[{"_1":2,"_431":-5,"_432":-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/3a7eefe9-0ade-4b18-832f-1c0746f73759","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_185":186,"_275":276,"_50":347,"_405":406,"_427":428,"_429":430},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_159":160,"_179":41,"_180":181,"_182":183,"_184":16},"correctOptionId","","difficulty","id","3a7eefe9-0ade-4b18-832f-1c0746f73759","metadata",{"_47":48,"_155":156,"_157":158},"pd",{"_49":-5,"_50":51,"_117":118,"_143":144,"_145":146,"_147":16,"_148":149,"_150":16,"_151":152,"_153":154},"area","tags",[52,58,62,65,69,73,77,81,85,89,93,97,101,105,109,113],{"_43":53,"_54":55,"_56":57},56,"name","CONCRETO","alias","concreto",{"_43":59,"_54":60,"_56":61},64,"Apostila","apostila",{"_43":63,"_54":64,"_56":64},117,"calculo",{"_43":66,"_54":67,"_56":68},415,"Mecânica","mecanica",{"_43":70,"_54":71,"_56":72},845,"Engenharia","engenharia",{"_43":74,"_54":75,"_56":76},961,"Estrutura","estrutura",{"_43":78,"_54":79,"_56":80},10224,"Aço","aco",{"_43":82,"_54":83,"_56":84},16975,"Estrutural","estrutural",{"_43":86,"_54":87,"_56":88},58413,"Tubulações","tubulacoes",{"_43":90,"_54":91,"_56":92},64675,"Estrutura-de-Aço","estrutura-de-aco",{"_43":94,"_54":95,"_56":96},68385,"metálica","metalica",{"_43":98,"_54":99,"_56":100},68392,"Tubulação","tubulacao",{"_43":102,"_54":103,"_56":104},96619,"#Artigo","%23artigo",{"_43":106,"_54":107,"_56":108},292558,"Tabela-Estruturas-de-Aço","tabela-estruturas-de-aco",{"_43":110,"_54":111,"_56":112},665760,"Perfil estrutural","perfil-estrutural",{"_43":114,"_54":115,"_56":116},739136,"1608mf","1608-mf","subjects",[119,123,127,131,135,139],{"_43":120,"_54":121,"_56":122},669656,"Sistema Estrutural","sistema-estrutural",{"_43":124,"_54":125,"_56":126},686546,"Estruturas de Aço","estruturas-de-aco",{"_43":128,"_54":129,"_56":130},686698,"Pontes","pontes",{"_43":132,"_54":133,"_56":134},754187,"Estruturas Metálicas","estruturas-metalicas",{"_43":136,"_54":137,"_56":138},1481802,"Engenharia Civil","engenharia-civil",{"_43":140,"_54":141,"_56":142},1663620,"Resistência dos Materiais","resistencia-dos-materiais","materialId","81386098","answerCount",1,"isIndexable","mainSubject",{"_43":140,"_54":141,"_56":142},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","132530576","options",[161,167,171,175],{"_43":162,"_163":164,"_165":166},"e873cb63-8f66-4600-ae22-2fae4e3f8567","label","A","text","1.25, 1.30, 1.35, 1.40, and 1.50.",{"_43":168,"_163":169,"_165":170},"5af92385-dc62-4ab6-bc5d-53944cc1a42e","B","0.6, 0.3, and 0.",{"_43":172,"_163":173,"_165":174},"c5ddbe6c-1e96-4108-be0a-ec70f6136ed0","C","1.0, 0.7, and 0.8.",{"_43":176,"_163":177,"_165":178},"c6532fe7-8896-4327-9eec-b8c4e67dc658","D","0.5, 0.7, and 0.8.","solution_explanation","statement","

What are the values of the coefficient of weighting γf for permanent actions?

","status","pending_classification","hasRelatedVideo","relatedVideos",[187],{"_188":189,"_207":208,"_50":223,"_256":257,"_274":224},"content",{"_43":190,"_54":191,"_192":-5,"_193":194,"_195":196,"_197":-5,"_45":198,"_201":202,"_203":202,"_204":-5,"_205":206},"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",{"_199":200},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_209":210,"_216":217,"_218":219,"_220":221,"_28":222},"provider",{"_43":211,"_212":213,"_214":215},"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",[224],{"_43":225,"_54":226,"_56":227,"_228":229,"_230":-5,"_201":231,"_203":231,"_45":232,"_205":227,"_239":240},"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",{"_233":234,"_235":236,"_237":238},"childrenCount",18,"content_count",0,"question_count",135489,"children",[241],{"_43":242,"_54":67,"_56":68,"_228":229,"_230":225,"_201":243,"_203":243,"_45":244,"_205":247,"_239":248},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_233":245,"_235":236,"_237":246},10,19948,"mecanica-2",[249],{"_43":250,"_54":141,"_56":142,"_228":229,"_230":242,"_201":251,"_203":251,"_45":252,"_205":254,"_239":255},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_233":236,"_235":236,"_237":253},3376,"resistencia-dos-materiais-4",[],"video",{"_43":196,"_13":191,"_192":-5,"_258":259,"_260":261,"_28":-5,"_262":-5,"_209":261,"_263":264,"_220":-5,"_265":-5,"_266":-5,"_267":-5,"_268":-5,"_45":269,"_270":236,"_271":-5,"_182":272,"_201":273,"_203":273},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_199":200},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[277,308,326],{"_40":278,"_42":41,"_43":279,"_159":280,"_179":296,"_180":297,"_50":298},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[281,284,287,290,293],{"_43":282,"_163":164,"_165":283},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":285,"_163":169,"_165":286},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":288,"_163":173,"_165":289},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":291,"_163":177,"_165":292},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":278,"_163":294,"_165":295},"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

",[299],{"_43":300,"_54":301,"_56":302,"_228":229,"_230":303,"_201":304,"_203":304,"_45":305,"_205":302},"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",{"_233":306,"_235":236,"_237":307},4,12302,{"_40":309,"_42":41,"_43":310,"_159":311,"_179":323,"_180":324,"_50":325},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[312,315,318,320],{"_43":313,"_163":164,"_165":314},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":316,"_163":169,"_165":317},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":309,"_163":173,"_165":319},"

Verdadeiro, falso, verdadeiro

",{"_43":321,"_163":177,"_165":322},"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?

",[299],{"_40":327,"_42":41,"_43":328,"_159":329,"_179":344,"_180":345,"_50":346},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[330,333,336,338,341],{"_43":331,"_163":164,"_165":332},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":334,"_163":169,"_165":335},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":327,"_163":173,"_165":337},"Indeterminado",{"_43":339,"_163":177,"_165":340},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":342,"_163":294,"_165":343},"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????",[299],[299,348,357,363,367,368,369,375,380,388,389,394,400],{"_43":349,"_54":350,"_56":351,"_228":229,"_230":352,"_201":243,"_203":243,"_45":353,"_205":356},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_233":354,"_235":236,"_237":355},5,30614,"engenharia-mecatronica-1",{"_43":358,"_54":141,"_56":142,"_228":229,"_230":359,"_201":360,"_203":360,"_45":361,"_205":362},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_233":236,"_235":236,"_237":253},"resistencia-dos-materiais-6",{"_43":359,"_54":67,"_56":68,"_228":229,"_230":349,"_201":304,"_203":304,"_45":364,"_205":366},{"_233":354,"_235":236,"_237":365},25741,"mecanica-3",{"_43":225,"_54":226,"_56":227,"_228":229,"_230":-5,"_201":231,"_203":231,"_45":232,"_205":227},{"_43":250,"_54":141,"_56":142,"_228":229,"_230":242,"_201":251,"_203":251,"_45":252,"_205":254},{"_43":370,"_54":137,"_56":138,"_228":229,"_230":352,"_201":243,"_203":243,"_45":371,"_205":374},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331",{"_233":372,"_235":236,"_237":373},21,45865,"engenharia-civil-3",{"_43":303,"_54":376,"_56":377,"_228":229,"_230":352,"_201":243,"_203":243,"_45":378,"_205":379},"Engenharia de Petróleo","engenharia-de-petroleo",{"_233":354,"_235":236,"_237":307},"engenharia-de-petroleo-1",{"_43":381,"_54":382,"_56":383,"_228":229,"_230":370,"_201":384,"_203":384,"_45":385,"_205":387},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_233":354,"_235":236,"_237":386},8852,"estruturas-1",{"_43":242,"_54":67,"_56":68,"_228":229,"_230":225,"_201":243,"_203":243,"_45":244,"_205":247},{"_43":390,"_54":141,"_56":142,"_228":229,"_230":300,"_201":391,"_203":391,"_45":392,"_205":393},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_233":236,"_235":236,"_237":253},"resistencia-dos-materiais-7",{"_43":395,"_54":396,"_56":142,"_228":229,"_230":381,"_201":397,"_203":397,"_45":398,"_205":399},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_233":236,"_235":236,"_237":253},"resistencia-dos-materiais-5",{"_43":352,"_54":71,"_56":72,"_228":229,"_230":-5,"_201":401,"_203":401,"_45":402,"_205":72},"2025-04-29T01:55:38.635246+00:00",{"_233":403,"_235":236,"_237":404},29,351586,"tagsTree",[224,407],{"_43":352,"_54":71,"_56":72,"_228":229,"_230":-5,"_201":401,"_203":401,"_45":402,"_205":72,"_239":408},[409,415,421],{"_43":349,"_54":350,"_56":351,"_228":229,"_230":352,"_201":243,"_203":243,"_45":353,"_205":356,"_239":410},[411],{"_43":359,"_54":67,"_56":68,"_228":229,"_230":349,"_201":304,"_203":304,"_45":364,"_205":366,"_239":412},[413],{"_43":358,"_54":141,"_56":142,"_228":229,"_230":359,"_201":360,"_203":360,"_45":361,"_205":362,"_239":414},[],{"_43":370,"_54":137,"_56":138,"_228":229,"_230":352,"_201":243,"_203":243,"_45":371,"_205":374,"_239":416},[417],{"_43":381,"_54":382,"_56":383,"_228":229,"_230":370,"_201":384,"_203":384,"_45":385,"_205":387,"_239":418},[419],{"_43":395,"_54":396,"_56":142,"_228":229,"_230":381,"_201":397,"_203":397,"_45":398,"_205":399,"_239":420},[],{"_43":303,"_54":376,"_56":377,"_228":229,"_230":352,"_201":243,"_203":243,"_45":378,"_205":379,"_239":422},[423],{"_43":300,"_54":301,"_56":302,"_228":229,"_230":303,"_201":304,"_203":304,"_45":305,"_205":302,"_239":424},[425],{"_43":390,"_54":141,"_56":142,"_228":229,"_230":300,"_201":391,"_203":391,"_45":392,"_205":393,"_239":426},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários