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O Word para edição de texto.","status","pending_classification","hasRelatedVideo","relatedVideos",[96],{"_97":98,"_116":117,"_50":132,"_167":168,"_185":133},"content",{"_43":99,"_56":100,"_101":-5,"_102":103,"_104":105,"_106":-5,"_45":107,"_110":111,"_112":111,"_113":-5,"_114":115},"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",{"_108":109},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_118":119,"_125":126,"_127":128,"_129":130,"_28":131},"provider",{"_43":120,"_121":122,"_123":124},"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",[133],{"_43":134,"_56":135,"_58":136,"_137":138,"_139":-5,"_110":140,"_112":140,"_45":141,"_114":136,"_148":149},"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",{"_142":143,"_144":145,"_146":147},"childrenCount",18,"content_count",0,"question_count",135489,"children",[150],{"_43":151,"_56":152,"_58":153,"_137":138,"_139":134,"_110":154,"_112":154,"_45":155,"_114":158,"_148":159},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_142":156,"_144":145,"_146":157},10,19948,"mecanica-2",[160],{"_43":161,"_56":57,"_58":59,"_137":138,"_139":151,"_110":162,"_112":162,"_45":163,"_114":165,"_148":166},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_142":145,"_144":145,"_146":164},3376,"resistencia-dos-materiais-4",[],"video",{"_43":105,"_13":100,"_101":-5,"_169":170,"_171":172,"_28":-5,"_173":-5,"_118":172,"_174":175,"_129":-5,"_176":-5,"_177":-5,"_178":-5,"_179":-5,"_45":180,"_181":145,"_182":-5,"_91":183,"_110":184,"_112":184},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_108":109},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[188,221,239],{"_40":189,"_42":41,"_43":190,"_76":191,"_88":209,"_89":210,"_50":211},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[192,195,198,202,206],{"_43":193,"_80":81,"_82":194},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":196,"_80":86,"_82":197},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":199,"_80":200,"_82":201},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_43":203,"_80":204,"_82":205},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":189,"_80":207,"_82":208},"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

",[212],{"_43":213,"_56":214,"_58":215,"_137":138,"_139":216,"_110":217,"_112":217,"_45":218,"_114":215},"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",{"_142":219,"_144":145,"_146":220},4,12302,{"_40":222,"_42":41,"_43":223,"_76":224,"_88":236,"_89":237,"_50":238},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[225,228,231,233],{"_43":226,"_80":81,"_82":227},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":229,"_80":86,"_82":230},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":222,"_80":200,"_82":232},"

Verdadeiro, falso, verdadeiro

",{"_43":234,"_80":204,"_82":235},"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?

",[212],{"_40":240,"_42":41,"_43":241,"_76":242,"_88":257,"_89":258,"_50":259},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[243,246,249,251,254],{"_43":244,"_80":81,"_82":245},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":247,"_80":86,"_82":248},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":240,"_80":200,"_82":250},"Indeterminado",{"_43":252,"_80":204,"_82":253},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":255,"_80":207,"_82":256},"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????",[212],[212,261,270,276,280,281,282,290,295,303,304,309,315],{"_43":262,"_56":263,"_58":264,"_137":138,"_139":265,"_110":154,"_112":154,"_45":266,"_114":269},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_142":267,"_144":145,"_146":268},5,30614,"engenharia-mecatronica-1",{"_43":271,"_56":57,"_58":59,"_137":138,"_139":272,"_110":273,"_112":273,"_45":274,"_114":275},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_142":145,"_144":145,"_146":164},"resistencia-dos-materiais-6",{"_43":272,"_56":152,"_58":153,"_137":138,"_139":262,"_110":217,"_112":217,"_45":277,"_114":279},{"_142":267,"_144":145,"_146":278},25741,"mecanica-3",{"_43":134,"_56":135,"_58":136,"_137":138,"_139":-5,"_110":140,"_112":140,"_45":141,"_114":136},{"_43":161,"_56":57,"_58":59,"_137":138,"_139":151,"_110":162,"_112":162,"_45":163,"_114":165},{"_43":283,"_56":284,"_58":285,"_137":138,"_139":265,"_110":154,"_112":154,"_45":286,"_114":289},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_142":287,"_144":145,"_146":288},21,45865,"engenharia-civil-3",{"_43":216,"_56":291,"_58":292,"_137":138,"_139":265,"_110":154,"_112":154,"_45":293,"_114":294},"Engenharia de Petróleo","engenharia-de-petroleo",{"_142":267,"_144":145,"_146":220},"engenharia-de-petroleo-1",{"_43":296,"_56":297,"_58":298,"_137":138,"_139":283,"_110":299,"_112":299,"_45":300,"_114":302},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_142":267,"_144":145,"_146":301},8852,"estruturas-1",{"_43":151,"_56":152,"_58":153,"_137":138,"_139":134,"_110":154,"_112":154,"_45":155,"_114":158},{"_43":305,"_56":57,"_58":59,"_137":138,"_139":213,"_110":306,"_112":306,"_45":307,"_114":308},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_142":145,"_144":145,"_146":164},"resistencia-dos-materiais-7",{"_43":310,"_56":311,"_58":59,"_137":138,"_139":296,"_110":312,"_112":312,"_45":313,"_114":314},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_142":145,"_144":145,"_146":164},"resistencia-dos-materiais-5",{"_43":265,"_56":316,"_58":317,"_137":138,"_139":-5,"_110":318,"_112":318,"_45":319,"_114":317},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_142":320,"_144":145,"_146":321},29,351586,"tagsTree",[133,324],{"_43":265,"_56":316,"_58":317,"_137":138,"_139":-5,"_110":318,"_112":318,"_45":319,"_114":317,"_148":325},[326,332,338],{"_43":262,"_56":263,"_58":264,"_137":138,"_139":265,"_110":154,"_112":154,"_45":266,"_114":269,"_148":327},[328],{"_43":272,"_56":152,"_58":153,"_137":138,"_139":262,"_110":217,"_112":217,"_45":277,"_114":279,"_148":329},[330],{"_43":271,"_56":57,"_58":59,"_137":138,"_139":272,"_110":273,"_112":273,"_45":274,"_114":275,"_148":331},[],{"_43":283,"_56":284,"_58":285,"_137":138,"_139":265,"_110":154,"_112":154,"_45":286,"_114":289,"_148":333},[334],{"_43":296,"_56":297,"_58":298,"_137":138,"_139":283,"_110":299,"_112":299,"_45":300,"_114":302,"_148":335},[336],{"_43":310,"_56":311,"_58":59,"_137":138,"_139":296,"_110":312,"_112":312,"_45":313,"_114":314,"_148":337},[],{"_43":216,"_56":291,"_58":292,"_137":138,"_139":265,"_110":154,"_112":154,"_45":293,"_114":294,"_148":339},[340],{"_43":213,"_56":214,"_58":215,"_137":138,"_139":216,"_110":217,"_112":217,"_45":218,"_114":215,"_148":341},[342],{"_43":305,"_56":57,"_58":59,"_137":138,"_139":213,"_110":306,"_112":306,"_45":307,"_114":308,"_148":343},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários