[{"_1":2,"_269":-5,"_270":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/f6b9a66c-1501-4fbe-a7e6-28319232c16a?video=true","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_86":87,"_170":171,"_30":241,"_257":258,"_265":266,"_267":268},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":21,"_22":23,"_24":25,"_57":58,"_80":21,"_81":82,"_83":84,"_85":45},"correctOptionId","b4c971a9-c580-4c7a-921a-b9c175d223e1","difficulty","","id","f6b9a66c-1501-4fbe-a7e6-28319232c16a","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},672071,"name","Mecânica","alias","mecanica","materialId","117664479","answerCount",1,"isIndexable",true,"mainSubject",{"_22":35,"_36":37,"_38":39},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","137185306","options",[59,65,69,73,77],{"_22":60,"_61":62,"_63":64},"14d5e5f4-8e8a-419e-8c1a-4d0ae93fb7b0","label","A","text","

Ser eficiente.

",{"_22":66,"_61":67,"_63":68},"bc80cc4e-893b-48a1-8a8c-da8f9fb9770a","B","

Ser pontual.

",{"_22":70,"_61":71,"_63":72},"d338b7e7-4229-4273-9143-8acb6b9ce8d5","C","

Servir as refeições na hora certa.

",{"_22":74,"_61":75,"_63":76},"1387eab9-cb4c-4fa5-abdb-d6df8c06ad1b","D","

Ter iniciativa.

",{"_22":19,"_61":78,"_63":79},"E","

Receber parentes e amigos diariamente no local de serviço.

","solution_explanation","statement","

São deveres da Merendeira, EXCETO:

","status","pending_classification","hasRelatedVideo","relatedVideos",[88],{"_89":90,"_108":109,"_30":124,"_150":151,"_169":125},"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":37,"_38":39,"_129":130,"_131":126,"_102":144,"_104":144,"_24":145,"_106":148,"_140":149},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_134":146,"_136":137,"_138":147},10,19948,"mecanica-2",[],"video",{"_22":97,"_152":92,"_93":-5,"_153":154,"_155":156,"_6":-5,"_157":-5,"_110":156,"_158":159,"_121":-5,"_160":-5,"_161":-5,"_162":-5,"_163":-5,"_24":164,"_165":137,"_166":-5,"_83":167,"_102":168,"_104":168},"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","similarQuestions",[172,202,220],{"_18":173,"_20":21,"_22":174,"_57":175,"_80":190,"_81":191,"_30":192},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[176,179,182,185,188],{"_22":177,"_61":62,"_63":178},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":180,"_61":67,"_63":181},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":183,"_61":71,"_63":184},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":186,"_61":75,"_63":187},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":173,"_61":78,"_63":189},"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

",[193],{"_22":194,"_36":195,"_38":196,"_129":130,"_131":197,"_102":144,"_104":144,"_24":198,"_106":201},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_134":199,"_136":137,"_138":200},5,30614,"engenharia-mecatronica-1",{"_18":203,"_20":21,"_22":204,"_57":205,"_80":217,"_81":218,"_30":219},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[206,209,212,214],{"_22":207,"_61":62,"_63":208},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":210,"_61":67,"_63":211},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":203,"_61":71,"_63":213},"

Verdadeiro, falso, verdadeiro

",{"_22":215,"_61":75,"_63":216},"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?

",[193],{"_18":221,"_20":21,"_22":222,"_57":223,"_80":238,"_81":239,"_30":240},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[224,227,230,232,235],{"_22":225,"_61":62,"_63":226},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":228,"_61":67,"_63":229},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":221,"_61":71,"_63":231},"Indeterminado",{"_22":233,"_61":75,"_63":234},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":236,"_61":78,"_63":237},"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????",[193],[193,242,248,249,250],{"_22":243,"_36":37,"_38":39,"_129":130,"_131":194,"_102":244,"_104":244,"_24":245,"_106":247},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_134":199,"_136":137,"_138":246},25741,"mecanica-3",{"_22":126,"_36":127,"_38":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_24":133,"_106":128},{"_22":143,"_36":37,"_38":39,"_129":130,"_131":126,"_102":144,"_104":144,"_24":145,"_106":148},{"_22":197,"_36":251,"_38":252,"_129":130,"_131":-5,"_102":253,"_104":253,"_24":254,"_106":252},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_134":255,"_136":137,"_138":256},29,351586,"tagsTree",[125,259],{"_22":197,"_36":251,"_38":252,"_129":130,"_131":-5,"_102":253,"_104":253,"_24":254,"_106":252,"_140":260},[261],{"_22":194,"_36":195,"_38":196,"_129":130,"_131":197,"_102":144,"_104":144,"_24":198,"_106":201,"_140":262},[263],{"_22":243,"_36":37,"_38":39,"_129":130,"_131":194,"_102":244,"_104":244,"_24":245,"_106":247,"_140":264},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários