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Um gás ideal é comprimido adiabaticamente de um volume de 0,5 \\, m^3 para 0,25 \\, m^3, aumentando sua temperatura de 300 \\, K para uma temperatura final desconhecida. Se a constante adiabática do gás é 1,4, qual será a temperatura final do gás?

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_51":141,"_160":161,"_178":142},"content",{"_43":108,"_57":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_45":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",{"_43":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],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":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",{"_43":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,"_45":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":41,"_43":183,"_77":184,"_97":200,"_98":201,"_51":202},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[185,188,191,194,197],{"_43":186,"_81":82,"_83":187},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":189,"_81":87,"_83":190},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":192,"_81":91,"_83":193},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":195,"_81":95,"_83":196},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":182,"_81":198,"_83":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],{"_43":204,"_57":205,"_59":206,"_146":147,"_148":207,"_119":208,"_121":208,"_45":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":41,"_43":214,"_77":215,"_97":227,"_98":228,"_51":229},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[216,219,222,224],{"_43":217,"_81":82,"_83":218},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":220,"_81":87,"_83":221},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

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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????",[203],[203,252,259,269,276,283,284,292,298,303,309,316],{"_43":253,"_57":58,"_59":60,"_146":147,"_148":254,"_119":150,"_121":150,"_45":255,"_123":258},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":256,"_154":155,"_156":257},2,11846,"termodinamica-3",{"_43":260,"_57":261,"_59":262,"_146":147,"_148":263,"_119":264,"_121":264,"_45":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",{"_43":270,"_57":271,"_59":272,"_146":147,"_148":260,"_119":208,"_121":208,"_45":273,"_123":275},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":266,"_154":155,"_156":274},25741,"mecanica-3",{"_43":254,"_57":277,"_59":278,"_146":147,"_148":263,"_119":264,"_121":264,"_45":279,"_123":282},"Engenharia Mecânica","engenharia-mecanica",{"_152":280,"_154":155,"_156":281},11,36318,"engenharia-mecanica-2",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":151,"_123":145},{"_43":285,"_57":286,"_59":287,"_146":147,"_148":-5,"_119":288,"_121":288,"_45":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,{"_43":293,"_57":58,"_59":60,"_146":147,"_148":204,"_119":294,"_121":294,"_45":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",{"_43":207,"_57":299,"_59":300,"_146":147,"_148":263,"_119":264,"_121":264,"_45":301,"_123":302},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":266,"_154":155,"_156":211},"engenharia-de-petroleo-1",{"_43":149,"_57":304,"_59":305,"_146":147,"_148":285,"_119":264,"_121":264,"_45":306,"_123":308},"Física","fisica",{"_152":280,"_154":155,"_156":307},13777,"fisica-4",{"_43":263,"_57":310,"_59":311,"_146":147,"_148":-5,"_119":312,"_121":312,"_45":313,"_123":311},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":314,"_154":155,"_156":315},29,351586,{"_43":317,"_57":58,"_59":60,"_146":147,"_148":270,"_119":318,"_121":318,"_45":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],{"_43":285,"_57":286,"_59":287,"_146":147,"_148":-5,"_119":288,"_121":288,"_45":289,"_123":287,"_158":324},[325],{"_43":149,"_57":304,"_59":305,"_146":147,"_148":285,"_119":264,"_121":264,"_45":306,"_123":308,"_158":326},[142],{"_43":263,"_57":310,"_59":311,"_146":147,"_148":-5,"_119":312,"_121":312,"_45":313,"_123":311,"_158":328},[329,335,339],{"_43":260,"_57":261,"_59":262,"_146":147,"_148":263,"_119":264,"_121":264,"_45":265,"_123":268,"_158":330},[331],{"_43":270,"_57":271,"_59":272,"_146":147,"_148":260,"_119":208,"_121":208,"_45":273,"_123":275,"_158":332},[333],{"_43":317,"_57":58,"_59":60,"_146":147,"_148":270,"_119":318,"_121":318,"_45":319,"_123":320,"_158":334},[],{"_43":254,"_57":277,"_59":278,"_146":147,"_148":263,"_119":264,"_121":264,"_45":279,"_123":282,"_158":336},[337],{"_43":253,"_57":58,"_59":60,"_146":147,"_148":254,"_119":150,"_121":150,"_45":255,"_123":258,"_158":338},[],{"_43":207,"_57":299,"_59":300,"_146":147,"_148":263,"_119":264,"_121":264,"_45":301,"_123":302,"_158":340},[341],{"_43":204,"_57":205,"_59":206,"_146":147,"_148":207,"_119":208,"_121":208,"_45":209,"_123":206,"_158":342},[343],{"_43":293,"_57":58,"_59":60,"_146":147,"_148":204,"_119":294,"_121":294,"_45":295,"_123":297,"_158":344},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários