[{"_1":2,"_310":-5,"_311":-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/e7be124d-56f5-4574-becf-762c8d158a05?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_107":108,"_194":195,"_51":269,"_289":290,"_306":307,"_308":309},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_101":41,"_102":103,"_104":105,"_106":16},"correctOptionId","","difficulty","id","e7be124d-56f5-4574-becf-762c8d158a05","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","64809336","answerCount",0,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","141845537","options",[79,85,89,93,97],{"_43":80,"_81":82,"_83":84},"98863cdd-dbfb-4db1-af24-f210415906fb","label","A","text","20,0 \\, kN e 28,3 \\, kN",{"_43":86,"_81":87,"_83":88},"23360d6d-22c7-450f-a438-e60d5ed0ec92","B","29,8 \\, kN e 32,0 \\, kN",{"_43":90,"_81":91,"_83":92},"9159a4cf-5558-45ca-92d1-06c04c24ceb6","C","25,0 \\, kN e 25,7 \\, kN",{"_43":94,"_81":95,"_83":96},"5c08ebc0-5935-4f25-b1d6-eb99cc0ebb18","D","28,3 \\, kN e 20,0 \\, kN",{"_43":98,"_81":99,"_83":100},"398c661d-5d0c-4aff-8d53-900d5863024b","E","29,8 \\, kN e 35,4 \\, kN","solution_explanation","statement","

As duas hastes de alumínio suportam a carga vertical P = 20 \\, kN. As forças F_{ab} e F_{ac} são:

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_51":145,"_170":171,"_187":188},"content",{"_43":112,"_57":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_45":120,"_123":124,"_125":124,"_126":-5,"_127":128},"25693a52-620c-4e8a-a1e0-301f6c974b07","Cônicas - 04 - Caracterização geométrica das cônicas - Parte 04","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f9f5befc-3526-45f3-8e46-bf287344e961","user_id",{"_121":122},"external_id","13405","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","conicas-04-caracterizacao-geometrica-das-conicas-parte-04","prometheusData",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_43":133,"_134":135,"_136":137},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","32997f8c-0eb9-4160-a641-d7233373486b","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/32997f8c-0eb9-4160-a641-d7233373486b/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/32997f8c-0eb9-4160-a641-d7233373486b/levels.m3u8",[146],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":154,"_127":149,"_160":161},"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",{"_155":156,"_157":64,"_158":159},"childrenCount",18,"content_count","question_count",135489,"children",[162],{"_43":163,"_57":58,"_59":60,"_150":151,"_152":147,"_123":164,"_125":164,"_45":165,"_127":168,"_160":169},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_155":166,"_157":64,"_158":167},10,19948,"mecanica-2",[],"video",{"_43":118,"_13":113,"_114":-5,"_172":64,"_173":174,"_28":-5,"_175":-5,"_131":174,"_176":177,"_142":-5,"_178":-5,"_179":-5,"_180":-5,"_181":-5,"_45":182,"_183":64,"_184":-5,"_104":185,"_123":186,"_125":186},"duration","source_type","prometheus","iframe_url","provider_video_id","eb9a22a9-38d1-4905-bdb3-d75bbe70f5d5","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":189,"_127":149,"_160":190},{"_155":156,"_157":64,"_158":159},[191],{"_43":163,"_57":58,"_59":60,"_150":151,"_152":147,"_123":164,"_125":164,"_45":192,"_127":168,"_160":193},{"_155":166,"_157":64,"_158":167},[],"similarQuestions",[196,226,246],{"_40":197,"_42":41,"_43":198,"_77":199,"_101":214,"_102":215,"_51":216},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[200,203,206,209,212],{"_43":201,"_81":82,"_83":202},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":204,"_81":87,"_83":205},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":207,"_81":91,"_83":208},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":210,"_81":95,"_83":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":197,"_81":99,"_83":213},"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

",[217],{"_43":218,"_57":219,"_59":220,"_150":151,"_152":221,"_123":164,"_125":164,"_45":222,"_127":225},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":223,"_157":64,"_158":224},5,30614,"engenharia-mecatronica-1",{"_40":227,"_42":41,"_43":228,"_77":229,"_101":241,"_102":242,"_51":243},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[230,233,236,238],{"_43":231,"_81":82,"_83":232},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":234,"_81":87,"_83":235},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":227,"_81":91,"_83":237},"

Verdadeiro, falso, verdadeiro

",{"_43":239,"_81":95,"_83":240},"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?

",[244],{"_43":218,"_57":219,"_59":220,"_150":151,"_152":221,"_123":164,"_125":164,"_45":245,"_127":225},{"_155":223,"_157":64,"_158":224},{"_40":247,"_42":41,"_43":248,"_77":249,"_101":264,"_102":265,"_51":266},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[250,253,256,258,261],{"_43":251,"_81":82,"_83":252},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":254,"_81":87,"_83":255},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":247,"_81":91,"_83":257},"Indeterminado",{"_43":259,"_81":95,"_83":260},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":262,"_81":99,"_83":263},"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????",[267],{"_43":218,"_57":219,"_59":220,"_150":151,"_152":221,"_123":164,"_125":164,"_45":268,"_127":225},{"_155":223,"_157":64,"_158":224},[270,272,278,280,282],{"_43":218,"_57":219,"_59":220,"_150":151,"_152":221,"_123":164,"_125":164,"_45":271,"_127":225},{"_155":223,"_157":64,"_158":224},{"_43":273,"_57":58,"_59":60,"_150":151,"_152":218,"_123":274,"_125":274,"_45":275,"_127":277},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_155":223,"_157":64,"_158":276},25741,"mecanica-3",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":279,"_127":149},{"_155":156,"_157":64,"_158":159},{"_43":163,"_57":58,"_59":60,"_150":151,"_152":147,"_123":164,"_125":164,"_45":281,"_127":168},{"_155":166,"_157":64,"_158":167},{"_43":221,"_57":283,"_59":284,"_150":151,"_152":-5,"_123":285,"_125":285,"_45":286,"_127":284},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":287,"_157":64,"_158":288},29,351586,"tagsTree",[291,297],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":292,"_127":149,"_160":293},{"_155":156,"_157":64,"_158":159},[294],{"_43":163,"_57":58,"_59":60,"_150":151,"_152":147,"_123":164,"_125":164,"_45":295,"_127":168,"_160":296},{"_155":166,"_157":64,"_158":167},[],{"_43":221,"_57":283,"_59":284,"_150":151,"_152":-5,"_123":285,"_125":285,"_45":298,"_127":284,"_160":299},{"_155":287,"_157":64,"_158":288},[300],{"_43":218,"_57":219,"_59":220,"_150":151,"_152":221,"_123":164,"_125":164,"_45":301,"_127":225,"_160":302},{"_155":223,"_157":64,"_158":224},[303],{"_43":273,"_57":58,"_59":60,"_150":151,"_152":218,"_123":274,"_125":274,"_45":304,"_127":277,"_160":305},{"_155":223,"_157":64,"_158":276},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários