Nesesito ayuda x favor
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Respuestas a la pregunta
Respuesta:
a) t₁ = 20 s, t₂ = 4 s
b) t = 24.01 s
Explicación paso a paso:
L = - 16t² + 384t + 4
a) L = 1284
1284 = - 16t² + 384t + 4
0 = - 16t² + 384t + 4 - 1284
0 = - 16t² + 384t - 1280
0 = - 16(t² - 24t + 80)
0 = t² - 24t + 80
t² - 24t + 80 = 0
t - 20 -------> - 20t
t - 4 -------> - 4t
- 24t
(t - 20)(t - 4) = 0
t - 20 = 0
t₁ = 20 s
t - 4 = 0
t₂ = 4 s
b) L = 0
0 = - 16t² + 384t + 4
0 = - 4(4t² - 96t - 1)
0 = 4t² - 96t - 1
4t² - 96t - 1 = 0
t₁ = [-(- 96) + √((- 96)² - 4(4)(- 1))] / (2(4))
t₁ = [96 + √(9216 + 16)] / 8
t₁ = [96 + √9232] / 8
t₁ = [96 + 96.0833] / 8
t₁ = [96 + 96.08] / 8
t₁ = 192.08 / 8
t₁ = 24.01 s, si
t₂ = [-(- 96) - √((- 96)² - 4(4)(- 1))] / (2(4))
t₂ = [96 - √(9216 + 16)] / 8
t₂ = [96 - √9232] / 8
t₂ = [96 - 96.0833] / 8
t₂ = [96 - 96.08] / 8
t₂ = - 0.08 / 8
t₂ = - 0.01 s, no