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Uma máquina produz 2.400 \text{ J} de trabalho mecânico e rejeita 4.200 \text{ J} de calor em cada ciclo. Qual será o valor de calor fornecido a cada ciclo e sua eficiência energética em percentual?

","status","pending_classification","hasRelatedVideo","relatedVideos",[92],{"_93":94,"_112":113,"_50":128,"_147":148,"_165":129},"content",{"_43":95,"_56":96,"_97":-5,"_98":99,"_100":101,"_102":-5,"_45":103,"_106":107,"_108":107,"_109":-5,"_110":111},"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",{"_104":105},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_114":115,"_121":122,"_123":124,"_125":126,"_28":127},"provider",{"_43":116,"_117":118,"_119":120},"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",[129],{"_43":130,"_56":131,"_58":132,"_133":134,"_135":136,"_106":137,"_108":137,"_45":138,"_110":132,"_145":146},"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",{"_139":140,"_141":142,"_143":144},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":101,"_13":96,"_97":-5,"_149":150,"_151":152,"_28":-5,"_153":-5,"_114":152,"_154":155,"_125":-5,"_156":-5,"_157":-5,"_158":-5,"_159":-5,"_45":160,"_161":142,"_162":-5,"_87":163,"_106":164,"_108":164},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_104":105},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[168,202,220],{"_40":169,"_42":41,"_43":170,"_76":171,"_84":190,"_85":191,"_50":192},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[172,175,179,183,187],{"_43":173,"_80":81,"_82":174},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":176,"_80":177,"_82":178},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","B","6y'' - y' - y = 0",{"_43":180,"_80":181,"_82":182},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_43":184,"_80":185,"_82":186},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":169,"_80":188,"_82":189},"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

",[193],{"_43":194,"_56":195,"_58":196,"_133":134,"_135":197,"_106":198,"_108":198,"_45":199,"_110":196},"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",{"_139":200,"_141":142,"_143":201},4,12302,{"_40":203,"_42":41,"_43":204,"_76":205,"_84":217,"_85":218,"_50":219},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[206,209,212,214],{"_43":207,"_80":81,"_82":208},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":210,"_80":177,"_82":211},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":203,"_80":181,"_82":213},"

Verdadeiro, falso, verdadeiro

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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?

",[193],{"_40":221,"_42":41,"_43":222,"_76":223,"_84":238,"_85":239,"_50":240},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[224,227,230,232,235],{"_43":225,"_80":81,"_82":226},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":228,"_80":177,"_82":229},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":221,"_80":181,"_82":231},"Indeterminado",{"_43":233,"_80":185,"_82":234},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":236,"_80":188,"_82":237},"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????",[193],[193,242,248,258,265,272,273,281,287,292,298,305],{"_43":243,"_56":57,"_58":59,"_133":134,"_135":244,"_106":137,"_108":137,"_45":245,"_110":247},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_139":63,"_141":142,"_143":246},11846,"termodinamica-3",{"_43":249,"_56":250,"_58":251,"_133":134,"_135":252,"_106":253,"_108":253,"_45":254,"_110":257},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_139":255,"_141":142,"_143":256},5,30614,"engenharia-mecatronica-1",{"_43":259,"_56":260,"_58":261,"_133":134,"_135":249,"_106":198,"_108":198,"_45":262,"_110":264},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_139":255,"_141":142,"_143":263},25741,"mecanica-3",{"_43":244,"_56":266,"_58":267,"_133":134,"_135":252,"_106":253,"_108":253,"_45":268,"_110":271},"Engenharia Mecânica","engenharia-mecanica",{"_139":269,"_141":142,"_143":270},11,36318,"engenharia-mecanica-2",{"_43":130,"_56":131,"_58":132,"_133":134,"_135":136,"_106":137,"_108":137,"_45":138,"_110":132},{"_43":274,"_56":275,"_58":276,"_133":134,"_135":-5,"_106":277,"_108":277,"_45":278,"_110":276},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_139":279,"_141":142,"_143":280},18,135489,{"_43":282,"_56":57,"_58":59,"_133":134,"_135":194,"_106":283,"_108":283,"_45":284,"_110":286},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_139":142,"_141":142,"_143":285},8597,"termodinamica-5",{"_43":197,"_56":288,"_58":289,"_133":134,"_135":252,"_106":253,"_108":253,"_45":290,"_110":291},"Engenharia de Petróleo","engenharia-de-petroleo",{"_139":255,"_141":142,"_143":201},"engenharia-de-petroleo-1",{"_43":136,"_56":293,"_58":294,"_133":134,"_135":274,"_106":253,"_108":253,"_45":295,"_110":297},"Física","fisica",{"_139":269,"_141":142,"_143":296},13777,"fisica-4",{"_43":252,"_56":299,"_58":300,"_133":134,"_135":-5,"_106":301,"_108":301,"_45":302,"_110":300},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_139":303,"_141":142,"_143":304},29,351586,{"_43":306,"_56":57,"_58":59,"_133":134,"_135":259,"_106":307,"_108":307,"_45":308,"_110":309},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_139":142,"_141":142,"_143":285},"termodinamica-4","tagsTree",[312,316],{"_43":274,"_56":275,"_58":276,"_133":134,"_135":-5,"_106":277,"_108":277,"_45":278,"_110":276,"_145":313},[314],{"_43":136,"_56":293,"_58":294,"_133":134,"_135":274,"_106":253,"_108":253,"_45":295,"_110":297,"_145":315},[129],{"_43":252,"_56":299,"_58":300,"_133":134,"_135":-5,"_106":301,"_108":301,"_45":302,"_110":300,"_145":317},[318,324,328],{"_43":249,"_56":250,"_58":251,"_133":134,"_135":252,"_106":253,"_108":253,"_45":254,"_110":257,"_145":319},[320],{"_43":259,"_56":260,"_58":261,"_133":134,"_135":249,"_106":198,"_108":198,"_45":262,"_110":264,"_145":321},[322],{"_43":306,"_56":57,"_58":59,"_133":134,"_135":259,"_106":307,"_108":307,"_45":308,"_110":309,"_145":323},[],{"_43":244,"_56":266,"_58":267,"_133":134,"_135":252,"_106":253,"_108":253,"_45":268,"_110":271,"_145":325},[326],{"_43":243,"_56":57,"_58":59,"_133":134,"_135":244,"_106":137,"_108":137,"_45":245,"_110":247,"_145":327},[],{"_43":197,"_56":288,"_58":289,"_133":134,"_135":252,"_106":253,"_108":253,"_45":290,"_110":291,"_145":329},[330],{"_43":194,"_56":195,"_58":196,"_133":134,"_135":197,"_106":198,"_108":198,"_45":199,"_110":196,"_145":331},[332],{"_43":282,"_56":57,"_58":59,"_133":134,"_135":194,"_106":283,"_108":283,"_45":284,"_110":286,"_145":333},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários