[{"_1":2,"_309":-5,"_310":-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/f068b2dc-550d-4540-99aa-3daafb75e498?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_192":193,"_51":268,"_288":289,"_305":306,"_307":308},"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","f068b2dc-550d-4540-99aa-3daafb75e498","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},672071,"name","Mecânica","alias","mecanica","materialId","125493955","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","135603909","options",[79,85,89,93],{"_43":80,"_81":82,"_83":84},"c9869313-da66-40db-98ff-e8bbe375e38e","label","A","text","2,8 m e 10,0 m/s.",{"_43":86,"_81":87,"_83":88},"b462df60-c4ca-4026-91ff-c85e592a92ac","B","12,5 m e 32,5 m/s.",{"_43":90,"_81":91,"_83":92},"904317b9-57ef-4f06-b627-87a0dd7df751","C","10,0 m e 15,5 m/s.",{"_43":94,"_81":95,"_83":96},"77742f30-bc96-432e-a7c9-3a5b558edcac","D","21,4 m e 20,8 m/s.","solution_explanation","statement","De um elevador em movimento ascendente, de velocidade 3,66 \\, \\text{m/s}, abandona-se uma pedra que atinge o fundo do poço em 2,5 \\, \\text{s}. A que altura (H) estava o elevador no momento do abandono da pedra? Qual a velocidade da pedra no instante do choque com o solo?","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_51":141,"_167":168,"_185":186},"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":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":162,"_123":165,"_157":166},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_151":163,"_153":154,"_155":164},10,19948,"mecanica-2",[],"video",{"_43":114,"_13":109,"_110":-5,"_169":170,"_171":172,"_28":-5,"_173":-5,"_127":172,"_174":175,"_138":-5,"_176":-5,"_177":-5,"_178":-5,"_179":-5,"_45":180,"_181":154,"_182":-5,"_100":183,"_119":184,"_121":184},"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":187,"_123":145,"_157":188},{"_151":152,"_153":154,"_155":156},[189],{"_43":160,"_57":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":190,"_123":165,"_157":191},{"_151":163,"_153":154,"_155":164},[],"similarQuestions",[194,225,245],{"_40":195,"_42":41,"_43":196,"_77":197,"_97":213,"_98":214,"_51":215},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[198,201,204,207,210],{"_43":199,"_81":82,"_83":200},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":202,"_81":87,"_83":203},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":205,"_81":91,"_83":206},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":208,"_81":95,"_83":209},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":195,"_81":211,"_83":212},"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

",[216],{"_43":217,"_57":218,"_59":219,"_146":147,"_148":220,"_119":161,"_121":161,"_45":221,"_123":224},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":222,"_153":154,"_155":223},5,30614,"engenharia-mecatronica-1",{"_40":226,"_42":41,"_43":227,"_77":228,"_97":240,"_98":241,"_51":242},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[229,232,235,237],{"_43":230,"_81":82,"_83":231},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":233,"_81":87,"_83":234},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":226,"_81":91,"_83":236},"

Verdadeiro, falso, verdadeiro

",{"_43":238,"_81":95,"_83":239},"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?

",[243],{"_43":217,"_57":218,"_59":219,"_146":147,"_148":220,"_119":161,"_121":161,"_45":244,"_123":224},{"_151":222,"_153":154,"_155":223},{"_40":246,"_42":41,"_43":247,"_77":248,"_97":263,"_98":264,"_51":265},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[249,252,255,257,260],{"_43":250,"_81":82,"_83":251},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":253,"_81":87,"_83":254},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":246,"_81":91,"_83":256},"Indeterminado",{"_43":258,"_81":95,"_83":259},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":261,"_81":211,"_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????",[266],{"_43":217,"_57":218,"_59":219,"_146":147,"_148":220,"_119":161,"_121":161,"_45":267,"_123":224},{"_151":222,"_153":154,"_155":223},[269,271,277,279,281],{"_43":217,"_57":218,"_59":219,"_146":147,"_148":220,"_119":161,"_121":161,"_45":270,"_123":224},{"_151":222,"_153":154,"_155":223},{"_43":272,"_57":58,"_59":60,"_146":147,"_148":217,"_119":273,"_121":273,"_45":274,"_123":276},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_151":222,"_153":154,"_155":275},25741,"mecanica-3",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":278,"_123":145},{"_151":152,"_153":154,"_155":156},{"_43":160,"_57":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":280,"_123":165},{"_151":163,"_153":154,"_155":164},{"_43":220,"_57":282,"_59":283,"_146":147,"_148":-5,"_119":284,"_121":284,"_45":285,"_123":283},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":286,"_153":154,"_155":287},29,351586,"tagsTree",[290,296],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":291,"_123":145,"_157":292},{"_151":152,"_153":154,"_155":156},[293],{"_43":160,"_57":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":294,"_123":165,"_157":295},{"_151":163,"_153":154,"_155":164},[],{"_43":220,"_57":282,"_59":283,"_146":147,"_148":-5,"_119":284,"_121":284,"_45":297,"_123":283,"_157":298},{"_151":286,"_153":154,"_155":287},[299],{"_43":217,"_57":218,"_59":219,"_146":147,"_148":220,"_119":161,"_121":161,"_45":300,"_123":224,"_157":301},{"_151":222,"_153":154,"_155":223},[302],{"_43":272,"_57":58,"_59":60,"_146":147,"_148":217,"_119":273,"_121":273,"_45":303,"_123":276,"_157":304},{"_151":222,"_153":154,"_155":275},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários