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(Hibbeler, Estática, 10ª ed, 2005)","status","pending_classification","hasRelatedVideo","relatedVideos",[84],{"_85":86,"_104":105,"_30":120,"_155":156,"_174":121},"content",{"_22":87,"_36":88,"_89":-5,"_90":91,"_92":93,"_94":-5,"_24":95,"_98":99,"_100":99,"_101":-5,"_102":103},"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",{"_96":97},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_106":107,"_113":114,"_115":116,"_117":118,"_6":119},"provider",{"_22":108,"_109":110,"_111":112},"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",[121],{"_22":122,"_36":123,"_38":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_24":129,"_102":124,"_136":137},"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",{"_130":131,"_132":133,"_134":135},"childrenCount",18,"content_count",0,"question_count",135489,"children",[138],{"_22":139,"_36":140,"_38":141,"_125":126,"_127":122,"_98":142,"_100":142,"_24":143,"_102":146,"_136":147},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_130":144,"_132":133,"_134":145},10,19948,"mecanica-2",[148],{"_22":149,"_36":37,"_38":39,"_125":126,"_127":139,"_98":150,"_100":150,"_24":151,"_102":153,"_136":154},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_130":133,"_132":133,"_134":152},3376,"resistencia-dos-materiais-4",[],"video",{"_22":93,"_157":88,"_89":-5,"_158":159,"_160":161,"_6":-5,"_162":-5,"_106":161,"_163":164,"_117":-5,"_165":-5,"_166":-5,"_167":-5,"_168":-5,"_24":169,"_170":133,"_171":-5,"_79":172,"_98":173,"_100":173},"title","duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_96":97},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[177,208,226],{"_18":178,"_20":21,"_22":179,"_57":180,"_76":196,"_77":197,"_30":198},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[181,184,187,190,193],{"_22":182,"_60":61,"_62":183},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":185,"_60":66,"_62":186},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":188,"_60":70,"_62":189},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":191,"_60":74,"_62":192},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":178,"_60":194,"_62":195},"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

",[199],{"_22":200,"_36":201,"_38":202,"_125":126,"_127":203,"_98":204,"_100":204,"_24":205,"_102":202},"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",{"_130":206,"_132":133,"_134":207},4,12302,{"_18":209,"_20":21,"_22":210,"_57":211,"_76":223,"_77":224,"_30":225},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[212,215,218,220],{"_22":213,"_60":61,"_62":214},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":216,"_60":66,"_62":217},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":209,"_60":70,"_62":219},"

Verdadeiro, falso, verdadeiro

",{"_22":221,"_60":74,"_62":222},"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?

",[199],{"_18":227,"_20":21,"_22":228,"_57":229,"_76":244,"_77":245,"_30":246},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,238,241],{"_22":231,"_60":61,"_62":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":234,"_60":66,"_62":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":227,"_60":70,"_62":237},"Indeterminado",{"_22":239,"_60":74,"_62":240},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":242,"_60":194,"_62":243},"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????",[199],[199,248,257,263,267,268,269,277,282,290,291,296,302],{"_22":249,"_36":250,"_38":251,"_125":126,"_127":252,"_98":142,"_100":142,"_24":253,"_102":256},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_130":254,"_132":133,"_134":255},5,30614,"engenharia-mecatronica-1",{"_22":258,"_36":37,"_38":39,"_125":126,"_127":259,"_98":260,"_100":260,"_24":261,"_102":262},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-6",{"_22":259,"_36":140,"_38":141,"_125":126,"_127":249,"_98":204,"_100":204,"_24":264,"_102":266},{"_130":254,"_132":133,"_134":265},25741,"mecanica-3",{"_22":122,"_36":123,"_38":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_24":129,"_102":124},{"_22":149,"_36":37,"_38":39,"_125":126,"_127":139,"_98":150,"_100":150,"_24":151,"_102":153},{"_22":270,"_36":271,"_38":272,"_125":126,"_127":252,"_98":142,"_100":142,"_24":273,"_102":276},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_130":274,"_132":133,"_134":275},21,45865,"engenharia-civil-3",{"_22":203,"_36":278,"_38":279,"_125":126,"_127":252,"_98":142,"_100":142,"_24":280,"_102":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":254,"_132":133,"_134":207},"engenharia-de-petroleo-1",{"_22":283,"_36":284,"_38":285,"_125":126,"_127":270,"_98":286,"_100":286,"_24":287,"_102":289},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_130":254,"_132":133,"_134":288},8852,"estruturas-1",{"_22":139,"_36":140,"_38":141,"_125":126,"_127":122,"_98":142,"_100":142,"_24":143,"_102":146},{"_22":292,"_36":37,"_38":39,"_125":126,"_127":200,"_98":293,"_100":293,"_24":294,"_102":295},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-7",{"_22":297,"_36":298,"_38":39,"_125":126,"_127":283,"_98":299,"_100":299,"_24":300,"_102":301},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-5",{"_22":252,"_36":303,"_38":304,"_125":126,"_127":-5,"_98":305,"_100":305,"_24":306,"_102":304},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":307,"_132":133,"_134":308},29,351586,"tagsTree",[121,311],{"_22":252,"_36":303,"_38":304,"_125":126,"_127":-5,"_98":305,"_100":305,"_24":306,"_102":304,"_136":312},[313,319,325],{"_22":249,"_36":250,"_38":251,"_125":126,"_127":252,"_98":142,"_100":142,"_24":253,"_102":256,"_136":314},[315],{"_22":259,"_36":140,"_38":141,"_125":126,"_127":249,"_98":204,"_100":204,"_24":264,"_102":266,"_136":316},[317],{"_22":258,"_36":37,"_38":39,"_125":126,"_127":259,"_98":260,"_100":260,"_24":261,"_102":262,"_136":318},[],{"_22":270,"_36":271,"_38":272,"_125":126,"_127":252,"_98":142,"_100":142,"_24":273,"_102":276,"_136":320},[321],{"_22":283,"_36":284,"_38":285,"_125":126,"_127":270,"_98":286,"_100":286,"_24":287,"_102":289,"_136":322},[323],{"_22":297,"_36":298,"_38":39,"_125":126,"_127":283,"_98":299,"_100":299,"_24":300,"_102":301,"_136":324},[],{"_22":203,"_36":278,"_38":279,"_125":126,"_127":252,"_98":142,"_100":142,"_24":280,"_102":281,"_136":326},[327],{"_22":200,"_36":201,"_38":202,"_125":126,"_127":203,"_98":204,"_100":204,"_24":205,"_102":202,"_136":328},[329],{"_22":292,"_36":37,"_38":39,"_125":126,"_127":200,"_98":293,"_100":293,"_24":294,"_102":295,"_136":330},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários