[{"_1":2,"_351":-5,"_352":-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/a21f7a01-7439-48cd-9b8a-5f50506f11c7","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_182":183,"_50":253,"_323":324,"_347":348,"_349":350},"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","a21f7a01-7439-48cd-9b8a-5f50506f11c7","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},669639,"name","Termodinâmica","alias","termodinamica","materialId","103250181","answerCount",1,"isIndexable","mainSubject",{"_43":55,"_56":57,"_58":59},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","136581542","options",[78,84,88,92,96],{"_43":79,"_80":81,"_82":83},"cdf07cbd-a50c-4d42-a286-88df339b19c6","label","A","text","50 \\, \text{kJ} e 30 \\, \text{kJ}.",{"_43":85,"_80":86,"_82":87},"cae3c079-c313-40ba-a183-93b7eb735b07","B","70 \\, \text{kJ} e 30 \\, \text{kJ}.",{"_43":89,"_80":90,"_82":91},"62ff857f-8754-494d-a7b2-155a0d84103b","C","75 \\, \text{kJ} e 25 \\, \text{kJ}.",{"_43":93,"_80":94,"_82":95},"243e9d81-fd65-4e45-ab1e-e2fac204323e","D","50 \\, \text{kJ} e 70 \\, \text{kJ}.",{"_43":97,"_80":98,"_82":99},"aad9e130-a1bd-4342-87b8-c23dcf6ad2c0","E","25 \\, \text{kJ} e 30 \\, \text{kJ}.","solution_explanation","statement","Uma quantia de 100 \\, \text{kJ} de calor é adicionada a um ciclo de Carnot a 1000 \\, \text{K}. O ciclo rejeita calor a 300 \\, \text{K}. Quanto trabalho o ciclo produz e quanto calor o ciclo rejeita?","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_163":164,"_181":145},"content",{"_43":111,"_56":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-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","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",[145],{"_43":146,"_56":147,"_58":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":154,"_126":148,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":117,"_13":112,"_113":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_130":168,"_170":171,"_141":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_45":176,"_177":158,"_178":-5,"_103":179,"_122":180,"_124":180},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[184,214,232],{"_40":185,"_42":41,"_43":186,"_76":187,"_100":202,"_101":203,"_50":204},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[188,191,194,197,200],{"_43":189,"_80":81,"_82":190},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":192,"_80":86,"_82":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":195,"_80":90,"_82":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":198,"_80":94,"_82":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":185,"_80":98,"_82":201},"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

",[205],{"_43":206,"_56":207,"_58":208,"_149":150,"_151":209,"_122":210,"_124":210,"_45":211,"_126":208},"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",{"_155":212,"_157":158,"_159":213},4,12302,{"_40":215,"_42":41,"_43":216,"_76":217,"_100":229,"_101":230,"_50":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_43":219,"_80":81,"_82":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":222,"_80":86,"_82":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":215,"_80":90,"_82":225},"

Verdadeiro, falso, verdadeiro

",{"_43":227,"_80":94,"_82":228},"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?

",[205],{"_40":233,"_42":41,"_43":234,"_76":235,"_100":250,"_101":251,"_50":252},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,244,247],{"_43":237,"_80":81,"_82":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":240,"_80":86,"_82":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":233,"_80":90,"_82":243},"Indeterminado",{"_43":245,"_80":94,"_82":246},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":248,"_80":98,"_82":249},"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????",[205],[205,254,261,271,278,285,286,294,300,305,311,318],{"_43":255,"_56":57,"_58":59,"_149":150,"_151":256,"_122":153,"_124":153,"_45":257,"_126":260},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":258,"_157":158,"_159":259},2,11846,"termodinamica-3",{"_43":262,"_56":263,"_58":264,"_149":150,"_151":265,"_122":266,"_124":266,"_45":267,"_126":270},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":268,"_157":158,"_159":269},5,30614,"engenharia-mecatronica-1",{"_43":272,"_56":273,"_58":274,"_149":150,"_151":262,"_122":210,"_124":210,"_45":275,"_126":277},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":268,"_157":158,"_159":276},25741,"mecanica-3",{"_43":256,"_56":279,"_58":280,"_149":150,"_151":265,"_122":266,"_124":266,"_45":281,"_126":284},"Engenharia Mecânica","engenharia-mecanica",{"_155":282,"_157":158,"_159":283},11,36318,"engenharia-mecanica-2",{"_43":146,"_56":147,"_58":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":154,"_126":148},{"_43":287,"_56":288,"_58":289,"_149":150,"_151":-5,"_122":290,"_124":290,"_45":291,"_126":289},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":292,"_157":158,"_159":293},18,135489,{"_43":295,"_56":57,"_58":59,"_149":150,"_151":206,"_122":296,"_124":296,"_45":297,"_126":299},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":298},8597,"termodinamica-5",{"_43":209,"_56":301,"_58":302,"_149":150,"_151":265,"_122":266,"_124":266,"_45":303,"_126":304},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":268,"_157":158,"_159":213},"engenharia-de-petroleo-1",{"_43":152,"_56":306,"_58":307,"_149":150,"_151":287,"_122":266,"_124":266,"_45":308,"_126":310},"Física","fisica",{"_155":282,"_157":158,"_159":309},13777,"fisica-4",{"_43":265,"_56":312,"_58":313,"_149":150,"_151":-5,"_122":314,"_124":314,"_45":315,"_126":313},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":316,"_157":158,"_159":317},29,351586,{"_43":319,"_56":57,"_58":59,"_149":150,"_151":272,"_122":320,"_124":320,"_45":321,"_126":322},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":298},"termodinamica-4","tagsTree",[325,329],{"_43":287,"_56":288,"_58":289,"_149":150,"_151":-5,"_122":290,"_124":290,"_45":291,"_126":289,"_161":326},[327],{"_43":152,"_56":306,"_58":307,"_149":150,"_151":287,"_122":266,"_124":266,"_45":308,"_126":310,"_161":328},[145],{"_43":265,"_56":312,"_58":313,"_149":150,"_151":-5,"_122":314,"_124":314,"_45":315,"_126":313,"_161":330},[331,337,341],{"_43":262,"_56":263,"_58":264,"_149":150,"_151":265,"_122":266,"_124":266,"_45":267,"_126":270,"_161":332},[333],{"_43":272,"_56":273,"_58":274,"_149":150,"_151":262,"_122":210,"_124":210,"_45":275,"_126":277,"_161":334},[335],{"_43":319,"_56":57,"_58":59,"_149":150,"_151":272,"_122":320,"_124":320,"_45":321,"_126":322,"_161":336},[],{"_43":256,"_56":279,"_58":280,"_149":150,"_151":265,"_122":266,"_124":266,"_45":281,"_126":284,"_161":338},[339],{"_43":255,"_56":57,"_58":59,"_149":150,"_151":256,"_122":153,"_124":153,"_45":257,"_126":260,"_161":340},[],{"_43":209,"_56":301,"_58":302,"_149":150,"_151":265,"_122":266,"_124":266,"_45":303,"_126":304,"_161":342},[343],{"_43":206,"_56":207,"_58":208,"_149":150,"_151":209,"_122":210,"_124":210,"_45":211,"_126":208,"_161":344},[345],{"_43":295,"_56":57,"_58":59,"_149":150,"_151":206,"_122":296,"_124":296,"_45":297,"_126":299,"_161":346},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários