Question

por favor me pueden ayudar, la solución y la respuesta porfavor

Answer 1

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