[{"_1":2,"_376":-5,"_377":-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/be0f4022-449d-4f15-bd25-0bc626b360a9?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_185":186,"_50":261,"_334":335,"_372":373,"_374":375},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_80":81,"_100":41,"_101":102,"_103":104,"_105":16},"correctOptionId","","difficulty","id","be0f4022-449d-4f15-bd25-0bc626b360a9","metadata",{"_47":48,"_76":77,"_78":79},"pd",{"_49":-5,"_50":51,"_58":59,"_64":65,"_66":67,"_68":16,"_69":70,"_71":16,"_72":73,"_74":75},"area","tags",[52],{"_43":53,"_54":55,"_56":57},98,"name","Exercício","alias","exercicio","subjects",[60],{"_43":61,"_54":62,"_56":63},669639,"Termodinâmica","termodinamica","materialId","122612960","answerCount",1,"isIndexable","mainSubject",{"_43":61,"_54":62,"_56":63},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122726063","options",[82,88,92,96],{"_43":83,"_84":85,"_86":87},"57202c99-e633-4dd7-8bd9-b9cd3d2aa7e7","label","A","text","Apenas as afirmações I, II e III estão corretas.",{"_43":89,"_84":90,"_86":91},"e1568791-7b0f-41ff-9315-34a470d10620","B","Apenas as afirmações II, IV e V estão corretas.",{"_43":93,"_84":94,"_86":95},"70f8968b-6220-44eb-a7f8-2e29e468de32","C","Apenas as afirmações III, IV e VI estão corretas.",{"_43":97,"_84":98,"_86":99},"dcf64b94-41ca-400d-af06-b489165d974b","D","Todas as afirmações estão corretas.","solution_explanation","statement","

Quais são as características dos produtos derivados da destilação do petróleo?

","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_163":164,"_181":182},"content",{"_43":111,"_54":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,"_54":147,"_56":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",{"_43":146,"_54":147,"_56":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":183,"_126":148,"_161":184},{"_155":156,"_157":158,"_159":160},[],"similarQuestions",[187,218,238],{"_40":188,"_42":41,"_43":189,"_80":190,"_100":206,"_101":207,"_50":208},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[191,194,197,200,203],{"_43":192,"_84":85,"_86":193},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":195,"_84":90,"_86":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":198,"_84":94,"_86":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":201,"_84":98,"_86":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":188,"_84":204,"_86":205},"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

",[209],{"_43":210,"_54":211,"_56":212,"_149":150,"_151":213,"_122":214,"_124":214,"_45":215,"_126":212},"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":216,"_157":158,"_159":217},4,12302,{"_40":219,"_42":41,"_43":220,"_80":221,"_100":233,"_101":234,"_50":235},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[222,225,228,230],{"_43":223,"_84":85,"_86":224},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":226,"_84":90,"_86":227},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":219,"_84":94,"_86":229},"

Verdadeiro, falso, verdadeiro

",{"_43":231,"_84":98,"_86":232},"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?

",[236],{"_43":210,"_54":211,"_56":212,"_149":150,"_151":213,"_122":214,"_124":214,"_45":237,"_126":212},{"_155":216,"_157":158,"_159":217},{"_40":239,"_42":41,"_43":240,"_80":241,"_100":256,"_101":257,"_50":258},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[242,245,248,250,253],{"_43":243,"_84":85,"_86":244},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":246,"_84":90,"_86":247},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":239,"_84":94,"_86":249},"Indeterminado",{"_43":251,"_84":98,"_86":252},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":254,"_84":204,"_86":255},"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????",[259],{"_43":210,"_54":211,"_56":212,"_149":150,"_151":213,"_122":214,"_124":214,"_45":260,"_126":212},{"_155":216,"_157":158,"_159":217},[262,264,271,281,288,295,297,305,311,316,322,329],{"_43":210,"_54":211,"_56":212,"_149":150,"_151":213,"_122":214,"_124":214,"_45":263,"_126":212},{"_155":216,"_157":158,"_159":217},{"_43":265,"_54":62,"_56":63,"_149":150,"_151":266,"_122":153,"_124":153,"_45":267,"_126":270},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":268,"_157":158,"_159":269},2,11846,"termodinamica-3",{"_43":272,"_54":273,"_56":274,"_149":150,"_151":275,"_122":276,"_124":276,"_45":277,"_126":280},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":278,"_157":158,"_159":279},5,30614,"engenharia-mecatronica-1",{"_43":282,"_54":283,"_56":284,"_149":150,"_151":272,"_122":214,"_124":214,"_45":285,"_126":287},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":278,"_157":158,"_159":286},25741,"mecanica-3",{"_43":266,"_54":289,"_56":290,"_149":150,"_151":275,"_122":276,"_124":276,"_45":291,"_126":294},"Engenharia Mecânica","engenharia-mecanica",{"_155":292,"_157":158,"_159":293},11,36318,"engenharia-mecanica-2",{"_43":146,"_54":147,"_56":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":296,"_126":148},{"_155":156,"_157":158,"_159":160},{"_43":298,"_54":299,"_56":300,"_149":150,"_151":-5,"_122":301,"_124":301,"_45":302,"_126":300},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":303,"_157":158,"_159":304},18,135489,{"_43":306,"_54":62,"_56":63,"_149":150,"_151":210,"_122":307,"_124":307,"_45":308,"_126":310},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":309},8597,"termodinamica-5",{"_43":213,"_54":312,"_56":313,"_149":150,"_151":275,"_122":276,"_124":276,"_45":314,"_126":315},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":278,"_157":158,"_159":217},"engenharia-de-petroleo-1",{"_43":152,"_54":317,"_56":318,"_149":150,"_151":298,"_122":276,"_124":276,"_45":319,"_126":321},"Física","fisica",{"_155":292,"_157":158,"_159":320},13777,"fisica-4",{"_43":275,"_54":323,"_56":324,"_149":150,"_151":-5,"_122":325,"_124":325,"_45":326,"_126":324},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":327,"_157":158,"_159":328},29,351586,{"_43":330,"_54":62,"_56":63,"_149":150,"_151":282,"_122":331,"_124":331,"_45":332,"_126":333},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":309},"termodinamica-4","tagsTree",[336,345],{"_43":298,"_54":299,"_56":300,"_149":150,"_151":-5,"_122":301,"_124":301,"_45":337,"_126":300,"_161":338},{"_155":303,"_157":158,"_159":304},[339],{"_43":152,"_54":317,"_56":318,"_149":150,"_151":298,"_122":276,"_124":276,"_45":340,"_126":321,"_161":341},{"_155":292,"_157":158,"_159":320},[342],{"_43":146,"_54":147,"_56":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":343,"_126":148,"_161":344},{"_155":156,"_157":158,"_159":160},[],{"_43":275,"_54":323,"_56":324,"_149":150,"_151":-5,"_122":325,"_124":325,"_45":346,"_126":324,"_161":347},{"_155":327,"_157":158,"_159":328},[348,357,363],{"_43":272,"_54":273,"_56":274,"_149":150,"_151":275,"_122":276,"_124":276,"_45":349,"_126":280,"_161":350},{"_155":278,"_157":158,"_159":279},[351],{"_43":282,"_54":283,"_56":284,"_149":150,"_151":272,"_122":214,"_124":214,"_45":352,"_126":287,"_161":353},{"_155":278,"_157":158,"_159":286},[354],{"_43":330,"_54":62,"_56":63,"_149":150,"_151":282,"_122":331,"_124":331,"_45":355,"_126":333,"_161":356},{"_155":158,"_157":158,"_159":309},[],{"_43":266,"_54":289,"_56":290,"_149":150,"_151":275,"_122":276,"_124":276,"_45":358,"_126":294,"_161":359},{"_155":292,"_157":158,"_159":293},[360],{"_43":265,"_54":62,"_56":63,"_149":150,"_151":266,"_122":153,"_124":153,"_45":361,"_126":270,"_161":362},{"_155":268,"_157":158,"_159":269},[],{"_43":213,"_54":312,"_56":313,"_149":150,"_151":275,"_122":276,"_124":276,"_45":364,"_126":315,"_161":365},{"_155":278,"_157":158,"_159":217},[366],{"_43":210,"_54":211,"_56":212,"_149":150,"_151":213,"_122":214,"_124":214,"_45":367,"_126":212,"_161":368},{"_155":216,"_157":158,"_159":217},[369],{"_43":306,"_54":62,"_56":63,"_149":150,"_151":210,"_122":307,"_124":307,"_45":370,"_126":310,"_161":371},{"_155":158,"_157":158,"_159":309},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários