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Um mergulhador precisa encher seu tanque de mergulho, cuja capacidade é de 1,42 \\times 10^{22} \\text{ m}^3, a uma pressão de 140 \\text{ atm} e sob temperatura constante. O volume de ar, em m^3, necessário para essa operação, à pressão de 1 \\text{ atm}, é aproximadamente igual a:

","status","pending_classification","hasRelatedVideo","relatedVideos",[104],{"_105":106,"_124":125,"_51":140,"_159":160,"_177":178},"content",{"_43":107,"_57":108,"_109":-5,"_110":111,"_112":113,"_114":-5,"_45":115,"_118":119,"_120":119,"_121":-5,"_122":123},"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",{"_116":117},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_126":127,"_133":134,"_135":136,"_137":138,"_28":139},"provider",{"_43":128,"_129":130,"_131":132},"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",[141],{"_43":142,"_57":143,"_59":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":150,"_122":144,"_157":158},"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",{"_151":152,"_153":154,"_155":156},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":113,"_13":108,"_109":-5,"_161":162,"_163":164,"_28":-5,"_165":-5,"_126":164,"_166":167,"_137":-5,"_168":-5,"_169":-5,"_170":-5,"_171":-5,"_45":172,"_173":154,"_174":-5,"_99":175,"_118":176,"_120":176},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_116":117},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_43":142,"_57":143,"_59":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":179,"_122":144,"_157":180},{"_151":152,"_153":154,"_155":156},[],"similarQuestions",[183,214,234],{"_40":184,"_42":41,"_43":185,"_77":186,"_96":202,"_97":203,"_51":204},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[187,190,193,196,199],{"_43":188,"_81":82,"_83":189},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":191,"_81":87,"_83":192},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":194,"_81":90,"_83":195},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":197,"_81":94,"_83":198},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":184,"_81":200,"_83":201},"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

",[205],{"_43":206,"_57":207,"_59":208,"_145":146,"_147":209,"_118":210,"_120":210,"_45":211,"_122":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",{"_151":212,"_153":154,"_155":213},4,12302,{"_40":215,"_42":41,"_43":216,"_77":217,"_96":229,"_97":230,"_51":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_43":219,"_81":82,"_83":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":222,"_81":87,"_83":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":215,"_81":90,"_83":225},"

Verdadeiro, falso, verdadeiro

",{"_43":227,"_81":94,"_83":228},"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????",[255],{"_43":206,"_57":207,"_59":208,"_145":146,"_147":209,"_118":210,"_120":210,"_45":256,"_122":208},{"_151":212,"_153":154,"_155":213},[258,260,267,277,284,291,293,301,307,312,318,325],{"_43":206,"_57":207,"_59":208,"_145":146,"_147":209,"_118":210,"_120":210,"_45":259,"_122":208},{"_151":212,"_153":154,"_155":213},{"_43":261,"_57":58,"_59":60,"_145":146,"_147":262,"_118":149,"_120":149,"_45":263,"_122":266},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_151":264,"_153":154,"_155":265},2,11846,"termodinamica-3",{"_43":268,"_57":269,"_59":270,"_145":146,"_147":271,"_118":272,"_120":272,"_45":273,"_122":276},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_151":274,"_153":154,"_155":275},5,30614,"engenharia-mecatronica-1",{"_43":278,"_57":279,"_59":280,"_145":146,"_147":268,"_118":210,"_120":210,"_45":281,"_122":283},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_151":274,"_153":154,"_155":282},25741,"mecanica-3",{"_43":262,"_57":285,"_59":286,"_145":146,"_147":271,"_118":272,"_120":272,"_45":287,"_122":290},"Engenharia Mecânica","engenharia-mecanica",{"_151":288,"_153":154,"_155":289},11,36318,"engenharia-mecanica-2",{"_43":142,"_57":143,"_59":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":292,"_122":144},{"_151":152,"_153":154,"_155":156},{"_43":294,"_57":295,"_59":296,"_145":146,"_147":-5,"_118":297,"_120":297,"_45":298,"_122":296},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_151":299,"_153":154,"_155":300},18,135489,{"_43":302,"_57":58,"_59":60,"_145":146,"_147":206,"_118":303,"_120":303,"_45":304,"_122":306},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_151":154,"_153":154,"_155":305},8597,"termodinamica-5",{"_43":209,"_57":308,"_59":309,"_145":146,"_147":271,"_118":272,"_120":272,"_45":310,"_122":311},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":274,"_153":154,"_155":213},"engenharia-de-petroleo-1",{"_43":148,"_57":313,"_59":314,"_145":146,"_147":294,"_118":272,"_120":272,"_45":315,"_122":317},"Física","fisica",{"_151":288,"_153":154,"_155":316},13777,"fisica-4",{"_43":271,"_57":319,"_59":320,"_145":146,"_147":-5,"_118":321,"_120":321,"_45":322,"_122":320},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":323,"_153":154,"_155":324},29,351586,{"_43":326,"_57":58,"_59":60,"_145":146,"_147":278,"_118":327,"_120":327,"_45":328,"_122":329},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_151":154,"_153":154,"_155":305},"termodinamica-4","tagsTree",[332,341],{"_43":294,"_57":295,"_59":296,"_145":146,"_147":-5,"_118":297,"_120":297,"_45":333,"_122":296,"_157":334},{"_151":299,"_153":154,"_155":300},[335],{"_43":148,"_57":313,"_59":314,"_145":146,"_147":294,"_118":272,"_120":272,"_45":336,"_122":317,"_157":337},{"_151":288,"_153":154,"_155":316},[338],{"_43":142,"_57":143,"_59":144,"_145":146,"_147":148,"_118":149,"_120":149,"_45":339,"_122":144,"_157":340},{"_151":152,"_153":154,"_155":156},[],{"_43":271,"_57":319,"_59":320,"_145":146,"_147":-5,"_118":321,"_120":321,"_45":342,"_122":320,"_157":343},{"_151":323,"_153":154,"_155":324},[344,353,359],{"_43":268,"_57":269,"_59":270,"_145":146,"_147":271,"_118":272,"_120":272,"_45":345,"_122":276,"_157":346},{"_151":274,"_153":154,"_155":275},[347],{"_43":278,"_57":279,"_59":280,"_145":146,"_147":268,"_118":210,"_120":210,"_45":348,"_122":283,"_157":349},{"_151":274,"_153":154,"_155":282},[350],{"_43":326,"_57":58,"_59":60,"_145":146,"_147":278,"_118":327,"_120":327,"_45":351,"_122":329,"_157":352},{"_151":154,"_153":154,"_155":305},[],{"_43":262,"_57":285,"_59":286,"_145":146,"_147":271,"_118":272,"_120":272,"_45":354,"_122":290,"_157":355},{"_151":288,"_153":154,"_155":289},[356],{"_43":261,"_57":58,"_59":60,"_145":146,"_147":262,"_118":149,"_120":149,"_45":357,"_122":266,"_157":358},{"_151":264,"_153":154,"_155":265},[],{"_43":209,"_57":308,"_59":309,"_145":146,"_147":271,"_118":272,"_120":272,"_45":360,"_122":311,"_157":361},{"_151":274,"_153":154,"_155":213},[362],{"_43":206,"_57":207,"_59":208,"_145":146,"_147":209,"_118":210,"_120":210,"_45":363,"_122":208,"_157":364},{"_151":212,"_153":154,"_155":213},[365],{"_43":302,"_57":58,"_59":60,"_145":146,"_147":206,"_118":303,"_120":303,"_45":366,"_122":306,"_157":367},{"_151":154,"_153":154,"_155":305},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários