[{"_1":2,"_288":-5,"_289":-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/f0c9daee-aef6-4def-a3fc-b076944870db?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_189":190,"_50":260,"_276":277,"_284":285,"_286":287},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_76":77,"_100":41,"_101":102,"_103":104,"_105":16},"correctOptionId","","difficulty","id","f0c9daee-aef6-4def-a3fc-b076944870db","metadata",{"_47":48,"_72":73,"_74":75},"pd",{"_49":-5,"_50":51,"_52":53,"_60":61,"_62":63,"_64":16,"_65":66,"_67":16,"_68":69,"_70":71},"area","tags",[],"subjects",[54],{"_43":55,"_56":57,"_58":59},672071,"name","Mecânica","alias","mecanica","materialId","23821741","answerCount",1,"isIndexable","mainSubject",{"_43":55,"_56":57,"_58":59},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","137387163","options",[78,84,88,92,96],{"_43":79,"_80":81,"_82":83},"d5d22d3c-b120-45d1-9e3f-220da3b36840","label","A","text","F_x = F_y = 126,6 \\, \text{N}",{"_43":85,"_80":86,"_82":87},"63f79ba8-f823-4633-8f47-4ca62fa38163","B","F_x = F_y = 192,6 \\, \text{N}",{"_43":89,"_80":90,"_82":91},"bbc82e9b-a2ef-44f5-b23b-60d3bdd9af2c","C","F_x = F_y = 182,6 \\, \text{N}",{"_43":93,"_80":94,"_82":95},"c87e9a62-ec88-462a-ace8-085aac905216","D","F_x = F_y = 172,6 \\, \text{N}",{"_43":97,"_80":98,"_82":99},"3acd0cad-57d0-4d2a-bd0d-cd0745b5ef2d","E","F_x = F_y = 162,6 \\, \text{N}","solution_explanation","statement","

Dois vetores que, possuem intensidades iguais, estão situados um no eixo x e outro no eixo y, forma entre si um ângulo de 45º. Determine as intensidades desses vetores sabendo que o vetor resultante entre eles é igual a 230 \\, \text{N}.

","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_170":171,"_188":145},"content",{"_43":111,"_56":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_130":131,"_137":138,"_139":140,"_141":142,"_28":143},"provider",{"_43":132,"_133":134,"_135":136},"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",[145],{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":153,"_126":148,"_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",{"_154":155,"_156":157,"_158":159},"childrenCount",18,"content_count",0,"question_count",135489,"children",[162],{"_43":163,"_56":57,"_58":59,"_149":150,"_151":146,"_122":164,"_124":164,"_45":165,"_126":168,"_160":169},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_154":166,"_156":157,"_158":167},10,19948,"mecanica-2",[],"video",{"_43":117,"_13":112,"_113":-5,"_172":173,"_174":175,"_28":-5,"_176":-5,"_130":175,"_177":178,"_141":-5,"_179":-5,"_180":-5,"_181":-5,"_182":-5,"_45":183,"_184":157,"_185":-5,"_103":186,"_122":187,"_124":187},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[191,221,239],{"_40":192,"_42":41,"_43":193,"_76":194,"_100":209,"_101":210,"_50":211},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[195,198,201,204,207],{"_43":196,"_80":81,"_82":197},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":199,"_80":86,"_82":200},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":202,"_80":90,"_82":203},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":205,"_80":94,"_82":206},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":192,"_80":98,"_82":208},"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

",[212],{"_43":213,"_56":214,"_58":215,"_149":150,"_151":216,"_122":164,"_124":164,"_45":217,"_126":220},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_154":218,"_156":157,"_158":219},5,30614,"engenharia-mecatronica-1",{"_40":222,"_42":41,"_43":223,"_76":224,"_100":236,"_101":237,"_50":238},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[225,228,231,233],{"_43":226,"_80":81,"_82":227},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":229,"_80":86,"_82":230},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":222,"_80":90,"_82":232},"

Verdadeiro, falso, verdadeiro

",{"_43":234,"_80":94,"_82":235},"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?

",[212],{"_40":240,"_42":41,"_43":241,"_76":242,"_100":257,"_101":258,"_50":259},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[243,246,249,251,254],{"_43":244,"_80":81,"_82":245},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":247,"_80":86,"_82":248},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":240,"_80":90,"_82":250},"Indeterminado",{"_43":252,"_80":94,"_82":253},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":255,"_80":98,"_82":256},"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????",[212],[212,261,267,268,269],{"_43":262,"_56":57,"_58":59,"_149":150,"_151":213,"_122":263,"_124":263,"_45":264,"_126":266},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_154":218,"_156":157,"_158":265},25741,"mecanica-3",{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":153,"_126":148},{"_43":163,"_56":57,"_58":59,"_149":150,"_151":146,"_122":164,"_124":164,"_45":165,"_126":168},{"_43":216,"_56":270,"_58":271,"_149":150,"_151":-5,"_122":272,"_124":272,"_45":273,"_126":271},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_154":274,"_156":157,"_158":275},29,351586,"tagsTree",[145,278],{"_43":216,"_56":270,"_58":271,"_149":150,"_151":-5,"_122":272,"_124":272,"_45":273,"_126":271,"_160":279},[280],{"_43":213,"_56":214,"_58":215,"_149":150,"_151":216,"_122":164,"_124":164,"_45":217,"_126":220,"_160":281},[282],{"_43":262,"_56":57,"_58":59,"_149":150,"_151":213,"_122":263,"_124":263,"_45":264,"_126":266,"_160":283},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários