[{"_1":2,"_375":-5,"_376":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/ef4506ad-9d53-4488-ba18-fc2ce3de0b8d","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_86":87,"_188":189,"_30":263,"_330":331,"_371":372,"_373":374},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":21,"_22":23,"_24":25,"_57":58,"_80":21,"_81":82,"_83":84,"_85":45},"correctOptionId","be13871d-2fde-4009-89c8-6c748a2b3502","difficulty","","id","ef4506ad-9d53-4488-ba18-fc2ce3de0b8d","metadata",{"_26":27,"_53":54,"_55":56},"pd",{"_28":29,"_30":31,"_32":33,"_40":41,"_42":43,"_44":45,"_46":47,"_48":45,"_49":50,"_51":52},"area","Outros","tags",[],"subjects",[34],{"_22":35,"_36":37,"_38":39},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","162823165","answerCount",1,"isIndexable",true,"mainSubject",{"_22":35,"_36":37,"_38":39},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","163170535","options",[59,65,69,73,76],{"_22":60,"_61":62,"_63":64},"ae89fd88-3ff9-442e-8127-b97736bb14d9","label","A","text","

hexagonal compacta.

",{"_22":66,"_61":67,"_63":68},"d006923c-e7ca-4a3d-bf05-a1dd5e67c85d","B","

cúbica de face centrada.

",{"_22":70,"_61":71,"_63":72},"926a6919-31da-49d6-b177-d251c37a7101","C","

cúbica de cilindro aberto.

",{"_22":19,"_61":74,"_63":75},"D","

cúbica de corpo centrado.

",{"_22":77,"_61":78,"_63":79},"d4ff4614-5779-419a-806c-d26020ef8f27","E","

cúbica de empacotamento fechado.

","solution_explanation","statement","

Considerando que o ferro tem estrutura cúbica a temperatura ambiente, podemos dizer que essa estrutura é chamada de:

","status","pending_classification","hasRelatedVideo","relatedVideos",[88],{"_89":90,"_108":109,"_30":124,"_159":160,"_178":179},"content",{"_22":91,"_36":92,"_93":-5,"_94":95,"_96":97,"_98":-5,"_24":99,"_102":103,"_104":103,"_105":-5,"_106":107},"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",{"_100":101},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_110":111,"_117":118,"_119":120,"_121":122,"_6":123},"provider",{"_22":112,"_113":114,"_115":116},"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",[125],{"_22":126,"_36":127,"_38":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_24":133,"_106":128,"_140":141},"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",{"_134":135,"_136":137,"_138":139},"childrenCount",18,"content_count",0,"question_count",135489,"children",[142],{"_22":143,"_36":144,"_38":145,"_129":130,"_131":126,"_102":146,"_104":146,"_24":147,"_106":150,"_140":151},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_134":148,"_136":137,"_138":149},10,19948,"mecanica-2",[152],{"_22":153,"_36":37,"_38":39,"_129":130,"_131":143,"_102":154,"_104":154,"_24":155,"_106":157,"_140":158},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_134":137,"_136":137,"_138":156},3376,"resistencia-dos-materiais-4",[],"video",{"_22":97,"_161":92,"_93":-5,"_162":163,"_164":165,"_6":-5,"_166":-5,"_110":165,"_167":168,"_121":-5,"_169":-5,"_170":-5,"_171":-5,"_172":-5,"_24":173,"_174":137,"_175":-5,"_83":176,"_102":177,"_104":177},"title","duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_100":101},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_22":126,"_36":127,"_38":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_24":180,"_106":128,"_140":181},{"_134":135,"_136":137,"_138":139},[182],{"_22":143,"_36":144,"_38":145,"_129":130,"_131":126,"_102":146,"_104":146,"_24":183,"_106":150,"_140":184},{"_134":148,"_136":137,"_138":149},[185],{"_22":153,"_36":37,"_38":39,"_129":130,"_131":143,"_102":154,"_104":154,"_24":186,"_106":157,"_140":187},{"_134":137,"_136":137,"_138":156},[],"similarQuestions",[190,220,240],{"_18":191,"_20":21,"_22":192,"_57":193,"_80":208,"_81":209,"_30":210},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[194,197,200,203,206],{"_22":195,"_61":62,"_63":196},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":198,"_61":67,"_63":199},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":201,"_61":71,"_63":202},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":204,"_61":74,"_63":205},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":191,"_61":78,"_63":207},"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

",[211],{"_22":212,"_36":213,"_38":214,"_129":130,"_131":215,"_102":216,"_104":216,"_24":217,"_106":214},"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",{"_134":218,"_136":137,"_138":219},4,12302,{"_18":221,"_20":21,"_22":222,"_57":223,"_80":235,"_81":236,"_30":237},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[224,227,230,232],{"_22":225,"_61":62,"_63":226},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":228,"_61":67,"_63":229},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":221,"_61":71,"_63":231},"

Verdadeiro, falso, verdadeiro

",{"_22":233,"_61":74,"_63":234},"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?

",[238],{"_22":212,"_36":213,"_38":214,"_129":130,"_131":215,"_102":216,"_104":216,"_24":239,"_106":214},{"_134":218,"_136":137,"_138":219},{"_18":241,"_20":21,"_22":242,"_57":243,"_80":258,"_81":259,"_30":260},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[244,247,250,252,255],{"_22":245,"_61":62,"_63":246},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":248,"_61":67,"_63":249},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":241,"_61":71,"_63":251},"Indeterminado",{"_22":253,"_61":74,"_63":254},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":256,"_61":78,"_63":257},"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????",[261],{"_22":212,"_36":213,"_38":214,"_129":130,"_131":215,"_102":216,"_104":216,"_24":262,"_106":214},{"_134":218,"_136":137,"_138":219},[264,266,275,281,285,287,289,297,302,310,312,317,323],{"_22":212,"_36":213,"_38":214,"_129":130,"_131":215,"_102":216,"_104":216,"_24":265,"_106":214},{"_134":218,"_136":137,"_138":219},{"_22":267,"_36":268,"_38":269,"_129":130,"_131":270,"_102":146,"_104":146,"_24":271,"_106":274},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_134":272,"_136":137,"_138":273},5,30614,"engenharia-mecatronica-1",{"_22":276,"_36":37,"_38":39,"_129":130,"_131":277,"_102":278,"_104":278,"_24":279,"_106":280},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-6",{"_22":277,"_36":144,"_38":145,"_129":130,"_131":267,"_102":216,"_104":216,"_24":282,"_106":284},{"_134":272,"_136":137,"_138":283},25741,"mecanica-3",{"_22":126,"_36":127,"_38":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_24":286,"_106":128},{"_134":135,"_136":137,"_138":139},{"_22":153,"_36":37,"_38":39,"_129":130,"_131":143,"_102":154,"_104":154,"_24":288,"_106":157},{"_134":137,"_136":137,"_138":156},{"_22":290,"_36":291,"_38":292,"_129":130,"_131":270,"_102":146,"_104":146,"_24":293,"_106":296},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_134":294,"_136":137,"_138":295},21,45865,"engenharia-civil-3",{"_22":215,"_36":298,"_38":299,"_129":130,"_131":270,"_102":146,"_104":146,"_24":300,"_106":301},"Engenharia de Petróleo","engenharia-de-petroleo",{"_134":272,"_136":137,"_138":219},"engenharia-de-petroleo-1",{"_22":303,"_36":304,"_38":305,"_129":130,"_131":290,"_102":306,"_104":306,"_24":307,"_106":309},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_134":272,"_136":137,"_138":308},8852,"estruturas-1",{"_22":143,"_36":144,"_38":145,"_129":130,"_131":126,"_102":146,"_104":146,"_24":311,"_106":150},{"_134":148,"_136":137,"_138":149},{"_22":313,"_36":37,"_38":39,"_129":130,"_131":212,"_102":314,"_104":314,"_24":315,"_106":316},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-7",{"_22":318,"_36":319,"_38":39,"_129":130,"_131":303,"_102":320,"_104":320,"_24":321,"_106":322},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-5",{"_22":270,"_36":324,"_38":325,"_129":130,"_131":-5,"_102":326,"_104":326,"_24":327,"_106":325},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_134":328,"_136":137,"_138":329},29,351586,"tagsTree",[332,341],{"_22":126,"_36":127,"_38":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_24":333,"_106":128,"_140":334},{"_134":135,"_136":137,"_138":139},[335],{"_22":143,"_36":144,"_38":145,"_129":130,"_131":126,"_102":146,"_104":146,"_24":336,"_106":150,"_140":337},{"_134":148,"_136":137,"_138":149},[338],{"_22":153,"_36":37,"_38":39,"_129":130,"_131":143,"_102":154,"_104":154,"_24":339,"_106":157,"_140":340},{"_134":137,"_136":137,"_138":156},[],{"_22":270,"_36":324,"_38":325,"_129":130,"_131":-5,"_102":326,"_104":326,"_24":342,"_106":325,"_140":343},{"_134":328,"_136":137,"_138":329},[344,353,362],{"_22":267,"_36":268,"_38":269,"_129":130,"_131":270,"_102":146,"_104":146,"_24":345,"_106":274,"_140":346},{"_134":272,"_136":137,"_138":273},[347],{"_22":277,"_36":144,"_38":145,"_129":130,"_131":267,"_102":216,"_104":216,"_24":348,"_106":284,"_140":349},{"_134":272,"_136":137,"_138":283},[350],{"_22":276,"_36":37,"_38":39,"_129":130,"_131":277,"_102":278,"_104":278,"_24":351,"_106":280,"_140":352},{"_134":137,"_136":137,"_138":156},[],{"_22":290,"_36":291,"_38":292,"_129":130,"_131":270,"_102":146,"_104":146,"_24":354,"_106":296,"_140":355},{"_134":294,"_136":137,"_138":295},[356],{"_22":303,"_36":304,"_38":305,"_129":130,"_131":290,"_102":306,"_104":306,"_24":357,"_106":309,"_140":358},{"_134":272,"_136":137,"_138":308},[359],{"_22":318,"_36":319,"_38":39,"_129":130,"_131":303,"_102":320,"_104":320,"_24":360,"_106":322,"_140":361},{"_134":137,"_136":137,"_138":156},[],{"_22":215,"_36":298,"_38":299,"_129":130,"_131":270,"_102":146,"_104":146,"_24":363,"_106":301,"_140":364},{"_134":272,"_136":137,"_138":219},[365],{"_22":212,"_36":213,"_38":214,"_129":130,"_131":215,"_102":216,"_104":216,"_24":366,"_106":214,"_140":367},{"_134":218,"_136":137,"_138":219},[368],{"_22":313,"_36":37,"_38":39,"_129":130,"_131":212,"_102":314,"_104":314,"_24":369,"_106":316,"_140":370},{"_134":137,"_136":137,"_138":156},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários