[{"_1":2,"_349":-5,"_350":-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/9f242c16-bf78-4b76-92c4-7d6bc0a2f953","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_179":180,"_52":251,"_321":322,"_345":346,"_347":348},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_97":43,"_98":99,"_100":101,"_102":16},"correctOptionId","78b5db5f-f395-46e4-8449-3735e52be63a","difficulty","","id","9f242c16-bf78-4b76-92c4-7d6bc0a2f953","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},669639,"name","Termodinâmica","alias","termodinamica","materialId","80989136","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","163776149","options",[80,86,90,93],{"_44":81,"_82":83,"_84":85},"e4742a8f-00f5-400f-840b-df358fdb97cb","label","A","text","

40%

",{"_44":87,"_82":88,"_84":89},"e2cf8a4b-08d9-456f-8b47-4d806da88724","B","

60%

",{"_44":41,"_82":91,"_84":92},"C","

66,67%

",{"_44":94,"_82":95,"_84":96},"723782c7-3bb7-44e5-ae29-f67e0de8a952","D","

33,33%

","solution_explanation","statement","

Uma determinada máquina térmica recebe 200000 \\, \\text{cal/h}, realizando um trabalho de 120000 \\, \\text{cal/h}. Qual o rendimento deste equipamento?

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_52":141,"_160":161,"_178":142},"content",{"_44":108,"_58":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_46":116,"_119":120,"_121":120,"_122":-5,"_123":124},"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",{"_117":118},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_127":128,"_134":135,"_136":137,"_138":139,"_28":140},"provider",{"_44":129,"_130":131,"_132":133},"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",[142],{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":151,"_123":145,"_158":159},"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",{"_152":153,"_154":155,"_156":157},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":114,"_13":109,"_110":-5,"_162":163,"_164":165,"_28":-5,"_166":-5,"_127":165,"_167":168,"_138":-5,"_169":-5,"_170":-5,"_171":-5,"_172":-5,"_46":173,"_174":155,"_175":-5,"_100":176,"_119":177,"_121":177},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_117":118},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[181,212,230],{"_40":182,"_42":43,"_44":183,"_78":184,"_97":200,"_98":201,"_52":202},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[185,188,191,194,197],{"_44":186,"_82":83,"_84":187},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":189,"_82":88,"_84":190},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":192,"_82":91,"_84":193},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":195,"_82":95,"_84":196},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":182,"_82":198,"_84":199},"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

",[203],{"_44":204,"_58":205,"_60":206,"_146":147,"_148":207,"_119":208,"_121":208,"_46":209,"_123":206},"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",{"_152":210,"_154":155,"_156":211},4,12302,{"_40":213,"_42":43,"_44":214,"_78":215,"_97":227,"_98":228,"_52":229},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[216,219,222,224],{"_44":217,"_82":83,"_84":218},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":220,"_82":88,"_84":221},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":213,"_82":91,"_84":223},"

Verdadeiro, falso, verdadeiro

",{"_44":225,"_82":95,"_84":226},"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?

",[203],{"_40":231,"_42":43,"_44":232,"_78":233,"_97":248,"_98":249,"_52":250},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[234,237,240,242,245],{"_44":235,"_82":83,"_84":236},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":238,"_82":88,"_84":239},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":231,"_82":91,"_84":241},"Indeterminado",{"_44":243,"_82":95,"_84":244},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":246,"_82":198,"_84":247},"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????",[203],[203,252,259,269,276,283,284,292,298,303,309,316],{"_44":253,"_58":59,"_60":61,"_146":147,"_148":254,"_119":150,"_121":150,"_46":255,"_123":258},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":256,"_154":155,"_156":257},2,11846,"termodinamica-3",{"_44":260,"_58":261,"_60":262,"_146":147,"_148":263,"_119":264,"_121":264,"_46":265,"_123":268},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_152":266,"_154":155,"_156":267},5,30614,"engenharia-mecatronica-1",{"_44":270,"_58":271,"_60":272,"_146":147,"_148":260,"_119":208,"_121":208,"_46":273,"_123":275},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":266,"_154":155,"_156":274},25741,"mecanica-3",{"_44":254,"_58":277,"_60":278,"_146":147,"_148":263,"_119":264,"_121":264,"_46":279,"_123":282},"Engenharia Mecânica","engenharia-mecanica",{"_152":280,"_154":155,"_156":281},11,36318,"engenharia-mecanica-2",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":151,"_123":145},{"_44":285,"_58":286,"_60":287,"_146":147,"_148":-5,"_119":288,"_121":288,"_46":289,"_123":287},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_152":290,"_154":155,"_156":291},18,135489,{"_44":293,"_58":59,"_60":61,"_146":147,"_148":204,"_119":294,"_121":294,"_46":295,"_123":297},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_152":155,"_154":155,"_156":296},8597,"termodinamica-5",{"_44":207,"_58":299,"_60":300,"_146":147,"_148":263,"_119":264,"_121":264,"_46":301,"_123":302},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":266,"_154":155,"_156":211},"engenharia-de-petroleo-1",{"_44":149,"_58":304,"_60":305,"_146":147,"_148":285,"_119":264,"_121":264,"_46":306,"_123":308},"Física","fisica",{"_152":280,"_154":155,"_156":307},13777,"fisica-4",{"_44":263,"_58":310,"_60":311,"_146":147,"_148":-5,"_119":312,"_121":312,"_46":313,"_123":311},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":314,"_154":155,"_156":315},29,351586,{"_44":317,"_58":59,"_60":61,"_146":147,"_148":270,"_119":318,"_121":318,"_46":319,"_123":320},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_152":155,"_154":155,"_156":296},"termodinamica-4","tagsTree",[323,327],{"_44":285,"_58":286,"_60":287,"_146":147,"_148":-5,"_119":288,"_121":288,"_46":289,"_123":287,"_158":324},[325],{"_44":149,"_58":304,"_60":305,"_146":147,"_148":285,"_119":264,"_121":264,"_46":306,"_123":308,"_158":326},[142],{"_44":263,"_58":310,"_60":311,"_146":147,"_148":-5,"_119":312,"_121":312,"_46":313,"_123":311,"_158":328},[329,335,339],{"_44":260,"_58":261,"_60":262,"_146":147,"_148":263,"_119":264,"_121":264,"_46":265,"_123":268,"_158":330},[331],{"_44":270,"_58":271,"_60":272,"_146":147,"_148":260,"_119":208,"_121":208,"_46":273,"_123":275,"_158":332},[333],{"_44":317,"_58":59,"_60":61,"_146":147,"_148":270,"_119":318,"_121":318,"_46":319,"_123":320,"_158":334},[],{"_44":254,"_58":277,"_60":278,"_146":147,"_148":263,"_119":264,"_121":264,"_46":279,"_123":282,"_158":336},[337],{"_44":253,"_58":59,"_60":61,"_146":147,"_148":254,"_119":150,"_121":150,"_46":255,"_123":258,"_158":338},[],{"_44":207,"_58":299,"_60":300,"_146":147,"_148":263,"_119":264,"_121":264,"_46":301,"_123":302,"_158":340},[341],{"_44":204,"_58":205,"_60":206,"_146":147,"_148":207,"_119":208,"_121":208,"_46":209,"_123":206,"_158":342},[343],{"_44":293,"_58":59,"_60":61,"_146":147,"_148":204,"_119":294,"_121":294,"_46":295,"_123":297,"_158":344},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários