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According to the Clausius statement:

It is impossible to remove heat from a cold source and transfer it completely to a hot source without using work.

","status","pending_classification","hasRelatedVideo","relatedVideos",[96],{"_97":98,"_116":117,"_51":132,"_151":152,"_169":133},"content",{"_44":99,"_57":100,"_101":-5,"_102":103,"_104":105,"_106":-5,"_46":107,"_110":111,"_112":111,"_113":-5,"_114":115},"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",{"_108":109},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_118":119,"_125":126,"_127":128,"_129":130,"_28":131},"provider",{"_44":120,"_121":122,"_123":124},"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",[133],{"_44":134,"_57":135,"_59":136,"_137":138,"_139":140,"_110":141,"_112":141,"_46":142,"_114":136,"_149":150},"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",{"_143":144,"_145":146,"_147":148},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":105,"_13":100,"_101":-5,"_153":154,"_155":156,"_28":-5,"_157":-5,"_118":156,"_158":159,"_129":-5,"_160":-5,"_161":-5,"_162":-5,"_163":-5,"_46":164,"_165":146,"_166":-5,"_91":167,"_110":168,"_112":168},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_108":109},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[172,205,223],{"_40":173,"_42":43,"_44":174,"_77":175,"_88":193,"_89":194,"_51":195},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[176,179,182,186,190],{"_44":177,"_80":81,"_82":178},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":180,"_80":86,"_82":181},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":183,"_80":184,"_82":185},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_44":187,"_80":188,"_82":189},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_44":173,"_80":191,"_82":192},"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

",[196],{"_44":197,"_57":198,"_59":199,"_137":138,"_139":200,"_110":201,"_112":201,"_46":202,"_114":199},"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",{"_143":203,"_145":146,"_147":204},4,12302,{"_40":206,"_42":43,"_44":207,"_77":208,"_88":220,"_89":221,"_51":222},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[209,212,215,217],{"_44":210,"_80":81,"_82":211},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":213,"_80":86,"_82":214},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":206,"_80":184,"_82":216},"

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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[196],[196,245,252,262,269,276,277,285,291,296,302,309],{"_44":246,"_57":58,"_59":60,"_137":138,"_139":247,"_110":141,"_112":141,"_46":248,"_114":251},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_143":249,"_145":146,"_147":250},2,11846,"termodinamica-3",{"_44":253,"_57":254,"_59":255,"_137":138,"_139":256,"_110":257,"_112":257,"_46":258,"_114":261},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_143":259,"_145":146,"_147":260},5,30614,"engenharia-mecatronica-1",{"_44":263,"_57":264,"_59":265,"_137":138,"_139":253,"_110":201,"_112":201,"_46":266,"_114":268},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_143":259,"_145":146,"_147":267},25741,"mecanica-3",{"_44":247,"_57":270,"_59":271,"_137":138,"_139":256,"_110":257,"_112":257,"_46":272,"_114":275},"Engenharia Mecânica","engenharia-mecanica",{"_143":273,"_145":146,"_147":274},11,36318,"engenharia-mecanica-2",{"_44":134,"_57":135,"_59":136,"_137":138,"_139":140,"_110":141,"_112":141,"_46":142,"_114":136},{"_44":278,"_57":279,"_59":280,"_137":138,"_139":-5,"_110":281,"_112":281,"_46":282,"_114":280},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_143":283,"_145":146,"_147":284},18,135489,{"_44":286,"_57":58,"_59":60,"_137":138,"_139":197,"_110":287,"_112":287,"_46":288,"_114":290},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_143":146,"_145":146,"_147":289},8597,"termodinamica-5",{"_44":200,"_57":292,"_59":293,"_137":138,"_139":256,"_110":257,"_112":257,"_46":294,"_114":295},"Engenharia de Petróleo","engenharia-de-petroleo",{"_143":259,"_145":146,"_147":204},"engenharia-de-petroleo-1",{"_44":140,"_57":297,"_59":298,"_137":138,"_139":278,"_110":257,"_112":257,"_46":299,"_114":301},"Física","fisica",{"_143":273,"_145":146,"_147":300},13777,"fisica-4",{"_44":256,"_57":303,"_59":304,"_137":138,"_139":-5,"_110":305,"_112":305,"_46":306,"_114":304},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_143":307,"_145":146,"_147":308},29,351586,{"_44":310,"_57":58,"_59":60,"_137":138,"_139":263,"_110":311,"_112":311,"_46":312,"_114":313},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_143":146,"_145":146,"_147":289},"termodinamica-4","tagsTree",[316,320],{"_44":278,"_57":279,"_59":280,"_137":138,"_139":-5,"_110":281,"_112":281,"_46":282,"_114":280,"_149":317},[318],{"_44":140,"_57":297,"_59":298,"_137":138,"_139":278,"_110":257,"_112":257,"_46":299,"_114":301,"_149":319},[133],{"_44":256,"_57":303,"_59":304,"_137":138,"_139":-5,"_110":305,"_112":305,"_46":306,"_114":304,"_149":321},[322,328,332],{"_44":253,"_57":254,"_59":255,"_137":138,"_139":256,"_110":257,"_112":257,"_46":258,"_114":261,"_149":323},[324],{"_44":263,"_57":264,"_59":265,"_137":138,"_139":253,"_110":201,"_112":201,"_46":266,"_114":268,"_149":325},[326],{"_44":310,"_57":58,"_59":60,"_137":138,"_139":263,"_110":311,"_112":311,"_46":312,"_114":313,"_149":327},[],{"_44":247,"_57":270,"_59":271,"_137":138,"_139":256,"_110":257,"_112":257,"_46":272,"_114":275,"_149":329},[330],{"_44":246,"_57":58,"_59":60,"_137":138,"_139":247,"_110":141,"_112":141,"_46":248,"_114":251,"_149":331},[],{"_44":200,"_57":292,"_59":293,"_137":138,"_139":256,"_110":257,"_112":257,"_46":294,"_114":295,"_149":333},[334],{"_44":197,"_57":198,"_59":199,"_137":138,"_139":200,"_110":201,"_112":201,"_46":202,"_114":199,"_149":335},[336],{"_44":286,"_57":58,"_59":60,"_137":138,"_139":197,"_110":287,"_112":287,"_46":288,"_114":290,"_149":337},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários