"_57":78,"_357":358,"_359":492,"_330":441,"_332":441,"_45":507,"_334":509},{"_362":497,"_364":365,"_366":508},25741,"mecanica-3",{"_43":354,"_55":355,"_57":356,"_357":358,"_359":-5,"_330":360,"_332":360,"_45":511,"_334":356},{"_362":363,"_364":365,"_366":367},{"_43":379,"_55":259,"_57":114,"_357":358,"_359":371,"_330":380,"_332":380,"_45":513,"_334":383},{"_362":365,"_364":365,"_366":382},{"_43":515,"_55":516,"_57":517,"_357":358,"_359":495,"_330":372,"_332":372,"_45":518,"_334":521},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_362":519,"_364":365,"_366":520},21,45865,"engenharia-civil-3",{"_43":440,"_55":523,"_57":524,"_357":358,"_359":495,"_330":372,"_332":372,"_45":525,"_334":526},"Engenharia de Petróleo","engenharia-de-petroleo",{"_362":497,"_364":365,"_366":444},"engenharia-de-petroleo-1",{"_43":528,"_55":529,"_57":530,"_357":358,"_359":515,"_330":531,"_332":531,"_45":532,"_334":534},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_362":497,"_364":365,"_366":533},8852,"estruturas-1",{"_43":371,"_55":77,"_57":78,"_357":358,"_359":354,"_330":372,"_332":372,"_45":536,"_334":376},{"_362":374,"_364":365,"_366":375},{"_43":538,"_55":259,"_57":114,"_357":358,"_359":437,"_330":539,"_332":539,"_45":540,"_334":541},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_362":365,"_364":365,"_366":382},"resistencia-dos-materiais-7",{"_43":543,"_55":544,"_57":114,"_357":358,"_359":528,"_330":545,"_332":545,"_45":546,"_334":547},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_362":365,"_364":365,"_366":382},"resistencia-dos-materiais-5",{"_43":495,"_55":97,"_57":98,"_357":358,"_359":-5,"_330":549,"_332":549,"_45":550,"_334":98},"2025-04-29T01:55:38.635246+00:00",{"_362":551,"_364":365,"_366":552},29,351586,"tagsTree",[555,564],{"_43":354,"_55":355,"_57":356,"_357":358,"_359":-5,"_330":360,"_332":360,"_45":556,"_334":356,"_368":557},{"_362":363,"_364":365,"_366":367},[558],{"_43":371,"_55":77,"_57":78,"_357":358,"_359":354,"_330":372,"_332":372,"_45":559,"_334":376,"_368":560},{"_362":374,"_364":365,"_366":375},[561],{"_43":379,"_55":259,"_57":114,"_357":358,"_359":371,"_330":380,"_332":380,"_45":562,"_334":383,"_368":563},{"_362":365,"_364":365,"_366":382},[],{"_43":495,"_55":97,"_57":98,"_357":358,"_359":-5,"_330":549,"_332":549,"_45":565,"_334":98,"_368":566},{"_362":551,"_364":365,"_366":552},[567,576,585],{"_43":492,"_55":493,"_57":494,"_357":358,"_359":495,"_330":372,"_332":372,"_45":568,"_334":499,"_368":569},{"_362":497,"_364":365,"_366":498},[570],{"_43":502,"_55":77,"_57":78,"_357":358,"_359":492,"_330":441,"_332":441,"_45":571,"_334":509,"_368":572},{"_362":497,"_364":365,"_366":508},[573],{"_43":501,"_55":259,"_57":114,"_357":358,"_359":502,"_330":503,"_332":503,"_45":574,"_334":505,"_368":575},{"_362":365,"_364":365,"_366":382},[],{"_43":515,"_55":516,"_57":517,"_357":358,"_359":495,"_330":372,"_332":372,"_45":577,"_334":521,"_368":578},{"_362":519,"_364":365,"_366":520},[579],{"_43":528,"_55":529,"_57":530,"_357":358,"_359":515,"_330":531,"_332":531,"_45":580,"_334":534,"_368":581},{"_362":497,"_364":365,"_366":533},[582],{"_43":543,"_55":544,"_57":114,"_357":358,"_359":528,"_330":545,"_332":545,"_45":583,"_334":547,"_368":584},{"_362":365,"_364":365,"_366":382},[],{"_43":440,"_55":523,"_57":524,"_357":358,"_359":495,"_330":372,"_332":372,"_45":586,"_334":526,"_368":587},{"_362":497,"_364":365,"_366":444},[588],{"_43":437,"_55":438,"_57":439,"_357":358,"_359":440,"_330":441,"_332":441,"_45":589,"_334":439,"_368":590},{"_362":443,"_364":365,"_366":444},[591],{"_43":538,"_55":259,"_57":114,"_357":358,"_359":437,"_330":539,"_332":539,"_45":592,"_334":541,"_368":593},{"_362":365,"_364":365,"_366":382},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários