[{"_1":2,"_306":-5,"_307":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/dfa5aa3b-f6a5-4162-adff-361fc20c068f","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_99":100,"_188":189,"_51":265,"_285":286,"_302":303,"_304":305},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_93":41,"_94":95,"_96":97,"_98":16},"correctOptionId","","difficulty","id","dfa5aa3b-f6a5-4162-adff-361fc20c068f","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},672071,"name","Mecânica","alias","mecanica","materialId","75888993","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","139268564","options",[79,85,89],{"_43":80,"_81":82,"_83":84},"87c632ae-9b8b-4f75-991d-2c412c7c205e","label","A","text","permitir apenas deslocamento de peças leves;",{"_43":86,"_81":87,"_83":88},"5267ae85-0b91-4597-988b-a3ad9bf74f75","B","não permitir posicionamento fácil de dispositivos pesados;",{"_43":90,"_81":91,"_83":92},"5b95695e-e159-4454-92ab-2e475903ac86","C","não permitir que ranhuras da mesa de apoio criem dificuldades de deslocamentos.","solution_explanation","statement","

Uma das características da mesa com almofada de ar é:

","status","pending_classification","hasRelatedVideo","relatedVideos",[101],{"_102":103,"_121":122,"_51":137,"_163":164,"_181":182},"content",{"_43":104,"_57":105,"_106":-5,"_107":108,"_109":110,"_111":-5,"_45":112,"_115":116,"_117":116,"_118":-5,"_119":120},"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",{"_113":114},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_123":124,"_130":131,"_132":133,"_134":135,"_28":136},"provider",{"_43":125,"_126":127,"_128":129},"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",[138],{"_43":139,"_57":140,"_59":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_45":146,"_119":141,"_153":154},"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",{"_147":148,"_149":150,"_151":152},"childrenCount",18,"content_count",0,"question_count",135489,"children",[155],{"_43":156,"_57":58,"_59":60,"_142":143,"_144":139,"_115":157,"_117":157,"_45":158,"_119":161,"_153":162},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_147":159,"_149":150,"_151":160},10,19948,"mecanica-2",[],"video",{"_43":110,"_13":105,"_106":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_123":168,"_170":171,"_134":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_45":176,"_177":150,"_178":-5,"_96":179,"_115":180,"_117":180},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_113":114},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":139,"_57":140,"_59":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_45":183,"_119":141,"_153":184},{"_147":148,"_149":150,"_151":152},[185],{"_43":156,"_57":58,"_59":60,"_142":143,"_144":139,"_115":157,"_117":157,"_45":186,"_119":161,"_153":187},{"_147":159,"_149":150,"_151":160},[],"similarQuestions",[190,222,242],{"_40":191,"_42":41,"_43":192,"_77":193,"_93":210,"_94":211,"_51":212},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[194,197,200,203,207],{"_43":195,"_81":82,"_83":196},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":198,"_81":87,"_83":199},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":201,"_81":91,"_83":202},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":204,"_81":205,"_83":206},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":191,"_81":208,"_83":209},"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

",[213],{"_43":214,"_57":215,"_59":216,"_142":143,"_144":217,"_115":157,"_117":157,"_45":218,"_119":221},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_147":219,"_149":150,"_151":220},5,30614,"engenharia-mecatronica-1",{"_40":223,"_42":41,"_43":224,"_77":225,"_93":237,"_94":238,"_51":239},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[226,229,232,234],{"_43":227,"_81":82,"_83":228},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":230,"_81":87,"_83":231},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":223,"_81":91,"_83":233},"

Verdadeiro, falso, verdadeiro

",{"_43":235,"_81":205,"_83":236},"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?

",[240],{"_43":214,"_57":215,"_59":216,"_142":143,"_144":217,"_115":157,"_117":157,"_45":241,"_119":221},{"_147":219,"_149":150,"_151":220},{"_40":243,"_42":41,"_43":244,"_77":245,"_93":260,"_94":261,"_51":262},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[246,249,252,254,257],{"_43":247,"_81":82,"_83":248},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":250,"_81":87,"_83":251},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":243,"_81":91,"_83":253},"Indeterminado",{"_43":255,"_81":205,"_83":256},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":258,"_81":208,"_83":259},"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????",[263],{"_43":214,"_57":215,"_59":216,"_142":143,"_144":217,"_115":157,"_117":157,"_45":264,"_119":221},{"_147":219,"_149":150,"_151":220},[266,268,274,276,278],{"_43":214,"_57":215,"_59":216,"_142":143,"_144":217,"_115":157,"_117":157,"_45":267,"_119":221},{"_147":219,"_149":150,"_151":220},{"_43":269,"_57":58,"_59":60,"_142":143,"_144":214,"_115":270,"_117":270,"_45":271,"_119":273},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_147":219,"_149":150,"_151":272},25741,"mecanica-3",{"_43":139,"_57":140,"_59":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_45":275,"_119":141},{"_147":148,"_149":150,"_151":152},{"_43":156,"_57":58,"_59":60,"_142":143,"_144":139,"_115":157,"_117":157,"_45":277,"_119":161},{"_147":159,"_149":150,"_151":160},{"_43":217,"_57":279,"_59":280,"_142":143,"_144":-5,"_115":281,"_117":281,"_45":282,"_119":280},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_147":283,"_149":150,"_151":284},29,351586,"tagsTree",[287,293],{"_43":139,"_57":140,"_59":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_45":288,"_119":141,"_153":289},{"_147":148,"_149":150,"_151":152},[290],{"_43":156,"_57":58,"_59":60,"_142":143,"_144":139,"_115":157,"_117":157,"_45":291,"_119":161,"_153":292},{"_147":159,"_149":150,"_151":160},[],{"_43":217,"_57":279,"_59":280,"_142":143,"_144":-5,"_115":281,"_117":281,"_45":294,"_119":280,"_153":295},{"_147":283,"_149":150,"_151":284},[296],{"_43":214,"_57":215,"_59":216,"_142":143,"_144":217,"_115":157,"_117":157,"_45":297,"_119":221,"_153":298},{"_147":219,"_149":150,"_151":220},[299],{"_43":269,"_57":58,"_59":60,"_142":143,"_144":214,"_115":270,"_117":270,"_45":300,"_119":273,"_153":301},{"_147":219,"_149":150,"_151":272},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários