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Qual é a respectiva equação reduzida?","status","pending_classification","hasRelatedVideo","relatedVideos",[104],{"_105":106,"_124":125,"_50":140,"_175":176,"_193":141},"content",{"_43":107,"_56":108,"_109":-5,"_110":111,"_112":113,"_114":-5,"_45":115,"_118":119,"_120":119,"_121":-5,"_122":123},"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",{"_116":117},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_126":127,"_133":134,"_135":136,"_137":138,"_28":139},"provider",{"_43":128,"_129":130,"_131":132},"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",[141],{"_43":142,"_56":143,"_58":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_45":149,"_122":144,"_156":157},"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",{"_150":151,"_152":153,"_154":155},"childrenCount",18,"content_count",0,"question_count",135489,"children",[158],{"_43":159,"_56":160,"_58":161,"_145":146,"_147":142,"_118":162,"_120":162,"_45":163,"_122":166,"_156":167},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_150":164,"_152":153,"_154":165},10,19948,"mecanica-2",[168],{"_43":169,"_56":57,"_58":59,"_145":146,"_147":159,"_118":170,"_120":170,"_45":171,"_122":173,"_156":174},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_150":153,"_152":153,"_154":172},3376,"resistencia-dos-materiais-4",[],"video",{"_43":113,"_13":108,"_109":-5,"_177":178,"_179":180,"_28":-5,"_181":-5,"_126":180,"_182":183,"_137":-5,"_184":-5,"_185":-5,"_186":-5,"_187":-5,"_45":188,"_189":153,"_190":-5,"_99":191,"_118":192,"_120":192},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_116":117},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[196,227,245],{"_40":197,"_42":41,"_43":198,"_76":199,"_96":215,"_97":216,"_50":217},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[200,203,206,209,212],{"_43":201,"_80":81,"_82":202},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":204,"_80":86,"_82":205},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":207,"_80":90,"_82":208},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":210,"_80":94,"_82":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":197,"_80":213,"_82":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],{"_43":219,"_56":220,"_58":221,"_145":146,"_147":222,"_118":223,"_120":223,"_45":224,"_122":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",{"_150":225,"_152":153,"_154":226},4,12302,{"_40":228,"_42":41,"_43":229,"_76":230,"_96":242,"_97":243,"_50":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_43":232,"_80":81,"_82":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":235,"_80":86,"_82":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":228,"_80":90,"_82":238},"

Verdadeiro, falso, verdadeiro

",{"_43":240,"_80":94,"_82":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":41,"_43":247,"_76":248,"_96":263,"_97":264,"_50":265},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[249,252,255,257,260],{"_43":250,"_80":81,"_82":251},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":253,"_80":86,"_82":254},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":246,"_80":90,"_82":256},"Indeterminado",{"_43":258,"_80":94,"_82":259},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":261,"_80":213,"_82":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],{"_43":268,"_56":269,"_58":270,"_145":146,"_147":271,"_118":162,"_120":162,"_45":272,"_122":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_150":273,"_152":153,"_154":274},5,30614,"engenharia-mecatronica-1",{"_43":277,"_56":57,"_58":59,"_145":146,"_147":278,"_118":279,"_120":279,"_45":280,"_122":281},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-6",{"_43":278,"_56":160,"_58":161,"_145":146,"_147":268,"_118":223,"_120":223,"_45":283,"_122":285},{"_150":273,"_152":153,"_154":284},25741,"mecanica-3",{"_43":142,"_56":143,"_58":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_45":149,"_122":144},{"_43":169,"_56":57,"_58":59,"_145":146,"_147":159,"_118":170,"_120":170,"_45":171,"_122":173},{"_43":289,"_56":290,"_58":291,"_145":146,"_147":271,"_118":162,"_120":162,"_45":292,"_122":295},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_150":293,"_152":153,"_154":294},21,45865,"engenharia-civil-3",{"_43":222,"_56":297,"_58":298,"_145":146,"_147":271,"_118":162,"_120":162,"_45":299,"_122":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_150":273,"_152":153,"_154":226},"engenharia-de-petroleo-1",{"_43":302,"_56":303,"_58":304,"_145":146,"_147":289,"_118":305,"_120":305,"_45":306,"_122":308},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_150":273,"_152":153,"_154":307},8852,"estruturas-1",{"_43":159,"_56":160,"_58":161,"_145":146,"_147":142,"_118":162,"_120":162,"_45":163,"_122":166},{"_43":311,"_56":57,"_58":59,"_145":146,"_147":219,"_118":312,"_120":312,"_45":313,"_122":314},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-7",{"_43":316,"_56":317,"_58":59,"_145":146,"_147":302,"_118":318,"_120":318,"_45":319,"_122":320},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-5",{"_43":271,"_56":322,"_58":323,"_145":146,"_147":-5,"_118":324,"_120":324,"_45":325,"_122":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_150":326,"_152":153,"_154":327},29,351586,"tagsTree",[141,330],{"_43":271,"_56":322,"_58":323,"_145":146,"_147":-5,"_118":324,"_120":324,"_45":325,"_122":323,"_156":331},[332,338,344],{"_43":268,"_56":269,"_58":270,"_145":146,"_147":271,"_118":162,"_120":162,"_45":272,"_122":275,"_156":333},[334],{"_43":278,"_56":160,"_58":161,"_145":146,"_147":268,"_118":223,"_120":223,"_45":283,"_122":285,"_156":335},[336],{"_43":277,"_56":57,"_58":59,"_145":146,"_147":278,"_118":279,"_120":279,"_45":280,"_122":281,"_156":337},[],{"_43":289,"_56":290,"_58":291,"_145":146,"_147":271,"_118":162,"_120":162,"_45":292,"_122":295,"_156":339},[340],{"_43":302,"_56":303,"_58":304,"_145":146,"_147":289,"_118":305,"_120":305,"_45":306,"_122":308,"_156":341},[342],{"_43":316,"_56":317,"_58":59,"_145":146,"_147":302,"_118":318,"_120":318,"_45":319,"_122":320,"_156":343},[],{"_43":222,"_56":297,"_58":298,"_145":146,"_147":271,"_118":162,"_120":162,"_45":299,"_122":300,"_156":345},[346],{"_43":219,"_56":220,"_58":221,"_145":146,"_147":222,"_118":223,"_120":223,"_45":224,"_122":221,"_156":347},[348],{"_43":311,"_56":57,"_58":59,"_145":146,"_147":219,"_118":312,"_120":312,"_45":313,"_122":314,"_156":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários