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permeáveis",{"_44":234,"_229":235,"_231":236},"ed0c7aa9-ab19-4ea6-b47c-3bdac7e37d0c","B","Determinar o tamanho das partículas do agregado",{"_44":238,"_229":239,"_231":240},"d70cd797-dacb-46be-8830-50cdb9535e32","C","Determinar a composição química do agregado","solution_explanation","statement","

Qual é o propósito do teste de massa específica para agregados?

","status","pending_classification","hasRelatedVideo","relatedVideos",[249],{"_250":251,"_269":270,"_52":285,"_320":321,"_338":286},"content",{"_44":252,"_56":253,"_254":-5,"_255":256,"_257":258,"_259":-5,"_46":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",{"_44":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],{"_44":287,"_56":288,"_58":289,"_290":291,"_292":-5,"_263":293,"_265":293,"_46":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],{"_44":304,"_56":305,"_58":306,"_290":291,"_292":287,"_263":307,"_265":307,"_46":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],{"_44":314,"_56":205,"_58":206,"_290":291,"_292":304,"_263":315,"_265":315,"_46":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",{"_44":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,"_46":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":43,"_44":343,"_226":344,"_241":361,"_242":362,"_52":363},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[345,348,351,354,358],{"_44":346,"_229":230,"_231":347},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":349,"_229":235,"_231":350},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":352,"_229":239,"_231":353},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":355,"_229":356,"_231":357},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_44":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],{"_44":365,"_56":366,"_58":367,"_290":291,"_292":368,"_263":369,"_265":369,"_46":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":43,"_44":375,"_226":376,"_241":388,"_242":389,"_52":390},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[377,380,383,385],{"_44":378,"_229":230,"_231":379},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":381,"_229":235,"_231":382},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":374,"_229":239,"_231":384},"

Verdadeiro, falso, verdadeiro

",{"_44":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":43,"_44":393,"_226":394,"_241":409,"_242":410,"_52":411},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[395,398,401,403,406],{"_44":396,"_229":230,"_231":397},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":399,"_229":235,"_231":400},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":392,"_229":239,"_231":402},"Indeterminado",{"_44":404,"_229":356,"_231":405},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":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],{"_44":414,"_56":415,"_58":416,"_290":291,"_292":417,"_263":307,"_265":307,"_46":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",{"_44":423,"_56":205,"_58":206,"_290":291,"_292":424,"_263":425,"_265":425,"_46":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",{"_44":424,"_56":305,"_58":306,"_290":291,"_292":414,"_263":369,"_265":369,"_46":429,"_267":431},{"_295":419,"_297":298,"_299":430},25741,"mecanica-3",{"_44":287,"_56":288,"_58":289,"_290":291,"_292":-5,"_263":293,"_265":293,"_46":294,"_267":289},{"_44":314,"_56":205,"_58":206,"_290":291,"_292":304,"_263":315,"_265":315,"_46":316,"_267":318},{"_44":435,"_56":198,"_58":199,"_290":291,"_292":417,"_263":307,"_265":307,"_46":436,"_267":439},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331",{"_295":437,"_297":298,"_299":438},21,45865,"engenharia-civil-3",{"_44":368,"_56":441,"_58":442,"_290":291,"_292":417,"_263":307,"_265":307,"_46":443,"_267":444},"Engenharia de Petróleo","engenharia-de-petroleo",{"_295":419,"_297":298,"_299":372},"engenharia-de-petroleo-1",{"_44":446,"_56":447,"_58":448,"_290":291,"_292":435,"_263":449,"_265":449,"_46":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",{"_44":304,"_56":305,"_58":306,"_290":291,"_292":287,"_263":307,"_265":307,"_46":308,"_267":311},{"_44":455,"_56":205,"_58":206,"_290":291,"_292":365,"_263":456,"_265":456,"_46":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",{"_44":460,"_56":461,"_58":206,"_290":291,"_292":446,"_263":462,"_265":462,"_46":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",{"_44":417,"_56":84,"_58":85,"_290":291,"_292":-5,"_263":466,"_265":466,"_46":467,"_267":85},"2025-04-29T01:55:38.635246+00:00",{"_295":468,"_297":298,"_299":469},29,351586,"tagsTree",[286,472],{"_44":417,"_56":84,"_58":85,"_290":291,"_292":-5,"_263":466,"_265":466,"_46":467,"_267":85,"_301":473},[474,480,486],{"_44":414,"_56":415,"_58":416,"_290":291,"_292":417,"_263":307,"_265":307,"_46":418,"_267":421,"_301":475},[476],{"_44":424,"_56":305,"_58":306,"_290":291,"_292":414,"_263":369,"_265":369,"_46":429,"_267":431,"_301":477},[478],{"_44":423,"_56":205,"_58":206,"_290":291,"_292":424,"_263":425,"_265":425,"_46":426,"_267":427,"_301":479},[],{"_44":435,"_56":198,"_58":199,"_290":291,"_292":417,"_263":307,"_265":307,"_46":436,"_267":439,"_301":481},[482],{"_44":446,"_56":447,"_58":448,"_290":291,"_292":435,"_263":449,"_265":449,"_46":450,"_267":452,"_301":483},[484],{"_44":460,"_56":461,"_58":206,"_290":291,"_292":446,"_263":462,"_265":462,"_46":463,"_267":464,"_301":485},[],{"_44":368,"_56":441,"_58":442,"_290":291,"_292":417,"_263":307,"_265":307,"_46":443,"_267":444,"_301":487},[488],{"_44":365,"_56":366,"_58":367,"_290":291,"_292":368,"_263":369,"_265":369,"_46":370,"_267":367,"_301":489},[490],{"_44":455,"_56":205,"_58":206,"_290":291,"_292":365,"_263":456,"_265":456,"_46":457,"_267":458,"_301":491},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários