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3y = 0",{"_44":192,"_82":88,"_84":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":195,"_82":91,"_84":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":198,"_82":95,"_84":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":185,"_82":201,"_84":202},"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

",[206],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":212,"_123":209},"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":213,"_154":155,"_156":214},4,12302,{"_40":216,"_42":43,"_44":217,"_78":218,"_97":230,"_98":231,"_52":232},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[219,222,225,227],{"_44":220,"_82":83,"_84":221},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":223,"_82":88,"_84":224},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":216,"_82":91,"_84":226},"

Verdadeiro, falso, verdadeiro

",{"_44":228,"_82":95,"_84":229},"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????",[256],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":257,"_123":209},{"_152":213,"_154":155,"_156":214},[259,261,268,278,285,292,294,302,308,313,319,326],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":260,"_123":209},{"_152":213,"_154":155,"_156":214},{"_44":262,"_58":59,"_60":61,"_146":147,"_148":263,"_119":150,"_121":150,"_46":264,"_123":267},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":265,"_154":155,"_156":266},2,11846,"termodinamica-3",{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":273,"_121":273,"_46":274,"_123":277},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_152":275,"_154":155,"_156":276},5,30614,"engenharia-mecatronica-1",{"_44":279,"_58":280,"_60":281,"_146":147,"_148":269,"_119":211,"_121":211,"_46":282,"_123":284},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":275,"_154":155,"_156":283},25741,"mecanica-3",{"_44":263,"_58":286,"_60":287,"_146":147,"_148":272,"_119":273,"_121":273,"_46":288,"_123":291},"Engenharia Mecânica","engenharia-mecanica",{"_152":289,"_154":155,"_156":290},11,36318,"engenharia-mecanica-2",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":293,"_123":145},{"_152":153,"_154":155,"_156":157},{"_44":295,"_58":296,"_60":297,"_146":147,"_148":-5,"_119":298,"_121":298,"_46":299,"_123":297},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_152":300,"_154":155,"_156":301},18,135489,{"_44":303,"_58":59,"_60":61,"_146":147,"_148":207,"_119":304,"_121":304,"_46":305,"_123":307},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_152":155,"_154":155,"_156":306},8597,"termodinamica-5",{"_44":210,"_58":309,"_60":310,"_146":147,"_148":272,"_119":273,"_121":273,"_46":311,"_123":312},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":275,"_154":155,"_156":214},"engenharia-de-petroleo-1",{"_44":149,"_58":314,"_60":315,"_146":147,"_148":295,"_119":273,"_121":273,"_46":316,"_123":318},"Física","fisica",{"_152":289,"_154":155,"_156":317},13777,"fisica-4",{"_44":272,"_58":320,"_60":321,"_146":147,"_148":-5,"_119":322,"_121":322,"_46":323,"_123":321},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":324,"_154":155,"_156":325},29,351586,{"_44":327,"_58":59,"_60":61,"_146":147,"_148":279,"_119":328,"_121":328,"_46":329,"_123":330},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_152":155,"_154":155,"_156":306},"termodinamica-4","tagsTree",[333,342],{"_44":295,"_58":296,"_60":297,"_146":147,"_148":-5,"_119":298,"_121":298,"_46":334,"_123":297,"_158":335},{"_152":300,"_154":155,"_156":301},[336],{"_44":149,"_58":314,"_60":315,"_146":147,"_148":295,"_119":273,"_121":273,"_46":337,"_123":318,"_158":338},{"_152":289,"_154":155,"_156":317},[339],{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":340,"_123":145,"_158":341},{"_152":153,"_154":155,"_156":157},[],{"_44":272,"_58":320,"_60":321,"_146":147,"_148":-5,"_119":322,"_121":322,"_46":343,"_123":321,"_158":344},{"_152":324,"_154":155,"_156":325},[345,354,360],{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":273,"_121":273,"_46":346,"_123":277,"_158":347},{"_152":275,"_154":155,"_156":276},[348],{"_44":279,"_58":280,"_60":281,"_146":147,"_148":269,"_119":211,"_121":211,"_46":349,"_123":284,"_158":350},{"_152":275,"_154":155,"_156":283},[351],{"_44":327,"_58":59,"_60":61,"_146":147,"_148":279,"_119":328,"_121":328,"_46":352,"_123":330,"_158":353},{"_152":155,"_154":155,"_156":306},[],{"_44":263,"_58":286,"_60":287,"_146":147,"_148":272,"_119":273,"_121":273,"_46":355,"_123":291,"_158":356},{"_152":289,"_154":155,"_156":290},[357],{"_44":262,"_58":59,"_60":61,"_146":147,"_148":263,"_119":150,"_121":150,"_46":358,"_123":267,"_158":359},{"_152":265,"_154":155,"_156":266},[],{"_44":210,"_58":309,"_60":310,"_146":147,"_148":272,"_119":273,"_121":273,"_46":361,"_123":312,"_158":362},{"_152":275,"_154":155,"_156":214},[363],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":364,"_123":209,"_158":365},{"_152":213,"_154":155,"_156":214},[366],{"_44":303,"_58":59,"_60":61,"_146":147,"_148":207,"_119":304,"_121":304,"_46":367,"_123":307,"_158":368},{"_152":155,"_154":155,"_156":306},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários