[{"_1":2,"_392":-5,"_393":-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/88c87978-76a5-4572-96d4-0b5307c1573b?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_204":205,"_51":280,"_347":348,"_388":389,"_390":391},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_97":41,"_98":99,"_100":101,"_102":16},"correctOptionId","","difficulty","id","88c87978-76a5-4572-96d4-0b5307c1573b","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},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","162848202","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","163266962","options",[79,85,89,93],{"_43":80,"_81":82,"_83":84},"ebd09bfd-b942-41b4-93ac-1bb184ac639e","label","A","text","

A luz não é afetada pela gravidade.

",{"_43":86,"_81":87,"_83":88},"b33bb618-9a81-4fb7-a4ac-2db7affd5aec","B","

A luz se curva ao passar perto de um objeto massivo.

",{"_43":90,"_81":91,"_83":92},"67925c23-f16a-44bf-a473-229b8b4569ef","C","

A luz viaja mais rápido em campos gravitacionais fortes.

",{"_43":94,"_81":95,"_83":96},"62e413b8-7167-4664-a83d-973fb572c6c9","D","

A luz é refletida por buracos negros.

","solution_explanation","statement","

A teoria da relatividade geral de Einstein revolucionou a compreensão da gravidade. Qual é uma das principais previsões dessa teoria em relação à luz?

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_51":141,"_176":177,"_194":195},"content",{"_43":108,"_57":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_45":116,"_119":120,"_121":120,"_122":-5,"_123":124},"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",{"_117":118},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_127":128,"_134":135,"_136":137,"_138":139,"_28":140},"provider",{"_43":129,"_130":131,"_132":133},"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",[142],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":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],{"_43":160,"_57":161,"_59":162,"_146":147,"_148":143,"_119":163,"_121":163,"_45":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],{"_43":170,"_57":58,"_59":60,"_146":147,"_148":160,"_119":171,"_121":171,"_45":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",{"_43":114,"_13":109,"_110":-5,"_178":179,"_180":181,"_28":-5,"_182":-5,"_127":181,"_183":184,"_138":-5,"_185":-5,"_186":-5,"_187":-5,"_188":-5,"_45":189,"_190":154,"_191":-5,"_100":192,"_119":193,"_121":193},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_117":118},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":196,"_123":145,"_157":197},{"_151":152,"_153":154,"_155":156},[198],{"_43":160,"_57":161,"_59":162,"_146":147,"_148":143,"_119":163,"_121":163,"_45":199,"_123":167,"_157":200},{"_151":165,"_153":154,"_155":166},[201],{"_43":170,"_57":58,"_59":60,"_146":147,"_148":160,"_119":171,"_121":171,"_45":202,"_123":174,"_157":203},{"_151":154,"_153":154,"_155":173},[],"similarQuestions",[206,237,257],{"_40":207,"_42":41,"_43":208,"_77":209,"_97":225,"_98":226,"_51":227},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[210,213,216,219,222],{"_43":211,"_81":82,"_83":212},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":214,"_81":87,"_83":215},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":217,"_81":91,"_83":218},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":220,"_81":95,"_83":221},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":207,"_81":223,"_83":224},"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

",[228],{"_43":229,"_57":230,"_59":231,"_146":147,"_148":232,"_119":233,"_121":233,"_45":234,"_123":231},"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":235,"_153":154,"_155":236},4,12302,{"_40":238,"_42":41,"_43":239,"_77":240,"_97":252,"_98":253,"_51":254},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[241,244,247,249],{"_43":242,"_81":82,"_83":243},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":245,"_81":87,"_83":246},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":238,"_81":91,"_83":248},"

Verdadeiro, falso, verdadeiro

",{"_43":250,"_81":95,"_83":251},"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?

",[255],{"_43":229,"_57":230,"_59":231,"_146":147,"_148":232,"_119":233,"_121":233,"_45":256,"_123":231},{"_151":235,"_153":154,"_155":236},{"_40":258,"_42":41,"_43":259,"_77":260,"_97":275,"_98":276,"_51":277},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[261,264,267,269,272],{"_43":262,"_81":82,"_83":263},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":265,"_81":87,"_83":266},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":258,"_81":91,"_83":268},"Indeterminado",{"_43":270,"_81":95,"_83":271},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":273,"_81":223,"_83":274},"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????",[278],{"_43":229,"_57":230,"_59":231,"_146":147,"_148":232,"_119":233,"_121":233,"_45":279,"_123":231},{"_151":235,"_153":154,"_155":236},[281,283,292,298,302,304,306,314,319,327,329,334,340],{"_43":229,"_57":230,"_59":231,"_146":147,"_148":232,"_119":233,"_121":233,"_45":282,"_123":231},{"_151":235,"_153":154,"_155":236},{"_43":284,"_57":285,"_59":286,"_146":147,"_148":287,"_119":163,"_121":163,"_45":288,"_123":291},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":289,"_153":154,"_155":290},5,30614,"engenharia-mecatronica-1",{"_43":293,"_57":58,"_59":60,"_146":147,"_148":294,"_119":295,"_121":295,"_45":296,"_123":297},"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",{"_43":294,"_57":161,"_59":162,"_146":147,"_148":284,"_119":233,"_121":233,"_45":299,"_123":301},{"_151":289,"_153":154,"_155":300},25741,"mecanica-3",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":303,"_123":145},{"_151":152,"_153":154,"_155":156},{"_43":170,"_57":58,"_59":60,"_146":147,"_148":160,"_119":171,"_121":171,"_45":305,"_123":174},{"_151":154,"_153":154,"_155":173},{"_43":307,"_57":308,"_59":309,"_146":147,"_148":287,"_119":163,"_121":163,"_45":310,"_123":313},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_151":311,"_153":154,"_155":312},21,45865,"engenharia-civil-3",{"_43":232,"_57":315,"_59":316,"_146":147,"_148":287,"_119":163,"_121":163,"_45":317,"_123":318},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":289,"_153":154,"_155":236},"engenharia-de-petroleo-1",{"_43":320,"_57":321,"_59":322,"_146":147,"_148":307,"_119":323,"_121":323,"_45":324,"_123":326},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_151":289,"_153":154,"_155":325},8852,"estruturas-1",{"_43":160,"_57":161,"_59":162,"_146":147,"_148":143,"_119":163,"_121":163,"_45":328,"_123":167},{"_151":165,"_153":154,"_155":166},{"_43":330,"_57":58,"_59":60,"_146":147,"_148":229,"_119":331,"_121":331,"_45":332,"_123":333},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-7",{"_43":335,"_57":336,"_59":60,"_146":147,"_148":320,"_119":337,"_121":337,"_45":338,"_123":339},"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",{"_43":287,"_57":341,"_59":342,"_146":147,"_148":-5,"_119":343,"_121":343,"_45":344,"_123":342},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":345,"_153":154,"_155":346},29,351586,"tagsTree",[349,358],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":350,"_123":145,"_157":351},{"_151":152,"_153":154,"_155":156},[352],{"_43":160,"_57":161,"_59":162,"_146":147,"_148":143,"_119":163,"_121":163,"_45":353,"_123":167,"_157":354},{"_151":165,"_153":154,"_155":166},[355],{"_43":170,"_57":58,"_59":60,"_146":147,"_148":160,"_119":171,"_121":171,"_45":356,"_123":174,"_157":357},{"_151":154,"_153":154,"_155":173},[],{"_43":287,"_57":341,"_59":342,"_146":147,"_148":-5,"_119":343,"_121":343,"_45":359,"_123":342,"_157":360},{"_151":345,"_153":154,"_155":346},[361,370,379],{"_43":284,"_57":285,"_59":286,"_146":147,"_148":287,"_119":163,"_121":163,"_45":362,"_123":291,"_157":363},{"_151":289,"_153":154,"_155":290},[364],{"_43":294,"_57":161,"_59":162,"_146":147,"_148":284,"_119":233,"_121":233,"_45":365,"_123":301,"_157":366},{"_151":289,"_153":154,"_155":300},[367],{"_43":293,"_57":58,"_59":60,"_146":147,"_148":294,"_119":295,"_121":295,"_45":368,"_123":297,"_157":369},{"_151":154,"_153":154,"_155":173},[],{"_43":307,"_57":308,"_59":309,"_146":147,"_148":287,"_119":163,"_121":163,"_45":371,"_123":313,"_157":372},{"_151":311,"_153":154,"_155":312},[373],{"_43":320,"_57":321,"_59":322,"_146":147,"_148":307,"_119":323,"_121":323,"_45":374,"_123":326,"_157":375},{"_151":289,"_153":154,"_155":325},[376],{"_43":335,"_57":336,"_59":60,"_146":147,"_148":320,"_119":337,"_121":337,"_45":377,"_123":339,"_157":378},{"_151":154,"_153":154,"_155":173},[],{"_43":232,"_57":315,"_59":316,"_146":147,"_148":287,"_119":163,"_121":163,"_45":380,"_123":318,"_157":381},{"_151":289,"_153":154,"_155":236},[382],{"_43":229,"_57":230,"_59":231,"_146":147,"_148":232,"_119":233,"_121":233,"_45":383,"_123":231,"_157":384},{"_151":235,"_153":154,"_155":236},[385],{"_43":330,"_57":58,"_59":60,"_146":147,"_148":229,"_119":331,"_121":331,"_45":386,"_123":333,"_157":387},{"_151":154,"_153":154,"_155":173},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários