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Em um processo de resfriamento e desumidificação, ar úmido a uma vazão mássica de 10 \\, \text{kga/s} entra na serpentina de resfriamento a T_{BS} = 26^{\text{o}}C e T_{BU} = 18^{\text{o}}C sendo condicionado a uma T_{BS} = 13^{\text{o}}C e T_{BU} = 10^{\text{o}}C. Qual o calor total extraído pela serpentina?

","status","pending_classification","hasRelatedVideo","relatedVideos",[87],{"_88":89,"_107":108,"_28":123,"_142":143,"_161":162},"content",{"_21":90,"_34":91,"_92":-5,"_93":94,"_95":96,"_97":-5,"_23":98,"_101":102,"_103":102,"_104":-5,"_105":106},"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",{"_99":100},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_109":110,"_116":117,"_118":119,"_120":121,"_6":122},"provider",{"_21":111,"_112":113,"_114":115},"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",[124],{"_21":125,"_34":126,"_36":127,"_128":129,"_130":131,"_101":132,"_103":132,"_23":133,"_105":127,"_140":141},"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",{"_134":135,"_136":137,"_138":139},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_21":96,"_144":91,"_92":-5,"_145":146,"_147":148,"_6":-5,"_149":-5,"_109":148,"_150":151,"_120":-5,"_152":-5,"_153":-5,"_154":-5,"_155":-5,"_23":156,"_157":137,"_158":-5,"_82":159,"_101":160,"_103":160},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_99":100},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_21":125,"_34":126,"_36":127,"_128":129,"_130":131,"_101":132,"_103":132,"_23":163,"_105":127,"_140":164},{"_134":135,"_136":137,"_138":139},[],"similarQuestions",[167,197,217],{"_18":168,"_20":19,"_21":169,"_55":170,"_79":185,"_80":186,"_28":187},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[171,174,177,180,183],{"_21":172,"_59":60,"_61":173},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":175,"_59":65,"_61":176},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":178,"_59":69,"_61":179},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":181,"_59":73,"_61":182},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_21":168,"_59":77,"_61":184},"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

",[188],{"_21":189,"_34":190,"_36":191,"_128":129,"_130":192,"_101":193,"_103":193,"_23":194,"_105":191},"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",{"_134":195,"_136":137,"_138":196},4,12302,{"_18":198,"_20":19,"_21":199,"_55":200,"_79":212,"_80":213,"_28":214},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[201,204,207,209],{"_21":202,"_59":60,"_61":203},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":205,"_59":65,"_61":206},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":198,"_59":69,"_61":208},"

Verdadeiro, falso, verdadeiro

",{"_21":210,"_59":73,"_61":211},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[238],{"_21":189,"_34":190,"_36":191,"_128":129,"_130":192,"_101":193,"_103":193,"_23":239,"_105":191},{"_134":195,"_136":137,"_138":196},[241,243,250,260,267,274,276,284,290,295,301,308],{"_21":189,"_34":190,"_36":191,"_128":129,"_130":192,"_101":193,"_103":193,"_23":242,"_105":191},{"_134":195,"_136":137,"_138":196},{"_21":244,"_34":35,"_36":37,"_128":129,"_130":245,"_101":132,"_103":132,"_23":246,"_105":249},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_134":247,"_136":137,"_138":248},2,11846,"termodinamica-3",{"_21":251,"_34":252,"_36":253,"_128":129,"_130":254,"_101":255,"_103":255,"_23":256,"_105":259},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_134":257,"_136":137,"_138":258},5,30614,"engenharia-mecatronica-1",{"_21":261,"_34":262,"_36":263,"_128":129,"_130":251,"_101":193,"_103":193,"_23":264,"_105":266},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_134":257,"_136":137,"_138":265},25741,"mecanica-3",{"_21":245,"_34":268,"_36":269,"_128":129,"_130":254,"_101":255,"_103":255,"_23":270,"_105":273},"Engenharia Mecânica","engenharia-mecanica",{"_134":271,"_136":137,"_138":272},11,36318,"engenharia-mecanica-2",{"_21":125,"_34":126,"_36":127,"_128":129,"_130":131,"_101":132,"_103":132,"_23":275,"_105":127},{"_134":135,"_136":137,"_138":139},{"_21":277,"_34":278,"_36":279,"_128":129,"_130":-5,"_101":280,"_103":280,"_23":281,"_105":279},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_134":282,"_136":137,"_138":283},18,135489,{"_21":285,"_34":35,"_36":37,"_128":129,"_130":189,"_101":286,"_103":286,"_23":287,"_105":289},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_134":137,"_136":137,"_138":288},8597,"termodinamica-5",{"_21":192,"_34":291,"_36":292,"_128":129,"_130":254,"_101":255,"_103":255,"_23":293,"_105":294},"Engenharia de Petróleo","engenharia-de-petroleo",{"_134":257,"_136":137,"_138":196},"engenharia-de-petroleo-1",{"_21":131,"_34":296,"_36":297,"_128":129,"_130":277,"_101":255,"_103":255,"_23":298,"_105":300},"Física","fisica",{"_134":271,"_136":137,"_138":299},13777,"fisica-4",{"_21":254,"_34":302,"_36":303,"_128":129,"_130":-5,"_101":304,"_103":304,"_23":305,"_105":303},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_134":306,"_136":137,"_138":307},29,351586,{"_21":309,"_34":35,"_36":37,"_128":129,"_130":261,"_101":310,"_103":310,"_23":311,"_105":312},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_134":137,"_136":137,"_138":288},"termodinamica-4","tagsTree",[315,324],{"_21":277,"_34":278,"_36":279,"_128":129,"_130":-5,"_101":280,"_103":280,"_23":316,"_105":279,"_140":317},{"_134":282,"_136":137,"_138":283},[318],{"_21":131,"_34":296,"_36":297,"_128":129,"_130":277,"_101":255,"_103":255,"_23":319,"_105":300,"_140":320},{"_134":271,"_136":137,"_138":299},[321],{"_21":125,"_34":126,"_36":127,"_128":129,"_130":131,"_101":132,"_103":132,"_23":322,"_105":127,"_140":323},{"_134":135,"_136":137,"_138":139},[],{"_21":254,"_34":302,"_36":303,"_128":129,"_130":-5,"_101":304,"_103":304,"_23":325,"_105":303,"_140":326},{"_134":306,"_136":137,"_138":307},[327,336,342],{"_21":251,"_34":252,"_36":253,"_128":129,"_130":254,"_101":255,"_103":255,"_23":328,"_105":259,"_140":329},{"_134":257,"_136":137,"_138":258},[330],{"_21":261,"_34":262,"_36":263,"_128":129,"_130":251,"_101":193,"_103":193,"_23":331,"_105":266,"_140":332},{"_134":257,"_136":137,"_138":265},[333],{"_21":309,"_34":35,"_36":37,"_128":129,"_130":261,"_101":310,"_103":310,"_23":334,"_105":312,"_140":335},{"_134":137,"_136":137,"_138":288},[],{"_21":245,"_34":268,"_36":269,"_128":129,"_130":254,"_101":255,"_103":255,"_23":337,"_105":273,"_140":338},{"_134":271,"_136":137,"_138":272},[339],{"_21":244,"_34":35,"_36":37,"_128":129,"_130":245,"_101":132,"_103":132,"_23":340,"_105":249,"_140":341},{"_134":247,"_136":137,"_138":248},[],{"_21":192,"_34":291,"_36":292,"_128":129,"_130":254,"_101":255,"_103":255,"_23":343,"_105":294,"_140":344},{"_134":257,"_136":137,"_138":196},[345],{"_21":189,"_34":190,"_36":191,"_128":129,"_130":192,"_101":193,"_103":193,"_23":346,"_105":191,"_140":347},{"_134":195,"_136":137,"_138":196},[348],{"_21":285,"_34":35,"_36":37,"_128":129,"_130":189,"_101":286,"_103":286,"_23":349,"_105":289,"_140":350},{"_134":137,"_136":137,"_138":288},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários