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3y = 0",{"_44":205,"_82":87,"_84":206},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":208,"_82":91,"_84":209},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":211,"_82":95,"_84":212},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":198,"_82":214,"_84":215},"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

",[219],{"_44":220,"_58":221,"_60":222,"_146":147,"_148":223,"_119":224,"_121":224,"_46":225,"_123":222},"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":226,"_153":154,"_155":227},4,12302,{"_40":229,"_42":43,"_44":230,"_78":231,"_97":243,"_98":244,"_52":245},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[232,235,238,240],{"_44":233,"_82":83,"_84":234},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":236,"_82":87,"_84":237},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":229,"_82":91,"_84":239},"

Verdadeiro, falso, verdadeiro

",{"_44":241,"_82":95,"_84":242},"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????",[219],[219,268,277,283,287,288,289,297,302,310,311,316,322],{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":163,"_121":163,"_46":273,"_123":276},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":274,"_153":154,"_155":275},5,30614,"engenharia-mecatronica-1",{"_44":278,"_58":59,"_60":61,"_146":147,"_148":279,"_119":280,"_121":280,"_46":281,"_123":282},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-6",{"_44":279,"_58":161,"_60":162,"_146":147,"_148":269,"_119":224,"_121":224,"_46":284,"_123":286},{"_151":274,"_153":154,"_155":285},25741,"mecanica-3",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_46":150,"_123":145},{"_44":170,"_58":59,"_60":61,"_146":147,"_148":160,"_119":171,"_121":171,"_46":172,"_123":174},{"_44":290,"_58":291,"_60":292,"_146":147,"_148":272,"_119":163,"_121":163,"_46":293,"_123":296},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_151":294,"_153":154,"_155":295},21,45865,"engenharia-civil-3",{"_44":223,"_58":298,"_60":299,"_146":147,"_148":272,"_119":163,"_121":163,"_46":300,"_123":301},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":274,"_153":154,"_155":227},"engenharia-de-petroleo-1",{"_44":303,"_58":304,"_60":305,"_146":147,"_148":290,"_119":306,"_121":306,"_46":307,"_123":309},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_151":274,"_153":154,"_155":308},8852,"estruturas-1",{"_44":160,"_58":161,"_60":162,"_146":147,"_148":143,"_119":163,"_121":163,"_46":164,"_123":167},{"_44":312,"_58":59,"_60":61,"_146":147,"_148":220,"_119":313,"_121":313,"_46":314,"_123":315},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-7",{"_44":317,"_58":318,"_60":61,"_146":147,"_148":303,"_119":319,"_121":319,"_46":320,"_123":321},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_151":154,"_153":154,"_155":173},"resistencia-dos-materiais-5",{"_44":272,"_58":323,"_60":324,"_146":147,"_148":-5,"_119":325,"_121":325,"_46":326,"_123":324},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":327,"_153":154,"_155":328},29,351586,"tagsTree",[142,331],{"_44":272,"_58":323,"_60":324,"_146":147,"_148":-5,"_119":325,"_121":325,"_46":326,"_123":324,"_157":332},[333,339,345],{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":163,"_121":163,"_46":273,"_123":276,"_157":334},[335],{"_44":279,"_58":161,"_60":162,"_146":147,"_148":269,"_119":224,"_121":224,"_46":284,"_123":286,"_157":336},[337],{"_44":278,"_58":59,"_60":61,"_146":147,"_148":279,"_119":280,"_121":280,"_46":281,"_123":282,"_157":338},[],{"_44":290,"_58":291,"_60":292,"_146":147,"_148":272,"_119":163,"_121":163,"_46":293,"_123":296,"_157":340},[341],{"_44":303,"_58":304,"_60":305,"_146":147,"_148":290,"_119":306,"_121":306,"_46":307,"_123":309,"_157":342},[343],{"_44":317,"_58":318,"_60":61,"_146":147,"_148":303,"_119":319,"_121":319,"_46":320,"_123":321,"_157":344},[],{"_44":223,"_58":298,"_60":299,"_146":147,"_148":272,"_119":163,"_121":163,"_46":300,"_123":301,"_157":346},[347],{"_44":220,"_58":221,"_60":222,"_146":147,"_148":223,"_119":224,"_121":224,"_46":225,"_123":222,"_157":348},[349],{"_44":312,"_58":59,"_60":61,"_146":147,"_148":220,"_119":313,"_121":313,"_46":314,"_123":315,"_157":350},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários