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CARGO: MONITOR - CAPS

","status","pending_classification","hasRelatedVideo","relatedVideos",[104],{"_105":106,"_124":125,"_51":140,"_166":167,"_184":141},"content",{"_43":107,"_57":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,"_57":143,"_59":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,"_57":58,"_59":60,"_145":146,"_147":142,"_118":160,"_120":160,"_45":161,"_122":164,"_156":165},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_150":162,"_152":153,"_154":163},10,19948,"mecanica-2",[],"video",{"_43":113,"_13":108,"_109":-5,"_168":169,"_170":171,"_28":-5,"_172":-5,"_126":171,"_173":174,"_137":-5,"_175":-5,"_176":-5,"_177":-5,"_178":-5,"_45":179,"_180":153,"_181":-5,"_99":182,"_118":183,"_120":183},"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",[187,217,235],{"_40":188,"_42":41,"_43":189,"_77":190,"_96":205,"_97":206,"_51":207},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[191,194,197,200,203],{"_43":192,"_81":82,"_83":193},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":195,"_81":87,"_83":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":198,"_81":84,"_83":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":201,"_81":88,"_83":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":188,"_81":91,"_83":204},"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

",[208],{"_43":209,"_57":210,"_59":211,"_145":146,"_147":212,"_118":160,"_120":160,"_45":213,"_122":216},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_150":214,"_152":153,"_154":215},5,30614,"engenharia-mecatronica-1",{"_40":218,"_42":41,"_43":219,"_77":220,"_96":232,"_97":233,"_51":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_43":222,"_81":82,"_83":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":225,"_81":87,"_83":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":218,"_81":84,"_83":228},"

Verdadeiro, falso, verdadeiro

",{"_43":230,"_81":88,"_83":231},"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?

",[208],{"_40":236,"_42":41,"_43":237,"_77":238,"_96":253,"_97":254,"_51":255},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[239,242,245,247,250],{"_43":240,"_81":82,"_83":241},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":243,"_81":87,"_83":244},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":236,"_81":84,"_83":246},"Indeterminado",{"_43":248,"_81":88,"_83":249},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":251,"_81":91,"_83":252},"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????",[208],[208,257,263,264,265],{"_43":258,"_57":58,"_59":60,"_145":146,"_147":209,"_118":259,"_120":259,"_45":260,"_122":262},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_150":214,"_152":153,"_154":261},25741,"mecanica-3",{"_43":142,"_57":143,"_59":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_45":149,"_122":144},{"_43":159,"_57":58,"_59":60,"_145":146,"_147":142,"_118":160,"_120":160,"_45":161,"_122":164},{"_43":212,"_57":266,"_59":267,"_145":146,"_147":-5,"_118":268,"_120":268,"_45":269,"_122":267},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_150":270,"_152":153,"_154":271},29,351586,"tagsTree",[141,274],{"_43":212,"_57":266,"_59":267,"_145":146,"_147":-5,"_118":268,"_120":268,"_45":269,"_122":267,"_156":275},[276],{"_43":209,"_57":210,"_59":211,"_145":146,"_147":212,"_118":160,"_120":160,"_45":213,"_122":216,"_156":277},[278],{"_43":258,"_57":58,"_59":60,"_145":146,"_147":209,"_118":259,"_120":259,"_45":260,"_122":262,"_156":279},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários