[{"_1":2,"_289":-5,"_290":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/f5b3e649-6554-48d1-aaca-409ee50bedd4?video=true","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_82":83,"_172":173,"_30":248,"_268":269,"_285":286,"_287":288},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":21,"_22":23,"_24":25,"_57":58,"_76":21,"_77":78,"_79":80,"_81":45},"correctOptionId","529e48d0-07ac-40c9-8fab-5afcca86bf9c","difficulty","","id","f5b3e649-6554-48d1-aaca-409ee50bedd4","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","142180831","answerCount",1,"isIndexable",true,"mainSubject",{"_22":35,"_36":37,"_38":39},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","142182926","options",[59,64,68,72],{"_22":19,"_60":61,"_62":63},"label","A","text","

Pode atrapalhar o arrefecimento do motor, causando falha ou combustão.

",{"_22":65,"_60":66,"_62":67},"2b9db4b7-de02-4954-946d-7d4f486c394c","B","

Pode melhorar o desempenho do motor.

",{"_22":69,"_60":70,"_62":71},"1ceef218-9a0e-4da9-8248-a70cdbef9d82","C","

Não terá impacto no funcionamento do veículo.

",{"_22":73,"_60":74,"_62":75},"4235b453-36dc-46d4-93a5-469e06ee71a5","D","

Aumentará a vida útil do motor.

","solution_explanation","statement","

O que pode acontecer se objetos estranhos forem colocados no compartimento do motor do veículo?

","status","pending_classification","hasRelatedVideo","relatedVideos",[84],{"_85":86,"_104":105,"_30":120,"_146":147,"_165":166},"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":37,"_38":39,"_125":126,"_127":122,"_98":140,"_100":140,"_24":141,"_102":144,"_136":145},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_130":142,"_132":133,"_134":143},10,19948,"mecanica-2",[],"video",{"_22":93,"_148":88,"_89":-5,"_149":150,"_151":152,"_6":-5,"_153":-5,"_106":152,"_154":155,"_117":-5,"_156":-5,"_157":-5,"_158":-5,"_159":-5,"_24":160,"_161":133,"_162":-5,"_79":163,"_98":164,"_100":164},"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",{"_22":122,"_36":123,"_38":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_24":167,"_102":124,"_136":168},{"_130":131,"_132":133,"_134":135},[169],{"_22":139,"_36":37,"_38":39,"_125":126,"_127":122,"_98":140,"_100":140,"_24":170,"_102":144,"_136":171},{"_130":142,"_132":133,"_134":143},[],"similarQuestions",[174,205,225],{"_18":175,"_20":21,"_22":176,"_57":177,"_76":193,"_77":194,"_30":195},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[178,181,184,187,190],{"_22":179,"_60":61,"_62":180},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":182,"_60":66,"_62":183},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":185,"_60":70,"_62":186},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":188,"_60":74,"_62":189},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":175,"_60":191,"_62":192},"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

",[196],{"_22":197,"_36":198,"_38":199,"_125":126,"_127":200,"_98":140,"_100":140,"_24":201,"_102":204},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_130":202,"_132":133,"_134":203},5,30614,"engenharia-mecatronica-1",{"_18":206,"_20":21,"_22":207,"_57":208,"_76":220,"_77":221,"_30":222},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[209,212,215,217],{"_22":210,"_60":61,"_62":211},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":213,"_60":66,"_62":214},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":206,"_60":70,"_62":216},"

Verdadeiro, falso, verdadeiro

",{"_22":218,"_60":74,"_62":219},"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?

",[223],{"_22":197,"_36":198,"_38":199,"_125":126,"_127":200,"_98":140,"_100":140,"_24":224,"_102":204},{"_130":202,"_132":133,"_134":203},{"_18":226,"_20":21,"_22":227,"_57":228,"_76":243,"_77":244,"_30":245},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[229,232,235,237,240],{"_22":230,"_60":61,"_62":231},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":233,"_60":66,"_62":234},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":226,"_60":70,"_62":236},"Indeterminado",{"_22":238,"_60":74,"_62":239},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":241,"_60":191,"_62":242},"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????",[246],{"_22":197,"_36":198,"_38":199,"_125":126,"_127":200,"_98":140,"_100":140,"_24":247,"_102":204},{"_130":202,"_132":133,"_134":203},[249,251,257,259,261],{"_22":197,"_36":198,"_38":199,"_125":126,"_127":200,"_98":140,"_100":140,"_24":250,"_102":204},{"_130":202,"_132":133,"_134":203},{"_22":252,"_36":37,"_38":39,"_125":126,"_127":197,"_98":253,"_100":253,"_24":254,"_102":256},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_130":202,"_132":133,"_134":255},25741,"mecanica-3",{"_22":122,"_36":123,"_38":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_24":258,"_102":124},{"_130":131,"_132":133,"_134":135},{"_22":139,"_36":37,"_38":39,"_125":126,"_127":122,"_98":140,"_100":140,"_24":260,"_102":144},{"_130":142,"_132":133,"_134":143},{"_22":200,"_36":262,"_38":263,"_125":126,"_127":-5,"_98":264,"_100":264,"_24":265,"_102":263},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":266,"_132":133,"_134":267},29,351586,"tagsTree",[270,276],{"_22":122,"_36":123,"_38":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_24":271,"_102":124,"_136":272},{"_130":131,"_132":133,"_134":135},[273],{"_22":139,"_36":37,"_38":39,"_125":126,"_127":122,"_98":140,"_100":140,"_24":274,"_102":144,"_136":275},{"_130":142,"_132":133,"_134":143},[],{"_22":200,"_36":262,"_38":263,"_125":126,"_127":-5,"_98":264,"_100":264,"_24":277,"_102":263,"_136":278},{"_130":266,"_132":133,"_134":267},[279],{"_22":197,"_36":198,"_38":199,"_125":126,"_127":200,"_98":140,"_100":140,"_24":280,"_102":204,"_136":281},{"_130":202,"_132":133,"_134":203},[282],{"_22":252,"_36":37,"_38":39,"_125":126,"_127":197,"_98":253,"_100":253,"_24":283,"_102":256,"_136":284},{"_130":202,"_132":133,"_134":255},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários