[{"_1":2,"_354":-5,"_355":-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/6294e8f8-9e2c-4b97-beb5-ddcca8302f40","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_194":195,"_52":266,"_328":329,"_350":351,"_352":353},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_97":43,"_98":99,"_100":101,"_102":16},"correctOptionId","25be76a7-773b-4770-b604-eb45a467e4b9","difficulty","","id","6294e8f8-9e2c-4b97-beb5-ddcca8302f40","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","121006603","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","162980110","options",[80,85,89,93],{"_44":41,"_81":82,"_83":84},"label","A","text","Tração e compressão.",{"_44":86,"_81":87,"_83":88},"16576688-5487-4e33-876e-229489327c68","B","Torção e compressão.",{"_44":90,"_81":91,"_83":92},"9b09e56c-5bbc-4e58-a2c4-cc4bfc5069c5","C","Cortante e torção.",{"_44":94,"_81":95,"_83":96},"4ee283c4-6d26-46d8-9ac9-60fcfc44f7ad","D","Cortante e tração.","solution_explanation","statement","

A flexão acontece predominantemente nas vigas das estruturas. Podemos considerar a flexão como a combinação de dois esforços.
Sobre esses esforços, assinale a alternativa:

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_52":141,"_176":177,"_193":142},"content",{"_44":108,"_58":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_46":116,"_119":120,"_121":120,"_122":-5,"_123":124},"f3f32d5f-cda6-4695-afc1-c1b04af6fcff","Cônicas - 03 - Caracterização geométrica das cônicas - Parte 03","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","da5a3e7b-1215-4c06-bffc-4b84bbd46c85","user_id",{"_117":118},"external_id","13404","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","conicas-03-caracterizacao-geometrica-das-conicas-parte-03","prometheusData",{"_127":128,"_134":135,"_136":137,"_138":139,"_28":140},"provider",{"_44":129,"_130":131,"_132":133},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","2d365ea1-b71b-47ec-9f55-32ab97b700c0","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/2d365ea1-b71b-47ec-9f55-32ab97b700c0/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/2d365ea1-b71b-47ec-9f55-32ab97b700c0/levels.m3u8",[142],{"_44":143,"_58":144,"_60":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_46":150,"_123":145,"_157":158},"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",{"_151":152,"_153":154,"_155":156},"childrenCount",18,"content_count",0,"question_count",135489,"children",[159],{"_44":160,"_58":161,"_60":162,"_146":147,"_148":143,"_119":163,"_121":163,"_46":164,"_123":167,"_157":168},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_151":165,"_153":154,"_155":166},10,19948,"mecanica-2",[169],{"_44":170,"_58":59,"_60":61,"_146":147,"_148":160,"_119":171,"_121":171,"_46":172,"_123":174,"_157":175},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_151":154,"_153":154,"_155":173},3376,"resistencia-dos-materiais-4",[],"video",{"_44":114,"_13":109,"_110":-5,"_178":154,"_179":180,"_28":-5,"_181":-5,"_127":180,"_182":183,"_138":-5,"_184":-5,"_185":-5,"_186":-5,"_187":-5,"_46":188,"_189":154,"_190":-5,"_100":191,"_119":192,"_121":192},"duration","source_type","prometheus","iframe_url","provider_video_id","a1c61c9c-b294-4748-a100-3c451978d8cc","format","quality","file_path","file_size",{"_117":118},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag","similarQuestions",[196,227,245],{"_40":197,"_42":43,"_44":198,"_78":199,"_97":215,"_98":216,"_52":217},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[200,203,206,209,212],{"_44":201,"_81":82,"_83":202},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":204,"_81":87,"_83":205},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":207,"_81":91,"_83":208},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":210,"_81":95,"_83":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":197,"_81":213,"_83":214},"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

",[218],{"_44":219,"_58":220,"_60":221,"_146":147,"_148":222,"_119":223,"_121":223,"_46":224,"_123":221},"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":225,"_153":154,"_155":226},4,12302,{"_40":228,"_42":43,"_44":229,"_78":230,"_97":242,"_98":243,"_52":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_44":232,"_81":82,"_83":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":235,"_81":87,"_83":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":228,"_81":91,"_83":238},"

Verdadeiro, falso, verdadeiro

",{"_44":240,"_81":95,"_83":241},"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?

",[218],{"_40":246,"_42":43,"_44":247,"_78":248,"_97":263,"_98":264,"_52":265},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[249,252,255,257,260],{"_44":250,"_81":82,"_83":251},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":253,"_81":87,"_83":254},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":246,"_81":91,"_83":256},"Indeterminado",{"_44":258,"_81":95,"_83":259},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":261,"_81":213,"_83":262},"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????",[218],[218,267,276,282,286,287,288,296,301,309,310,315,321],{"_44":268,"_58":269,"_60":270,"_146":147,"_148":271,"_119":163,"_121":163,"_46":272,"_123":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":273,"_153":154,"_155":274},5,30614,"engenharia-mecatronica-1",{"_44":277,"_58":59,"_60":61,"_146":147,"_148":278,"_119":279,"_121":279,"_46":280,"_123":281},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-6",{"_44":278,"_58":161,"_60":162,"_146":147,"_148":268,"_119":223,"_121":223,"_46":283,"_123":285},{"_151":273,"_153":154,"_155":284},25741,"mecanica-3",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_46":150,"_123":145},{"_44":170,"_58":59,"_60":61,"_146":147,"_148":160,"_119":171,"_121":171,"_46":172,"_123":174},{"_44":289,"_58":290,"_60":291,"_146":147,"_148":271,"_119":163,"_121":163,"_46":292,"_123":295},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_151":293,"_153":154,"_155":294},21,45865,"engenharia-civil-3",{"_44":222,"_58":297,"_60":298,"_146":147,"_148":271,"_119":163,"_121":163,"_46":299,"_123":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":273,"_153":154,"_155":226},"engenharia-de-petroleo-1",{"_44":302,"_58":303,"_60":304,"_146":147,"_148":289,"_119":305,"_121":305,"_46":306,"_123":308},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_151":273,"_153":154,"_155":307},8852,"estruturas-1",{"_44":160,"_58":161,"_60":162,"_146":147,"_148":143,"_119":163,"_121":163,"_46":164,"_123":167},{"_44":311,"_58":59,"_60":61,"_146":147,"_148":219,"_119":312,"_121":312,"_46":313,"_123":314},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-7",{"_44":316,"_58":317,"_60":61,"_146":147,"_148":302,"_119":318,"_121":318,"_46":319,"_123":320},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-5",{"_44":271,"_58":322,"_60":323,"_146":147,"_148":-5,"_119":324,"_121":324,"_46":325,"_123":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":326,"_153":154,"_155":327},29,351586,"tagsTree",[142,330],{"_44":271,"_58":322,"_60":323,"_146":147,"_148":-5,"_119":324,"_121":324,"_46":325,"_123":323,"_157":331},[332,338,344],{"_44":268,"_58":269,"_60":270,"_146":147,"_148":271,"_119":163,"_121":163,"_46":272,"_123":275,"_157":333},[334],{"_44":278,"_58":161,"_60":162,"_146":147,"_148":268,"_119":223,"_121":223,"_46":283,"_123":285,"_157":335},[336],{"_44":277,"_58":59,"_60":61,"_146":147,"_148":278,"_119":279,"_121":279,"_46":280,"_123":281,"_157":337},[],{"_44":289,"_58":290,"_60":291,"_146":147,"_148":271,"_119":163,"_121":163,"_46":292,"_123":295,"_157":339},[340],{"_44":302,"_58":303,"_60":304,"_146":147,"_148":289,"_119":305,"_121":305,"_46":306,"_123":308,"_157":341},[342],{"_44":316,"_58":317,"_60":61,"_146":147,"_148":302,"_119":318,"_121":318,"_46":319,"_123":320,"_157":343},[],{"_44":222,"_58":297,"_60":298,"_146":147,"_148":271,"_119":163,"_121":163,"_46":299,"_123":300,"_157":345},[346],{"_44":219,"_58":220,"_60":221,"_146":147,"_148":222,"_119":223,"_121":223,"_46":224,"_123":221,"_157":347},[348],{"_44":311,"_58":59,"_60":61,"_146":147,"_148":219,"_119":312,"_121":312,"_46":313,"_123":314,"_157":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários