[{"_1":2,"_289":-5,"_290":-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/f45bad3a-57e5-4173-9a78-3c3b7a20b83b","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_107":108,"_190":191,"_52":261,"_277":278,"_285":286,"_287":288},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_101":43,"_102":103,"_104":105,"_106":16},"correctOptionId","32714751-7193-4edd-a065-c397bf98804c","difficulty","","id","f45bad3a-57e5-4173-9a78-3c3b7a20b83b","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},672071,"name","Mecânica","alias","mecanica","materialId","105726797","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","136597301","options",[80,86,90,94,98],{"_44":81,"_82":83,"_84":85},"4e49829d-4e1b-48e3-8a39-28ea1d0c0812","label","A","text","Lubrefil.",{"_44":87,"_82":88,"_84":89},"e855f9f7-02fb-4f7a-a883-22723c1a6cc2","B","Purgador automático.",{"_44":91,"_82":92,"_84":93},"e0cd267b-c263-4b72-bf12-7c875677e936","C","Compressor.",{"_44":95,"_82":96,"_84":97},"8dcf89dd-c7e8-4fba-80bd-d5dd8e1a0cff","D","Atuador.",{"_44":41,"_82":99,"_84":100},"E","Válvulas.","solution_explanation","statement","

Posição inicial, número de posições, número de vias, tipo de acionamento, tipo de retorno e vazão são dados necessários para qual componente?

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_52":145,"_171":172,"_189":146},"content",{"_44":112,"_58":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_46":120,"_123":124,"_125":124,"_126":-5,"_127":128},"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",{"_121":122},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_44":133,"_134":135,"_136":137},"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",[146],{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":154,"_127":149,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",18,"content_count",0,"question_count",135489,"children",[163],{"_44":164,"_58":59,"_60":61,"_150":151,"_152":147,"_123":165,"_125":165,"_46":166,"_127":169,"_161":170},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_155":167,"_157":158,"_159":168},10,19948,"mecanica-2",[],"video",{"_44":118,"_13":113,"_114":-5,"_173":174,"_175":176,"_28":-5,"_177":-5,"_131":176,"_178":179,"_142":-5,"_180":-5,"_181":-5,"_182":-5,"_183":-5,"_46":184,"_185":158,"_186":-5,"_104":187,"_123":188,"_125":188},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[192,222,240],{"_40":193,"_42":43,"_44":194,"_78":195,"_101":210,"_102":211,"_52":212},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[196,199,202,205,208],{"_44":197,"_82":83,"_84":198},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":200,"_82":88,"_84":201},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":203,"_82":92,"_84":204},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":206,"_82":96,"_84":207},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":193,"_82":99,"_84":209},"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

",[213],{"_44":214,"_58":215,"_60":216,"_150":151,"_152":217,"_123":165,"_125":165,"_46":218,"_127":221},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":219,"_157":158,"_159":220},5,30614,"engenharia-mecatronica-1",{"_40":223,"_42":43,"_44":224,"_78":225,"_101":237,"_102":238,"_52":239},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[226,229,232,234],{"_44":227,"_82":83,"_84":228},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":230,"_82":88,"_84":231},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":223,"_82":92,"_84":233},"

Verdadeiro, falso, verdadeiro

",{"_44":235,"_82":96,"_84":236},"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?

",[213],{"_40":241,"_42":43,"_44":242,"_78":243,"_101":258,"_102":259,"_52":260},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[244,247,250,252,255],{"_44":245,"_82":83,"_84":246},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":248,"_82":88,"_84":249},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":241,"_82":92,"_84":251},"Indeterminado",{"_44":253,"_82":96,"_84":254},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":256,"_82":99,"_84":257},"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????",[213],[213,262,268,269,270],{"_44":263,"_58":59,"_60":61,"_150":151,"_152":214,"_123":264,"_125":264,"_46":265,"_127":267},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_155":219,"_157":158,"_159":266},25741,"mecanica-3",{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":154,"_127":149},{"_44":164,"_58":59,"_60":61,"_150":151,"_152":147,"_123":165,"_125":165,"_46":166,"_127":169},{"_44":217,"_58":271,"_60":272,"_150":151,"_152":-5,"_123":273,"_125":273,"_46":274,"_127":272},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":275,"_157":158,"_159":276},29,351586,"tagsTree",[146,279],{"_44":217,"_58":271,"_60":272,"_150":151,"_152":-5,"_123":273,"_125":273,"_46":274,"_127":272,"_161":280},[281],{"_44":214,"_58":215,"_60":216,"_150":151,"_152":217,"_123":165,"_125":165,"_46":218,"_127":221,"_161":282},[283],{"_44":263,"_58":59,"_60":61,"_150":151,"_152":214,"_123":264,"_125":264,"_46":265,"_127":267,"_161":284},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários