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A partir do sistema de caldeira + turbina industrial, que consome um material combustível de 1.000 \text{ KJ/ton} e foi alimentada com 15 \text{ toneladas} de material combustível, e 7000 \text{ KJ} de energia térmica perderam-se na atmosfera, determine o rendimento dessa caldeira.

","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_51":144,"_163":164,"_181":145},"content",{"_44":111,"_57":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_46":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_130":131,"_137":138,"_139":140,"_141":142,"_28":143},"provider",{"_44":132,"_133":134,"_135":136},"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",[145],{"_44":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_46":154,"_126":148,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":117,"_13":112,"_113":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_130":168,"_170":171,"_141":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_46":176,"_177":158,"_178":-5,"_103":179,"_122":180,"_124":180},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[184,214,232],{"_40":185,"_42":43,"_44":186,"_77":187,"_100":202,"_101":203,"_51":204},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[188,191,194,197,200],{"_44":189,"_81":82,"_83":190},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":192,"_81":87,"_83":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":195,"_81":91,"_83":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":198,"_81":95,"_83":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":185,"_81":98,"_83":201},"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

",[205],{"_44":206,"_57":207,"_59":208,"_149":150,"_151":209,"_122":210,"_124":210,"_46":211,"_126":208},"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",{"_155":212,"_157":158,"_159":213},4,12302,{"_40":215,"_42":43,"_44":216,"_77":217,"_100":229,"_101":230,"_51":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_44":219,"_81":82,"_83":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":222,"_81":87,"_83":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":215,"_81":91,"_83":225},"

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?

",[205],{"_40":233,"_42":43,"_44":234,"_77":235,"_100":250,"_101":251,"_51":252},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,244,247],{"_44":237,"_81":82,"_83":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":240,"_81":87,"_83":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":233,"_81":91,"_83":243},"Indeterminado",{"_44":245,"_81":95,"_83":246},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":248,"_81":98,"_83":249},"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????",[205],[205,254,260,270,277,284,285,293,299,304,310,317],{"_44":255,"_57":58,"_59":60,"_149":150,"_151":256,"_122":153,"_124":153,"_46":257,"_126":259},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":64,"_157":158,"_159":258},11846,"termodinamica-3",{"_44":261,"_57":262,"_59":263,"_149":150,"_151":264,"_122":265,"_124":265,"_46":266,"_126":269},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":267,"_157":158,"_159":268},5,30614,"engenharia-mecatronica-1",{"_44":271,"_57":272,"_59":273,"_149":150,"_151":261,"_122":210,"_124":210,"_46":274,"_126":276},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":267,"_157":158,"_159":275},25741,"mecanica-3",{"_44":256,"_57":278,"_59":279,"_149":150,"_151":264,"_122":265,"_124":265,"_46":280,"_126":283},"Engenharia Mecânica","engenharia-mecanica",{"_155":281,"_157":158,"_159":282},11,36318,"engenharia-mecanica-2",{"_44":146,"_57":147,"_59":148,"_149":150,"_151":152,"_122":153,"_124":153,"_46":154,"_126":148},{"_44":286,"_57":287,"_59":288,"_149":150,"_151":-5,"_122":289,"_124":289,"_46":290,"_126":288},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":291,"_157":158,"_159":292},18,135489,{"_44":294,"_57":58,"_59":60,"_149":150,"_151":206,"_122":295,"_124":295,"_46":296,"_126":298},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":297},8597,"termodinamica-5",{"_44":209,"_57":300,"_59":301,"_149":150,"_151":264,"_122":265,"_124":265,"_46":302,"_126":303},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":267,"_157":158,"_159":213},"engenharia-de-petroleo-1",{"_44":152,"_57":305,"_59":306,"_149":150,"_151":286,"_122":265,"_124":265,"_46":307,"_126":309},"Física","fisica",{"_155":281,"_157":158,"_159":308},13777,"fisica-4",{"_44":264,"_57":311,"_59":312,"_149":150,"_151":-5,"_122":313,"_124":313,"_46":314,"_126":312},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":315,"_157":158,"_159":316},29,351586,{"_44":318,"_57":58,"_59":60,"_149":150,"_151":271,"_122":319,"_124":319,"_46":320,"_126":321},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":297},"termodinamica-4","tagsTree",[324,328],{"_44":286,"_57":287,"_59":288,"_149":150,"_151":-5,"_122":289,"_124":289,"_46":290,"_126":288,"_161":325},[326],{"_44":152,"_57":305,"_59":306,"_149":150,"_151":286,"_122":265,"_124":265,"_46":307,"_126":309,"_161":327},[145],{"_44":264,"_57":311,"_59":312,"_149":150,"_151":-5,"_122":313,"_124":313,"_46":314,"_126":312,"_161":329},[330,336,340],{"_44":261,"_57":262,"_59":263,"_149":150,"_151":264,"_122":265,"_124":265,"_46":266,"_126":269,"_161":331},[332],{"_44":271,"_57":272,"_59":273,"_149":150,"_151":261,"_122":210,"_124":210,"_46":274,"_126":276,"_161":333},[334],{"_44":318,"_57":58,"_59":60,"_149":150,"_151":271,"_122":319,"_124":319,"_46":320,"_126":321,"_161":335},[],{"_44":256,"_57":278,"_59":279,"_149":150,"_151":264,"_122":265,"_124":265,"_46":280,"_126":283,"_161":337},[338],{"_44":255,"_57":58,"_59":60,"_149":150,"_151":256,"_122":153,"_124":153,"_46":257,"_126":259,"_161":339},[],{"_44":209,"_57":300,"_59":301,"_149":150,"_151":264,"_122":265,"_124":265,"_46":302,"_126":303,"_161":341},[342],{"_44":206,"_57":207,"_59":208,"_149":150,"_151":209,"_122":210,"_124":210,"_46":211,"_126":208,"_161":343},[344],{"_44":294,"_57":58,"_59":60,"_149":150,"_151":206,"_122":295,"_124":295,"_46":296,"_126":298,"_161":345},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários