[{"_1":2,"_294":-5,"_295":-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/e827a7d7-95e1-44a0-9a2b-26619febc2da?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_112":113,"_195":196,"_51":266,"_282":283,"_290":291,"_292":293},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_83":84,"_106":43,"_107":108,"_109":110,"_111":16},"correctOptionId","99a09ab0-5f2d-41b5-aba8-7fdedb9893ae","difficulty","","id","e827a7d7-95e1-44a0-9a2b-26619febc2da","metadata",{"_48":49,"_79":80,"_81":82},"pd",{"_50":-5,"_51":52,"_61":62,"_67":68,"_69":70,"_71":16,"_72":73,"_74":16,"_75":76,"_77":78},"area","tags",[53,58],{"_44":54,"_55":56,"_57":56},1328788,"name","tecnicomecaninca","alias",{"_44":59,"_55":60,"_57":60},1328789,"transformacaomecanica","subjects",[63],{"_44":64,"_55":65,"_57":66},672071,"Mecânica","mecanica","materialId","124666202","answerCount",2,"isIndexable","mainSubject",{"_44":64,"_55":65,"_57":66},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","124667519","options",[85,91,94,98,102],{"_44":86,"_87":88,"_89":90},"26f7f559-986c-4bd4-85b4-3c1299f63642","label","A","text","Receber aço da panela",{"_44":41,"_87":92,"_89":93},"B","Determinar comprimento do lingote",{"_44":95,"_87":96,"_89":97},"412609bb-d03e-48f7-8f24-0d11913bd9d8","C","Distribui aço para os moldes",{"_44":99,"_87":100,"_89":101},"f70d2a63-7f28-495e-b73e-0a87ae6c3fe3","D","Permitir melhor monitoramento da temperatura do aço",{"_44":103,"_87":104,"_89":105},"b83c3d4b-0128-4051-b1ee-15a7455fd8a0","E","Controlar a velocidade de vazão do aço","solution_explanation","statement","

No lingotamento continuo distribuidor possui diversas funções exceto?

","status","pending_classification","hasRelatedVideo","relatedVideos",[114],{"_115":116,"_134":135,"_51":150,"_176":177,"_194":151},"content",{"_44":117,"_55":118,"_119":-5,"_120":121,"_122":123,"_124":-5,"_46":125,"_128":129,"_130":129,"_131":-5,"_132":133},"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",{"_126":127},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_136":137,"_143":144,"_145":146,"_147":148,"_28":149},"provider",{"_44":138,"_139":140,"_141":142},"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",[151],{"_44":152,"_55":153,"_57":154,"_155":156,"_157":-5,"_128":158,"_130":158,"_46":159,"_132":154,"_166":167},"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",{"_160":161,"_162":163,"_164":165},"childrenCount",18,"content_count",0,"question_count",135489,"children",[168],{"_44":169,"_55":65,"_57":66,"_155":156,"_157":152,"_128":170,"_130":170,"_46":171,"_132":174,"_166":175},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_160":172,"_162":163,"_164":173},10,19948,"mecanica-2",[],"video",{"_44":123,"_13":118,"_119":-5,"_178":179,"_180":181,"_28":-5,"_182":-5,"_136":181,"_183":184,"_147":-5,"_185":-5,"_186":-5,"_187":-5,"_188":-5,"_46":189,"_190":163,"_191":-5,"_109":192,"_128":193,"_130":193},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_126":127},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[197,227,245],{"_40":198,"_42":43,"_44":199,"_83":200,"_106":215,"_107":216,"_51":217},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[201,204,207,210,213],{"_44":202,"_87":88,"_89":203},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":205,"_87":92,"_89":206},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":208,"_87":96,"_89":209},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":211,"_87":100,"_89":212},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":198,"_87":104,"_89":214},"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

",[218],{"_44":219,"_55":220,"_57":221,"_155":156,"_157":222,"_128":170,"_130":170,"_46":223,"_132":226},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_160":224,"_162":163,"_164":225},5,30614,"engenharia-mecatronica-1",{"_40":228,"_42":43,"_44":229,"_83":230,"_106":242,"_107":243,"_51":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_44":232,"_87":88,"_89":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":235,"_87":92,"_89":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":228,"_87":96,"_89":238},"

Verdadeiro, falso, verdadeiro

",{"_44":240,"_87":100,"_89":241},"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?

",[218],{"_40":246,"_42":43,"_44":247,"_83":248,"_106":263,"_107":264,"_51":265},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[249,252,255,257,260],{"_44":250,"_87":88,"_89":251},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":253,"_87":92,"_89":254},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":246,"_87":96,"_89":256},"Indeterminado",{"_44":258,"_87":100,"_89":259},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":261,"_87":104,"_89":262},"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????",[218],[218,267,273,274,275],{"_44":268,"_55":65,"_57":66,"_155":156,"_157":219,"_128":269,"_130":269,"_46":270,"_132":272},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_160":224,"_162":163,"_164":271},25741,"mecanica-3",{"_44":152,"_55":153,"_57":154,"_155":156,"_157":-5,"_128":158,"_130":158,"_46":159,"_132":154},{"_44":169,"_55":65,"_57":66,"_155":156,"_157":152,"_128":170,"_130":170,"_46":171,"_132":174},{"_44":222,"_55":276,"_57":277,"_155":156,"_157":-5,"_128":278,"_130":278,"_46":279,"_132":277},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_160":280,"_162":163,"_164":281},29,351586,"tagsTree",[151,284],{"_44":222,"_55":276,"_57":277,"_155":156,"_157":-5,"_128":278,"_130":278,"_46":279,"_132":277,"_166":285},[286],{"_44":219,"_55":220,"_57":221,"_155":156,"_157":222,"_128":170,"_130":170,"_46":223,"_132":226,"_166":287},[288],{"_44":268,"_55":65,"_57":66,"_155":156,"_157":219,"_128":269,"_130":269,"_46":270,"_132":272,"_166":289},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários