[{"_1":2,"_360":-5,"_361":-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/9e3cea48-7e53-4e3d-b120-0f20ba5cfed0","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_114":115,"_190":191,"_50":262,"_332":333,"_356":357,"_358":359},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_88":89,"_108":41,"_109":110,"_111":112,"_113":16},"correctOptionId","","difficulty","id","9e3cea48-7e53-4e3d-b120-0f20ba5cfed0","metadata",{"_47":48,"_84":85,"_86":87},"pd",{"_49":-5,"_50":51,"_66":67,"_72":73,"_74":75,"_76":16,"_77":78,"_79":16,"_80":81,"_82":83},"area","tags",[52,58,62],{"_43":53,"_54":55,"_56":57},385731,"name","Ava AVA","alias","ava-ava",{"_43":59,"_54":60,"_56":61},430723,"Apol1-apol2-apol3-apol4-apol5-","apol-1-apol-2-apol-3-apol-4-apol-5",{"_43":63,"_54":64,"_56":65},881846,"UNINTER nota 100#Uninter","uninter-nota-100%23uninter","subjects",[68],{"_43":69,"_54":70,"_56":71},669639,"Termodinâmica","termodinamica","materialId","121495352","answerCount",1,"isIndexable","mainSubject",{"_43":69,"_54":70,"_56":71},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","121495480","options",[90,96,100,104],{"_43":91,"_92":93,"_94":95},"a378a00b-2052-4e06-ab95-a57857700bb1","label","A","text","Oxigênio - M = 32 \\, g/mol; T = 300 \\, K",{"_43":97,"_92":98,"_94":99},"14dda843-6810-4328-a193-3ecf6d9a6050","B","Nitrogênio - M = 28 \\, g/mol; T = 300 \\, K",{"_43":101,"_92":102,"_94":103},"1ec8ef46-852e-4095-9ac7-a8b80ad984f6","C","Oxigênio - M = 32 \\, g/mol; T = 330 \\, K",{"_43":105,"_92":106,"_94":107},"8ae741d2-e4e8-4e2c-a352-9d9ad0e98471","D","Nitrogênio - M = 28 \\, g/mol; T = 330 \\, K","solution_explanation","statement","

Qual dos seguintes gases apresenta a maior velocidade quadrática média?

","status","pending_classification","hasRelatedVideo","relatedVideos",[116],{"_117":118,"_136":137,"_50":152,"_171":172,"_189":153},"content",{"_43":119,"_54":120,"_121":-5,"_122":123,"_124":125,"_126":-5,"_45":127,"_130":131,"_132":131,"_133":-5,"_134":135},"162087be-594f-460e-bbdd-a339ac2f10ad","Calor Latente - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f2b62fc2-7079-40e7-a5b5-c4a9769b205d","user_id",{"_128":129},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_138":139,"_145":146,"_147":148,"_149":150,"_28":151},"provider",{"_43":140,"_141":142,"_143":144},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","bf8aacba-3de9-4b10-961c-47ada80dfe8c","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/levels.m3u8",[153],{"_43":154,"_54":155,"_56":156,"_157":158,"_159":160,"_130":161,"_132":161,"_45":162,"_134":156,"_169":170},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9","2025-04-29T03:44:27.560682+00:00",{"_163":164,"_165":166,"_167":168},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":125,"_13":120,"_121":-5,"_173":174,"_175":176,"_28":-5,"_177":-5,"_138":176,"_178":179,"_149":-5,"_180":-5,"_181":-5,"_182":-5,"_183":-5,"_45":184,"_185":166,"_186":-5,"_111":187,"_130":188,"_132":188},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_128":129},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[192,223,241],{"_40":193,"_42":41,"_43":194,"_88":195,"_108":211,"_109":212,"_50":213},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[196,199,202,205,208],{"_43":197,"_92":93,"_94":198},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":200,"_92":98,"_94":201},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":203,"_92":102,"_94":204},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":206,"_92":106,"_94":207},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":193,"_92":209,"_94":210},"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

",[214],{"_43":215,"_54":216,"_56":217,"_157":158,"_159":218,"_130":219,"_132":219,"_45":220,"_134":217},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_163":221,"_165":166,"_167":222},4,12302,{"_40":224,"_42":41,"_43":225,"_88":226,"_108":238,"_109":239,"_50":240},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[227,230,233,235],{"_43":228,"_92":93,"_94":229},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":231,"_92":98,"_94":232},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":224,"_92":102,"_94":234},"

Verdadeiro, falso, verdadeiro

",{"_43":236,"_92":106,"_94":237},"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?

",[214],{"_40":242,"_42":41,"_43":243,"_88":244,"_108":259,"_109":260,"_50":261},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[245,248,251,253,256],{"_43":246,"_92":93,"_94":247},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":249,"_92":98,"_94":250},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":242,"_92":102,"_94":252},"Indeterminado",{"_43":254,"_92":106,"_94":255},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":257,"_92":209,"_94":258},"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????",[214],[214,263,270,280,287,294,295,303,309,314,320,327],{"_43":264,"_54":70,"_56":71,"_157":158,"_159":265,"_130":161,"_132":161,"_45":266,"_134":269},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_163":267,"_165":166,"_167":268},2,11846,"termodinamica-3",{"_43":271,"_54":272,"_56":273,"_157":158,"_159":274,"_130":275,"_132":275,"_45":276,"_134":279},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_163":277,"_165":166,"_167":278},5,30614,"engenharia-mecatronica-1",{"_43":281,"_54":282,"_56":283,"_157":158,"_159":271,"_130":219,"_132":219,"_45":284,"_134":286},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_163":277,"_165":166,"_167":285},25741,"mecanica-3",{"_43":265,"_54":288,"_56":289,"_157":158,"_159":274,"_130":275,"_132":275,"_45":290,"_134":293},"Engenharia Mecânica","engenharia-mecanica",{"_163":291,"_165":166,"_167":292},11,36318,"engenharia-mecanica-2",{"_43":154,"_54":155,"_56":156,"_157":158,"_159":160,"_130":161,"_132":161,"_45":162,"_134":156},{"_43":296,"_54":297,"_56":298,"_157":158,"_159":-5,"_130":299,"_132":299,"_45":300,"_134":298},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_163":301,"_165":166,"_167":302},18,135489,{"_43":304,"_54":70,"_56":71,"_157":158,"_159":215,"_130":305,"_132":305,"_45":306,"_134":308},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_163":166,"_165":166,"_167":307},8597,"termodinamica-5",{"_43":218,"_54":310,"_56":311,"_157":158,"_159":274,"_130":275,"_132":275,"_45":312,"_134":313},"Engenharia de Petróleo","engenharia-de-petroleo",{"_163":277,"_165":166,"_167":222},"engenharia-de-petroleo-1",{"_43":160,"_54":315,"_56":316,"_157":158,"_159":296,"_130":275,"_132":275,"_45":317,"_134":319},"Física","fisica",{"_163":291,"_165":166,"_167":318},13777,"fisica-4",{"_43":274,"_54":321,"_56":322,"_157":158,"_159":-5,"_130":323,"_132":323,"_45":324,"_134":322},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_163":325,"_165":166,"_167":326},29,351586,{"_43":328,"_54":70,"_56":71,"_157":158,"_159":281,"_130":329,"_132":329,"_45":330,"_134":331},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_163":166,"_165":166,"_167":307},"termodinamica-4","tagsTree",[334,338],{"_43":296,"_54":297,"_56":298,"_157":158,"_159":-5,"_130":299,"_132":299,"_45":300,"_134":298,"_169":335},[336],{"_43":160,"_54":315,"_56":316,"_157":158,"_159":296,"_130":275,"_132":275,"_45":317,"_134":319,"_169":337},[153],{"_43":274,"_54":321,"_56":322,"_157":158,"_159":-5,"_130":323,"_132":323,"_45":324,"_134":322,"_169":339},[340,346,350],{"_43":271,"_54":272,"_56":273,"_157":158,"_159":274,"_130":275,"_132":275,"_45":276,"_134":279,"_169":341},[342],{"_43":281,"_54":282,"_56":283,"_157":158,"_159":271,"_130":219,"_132":219,"_45":284,"_134":286,"_169":343},[344],{"_43":328,"_54":70,"_56":71,"_157":158,"_159":281,"_130":329,"_132":329,"_45":330,"_134":331,"_169":345},[],{"_43":265,"_54":288,"_56":289,"_157":158,"_159":274,"_130":275,"_132":275,"_45":290,"_134":293,"_169":347},[348],{"_43":264,"_54":70,"_56":71,"_157":158,"_159":265,"_130":161,"_132":161,"_45":266,"_134":269,"_169":349},[],{"_43":218,"_54":310,"_56":311,"_157":158,"_159":274,"_130":275,"_132":275,"_45":312,"_134":313,"_169":351},[352],{"_43":215,"_54":216,"_56":217,"_157":158,"_159":218,"_130":219,"_132":219,"_45":220,"_134":217,"_169":353},[354],{"_43":304,"_54":70,"_56":71,"_157":158,"_159":215,"_130":305,"_132":305,"_45":306,"_134":308,"_169":355},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários