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Desenvolver novas técnicas para uso e pesquisar novos materiais

",{"_43":234,"_229":235,"_231":236},"efd7823a-5d79-486f-b5ca-76ea1609bec4","B","

Estudar a história dos materiais

",{"_43":238,"_229":239,"_231":240},"850380f3-3c9a-4d7e-a99c-073291a72671","C","

Compreender a composição química dos materiais

","solution_explanation","statement","

Qual é o propósito de estudar materiais na Engenharia?

","status","pending_classification","hasRelatedVideo","relatedVideos",[249],{"_250":251,"_269":270,"_51":285,"_320":321,"_338":286},"content",{"_43":252,"_55":253,"_254":-5,"_255":256,"_257":258,"_259":-5,"_45":260,"_263":264,"_265":264,"_266":-5,"_267":268},"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",{"_261":262},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_271":272,"_278":279,"_280":281,"_282":283,"_28":284},"provider",{"_43":273,"_274":275,"_276":277},"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",[286],{"_43":287,"_55":288,"_57":289,"_290":291,"_292":-5,"_263":293,"_265":293,"_45":294,"_267":289,"_301":302},"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",{"_295":296,"_297":298,"_299":300},"childrenCount",18,"content_count",0,"question_count",135489,"children",[303],{"_43":304,"_55":305,"_57":306,"_290":291,"_292":287,"_263":307,"_265":307,"_45":308,"_267":311,"_301":312},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_295":309,"_297":298,"_299":310},10,19948,"mecanica-2",[313],{"_43":314,"_55":204,"_57":205,"_290":291,"_292":304,"_263":315,"_265":315,"_45":316,"_267":318,"_301":319},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_295":298,"_297":298,"_299":317},3376,"resistencia-dos-materiais-4",[],"video",{"_43":258,"_13":253,"_254":-5,"_322":323,"_324":325,"_28":-5,"_326":-5,"_271":325,"_327":328,"_282":-5,"_329":-5,"_330":-5,"_331":-5,"_332":-5,"_45":333,"_334":298,"_335":-5,"_244":336,"_263":337,"_265":337},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_261":262},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[341,373,391],{"_40":342,"_42":41,"_43":343,"_225":344,"_241":361,"_242":362,"_51":363},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[345,348,351,354,358],{"_43":346,"_229":230,"_231":347},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":349,"_229":235,"_231":350},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":352,"_229":239,"_231":353},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":355,"_229":356,"_231":357},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":342,"_229":359,"_231":360},"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

",[364],{"_43":365,"_55":366,"_57":367,"_290":291,"_292":368,"_263":369,"_265":369,"_45":370,"_267":367},"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",{"_295":371,"_297":298,"_299":372},4,12302,{"_40":374,"_42":41,"_43":375,"_225":376,"_241":388,"_242":389,"_51":390},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[377,380,383,385],{"_43":378,"_229":230,"_231":379},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":381,"_229":235,"_231":382},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":374,"_229":239,"_231":384},"

Verdadeiro, falso, verdadeiro

",{"_43":386,"_229":356,"_231":387},"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?

",[364],{"_40":392,"_42":41,"_43":393,"_225":394,"_241":409,"_242":410,"_51":411},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[395,398,401,403,406],{"_43":396,"_229":230,"_231":397},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":399,"_229":235,"_231":400},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":392,"_229":239,"_231":402},"Indeterminado",{"_43":404,"_229":356,"_231":405},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":407,"_229":359,"_231":408},"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????",[364],[364,413,422,428,432,433,434,440,445,453,454,459,465],{"_43":414,"_55":415,"_57":416,"_290":291,"_292":417,"_263":307,"_265":307,"_45":418,"_267":421},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_295":419,"_297":298,"_299":420},5,30614,"engenharia-mecatronica-1",{"_43":423,"_55":204,"_57":205,"_290":291,"_292":424,"_263":425,"_265":425,"_45":426,"_267":427},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_295":298,"_297":298,"_299":317},"resistencia-dos-materiais-6",{"_43":424,"_55":305,"_57":306,"_290":291,"_292":414,"_263":369,"_265":369,"_45":429,"_267":431},{"_295":419,"_297":298,"_299":430},25741,"mecanica-3",{"_43":287,"_55":288,"_57":289,"_290":291,"_292":-5,"_263":293,"_265":293,"_45":294,"_267":289},{"_43":314,"_55":204,"_57":205,"_290":291,"_292":304,"_263":315,"_265":315,"_45":316,"_267":318},{"_43":435,"_55":197,"_57":198,"_290":291,"_292":417,"_263":307,"_265":307,"_45":436,"_267":439},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331",{"_295":437,"_297":298,"_299":438},21,45865,"engenharia-civil-3",{"_43":368,"_55":441,"_57":442,"_290":291,"_292":417,"_263":307,"_265":307,"_45":443,"_267":444},"Engenharia de Petróleo","engenharia-de-petroleo",{"_295":419,"_297":298,"_299":372},"engenharia-de-petroleo-1",{"_43":446,"_55":447,"_57":448,"_290":291,"_292":435,"_263":449,"_265":449,"_45":450,"_267":452},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_295":419,"_297":298,"_299":451},8852,"estruturas-1",{"_43":304,"_55":305,"_57":306,"_290":291,"_292":287,"_263":307,"_265":307,"_45":308,"_267":311},{"_43":455,"_55":204,"_57":205,"_290":291,"_292":365,"_263":456,"_265":456,"_45":457,"_267":458},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_295":298,"_297":298,"_299":317},"resistencia-dos-materiais-7",{"_43":460,"_55":461,"_57":205,"_290":291,"_292":446,"_263":462,"_265":462,"_45":463,"_267":464},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_295":298,"_297":298,"_299":317},"resistencia-dos-materiais-5",{"_43":417,"_55":83,"_57":84,"_290":291,"_292":-5,"_263":466,"_265":466,"_45":467,"_267":84},"2025-04-29T01:55:38.635246+00:00",{"_295":468,"_297":298,"_299":469},29,351586,"tagsTree",[286,472],{"_43":417,"_55":83,"_57":84,"_290":291,"_292":-5,"_263":466,"_265":466,"_45":467,"_267":84,"_301":473},[474,480,486],{"_43":414,"_55":415,"_57":416,"_290":291,"_292":417,"_263":307,"_265":307,"_45":418,"_267":421,"_301":475},[476],{"_43":424,"_55":305,"_57":306,"_290":291,"_292":414,"_263":369,"_265":369,"_45":429,"_267":431,"_301":477},[478],{"_43":423,"_55":204,"_57":205,"_290":291,"_292":424,"_263":425,"_265":425,"_45":426,"_267":427,"_301":479},[],{"_43":435,"_55":197,"_57":198,"_290":291,"_292":417,"_263":307,"_265":307,"_45":436,"_267":439,"_301":481},[482],{"_43":446,"_55":447,"_57":448,"_290":291,"_292":435,"_263":449,"_265":449,"_45":450,"_267":452,"_301":483},[484],{"_43":460,"_55":461,"_57":205,"_290":291,"_292":446,"_263":462,"_265":462,"_45":463,"_267":464,"_301":485},[],{"_43":368,"_55":441,"_57":442,"_290":291,"_292":417,"_263":307,"_265":307,"_45":443,"_267":444,"_301":487},[488],{"_43":365,"_55":366,"_57":367,"_290":291,"_292":368,"_263":369,"_265":369,"_45":370,"_267":367,"_301":489},[490],{"_43":455,"_55":204,"_57":205,"_290":291,"_292":365,"_263":456,"_265":456,"_45":457,"_267":458,"_301":491},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários