Question

здравствуйте помогите пожалуйста
44,3
44,4

Answer 1

44,3

$y = 5 \sin(x) - 3 \cos(4x)$

$y' = 5 \cos(x) - 3( - \sin(4x)) \times (4x) '= \\ = 5 \cos(x) + 3 \sin(4x) \times 4 = \\ = 5 \cos(x) + 12\sin(4x)$

$y ''= - 5 \sin(x) + 48 \cos(4x)$

1)

$x_0 = \frac{\pi}{6}$

$y''( \frac{\pi}{6} ) = - 5 \sin( \frac{\pi}{6} ) + 48 \cos( \frac{4 \times \pi}{6} ) = \\ = - \frac{5}{2} + 48 \times \cos( \frac{2\pi}{3} ) = - 2.5 + 48 \times ( - \frac{1}{2} ) = \\ = - 2.5 - 24 = - 26. 5$

2)

$x_0 = - \frac{\pi}{2}$

$y''( - \frac{\pi}{2} ) = - 5 \sin( - \frac{\pi}{2} ) + 48 \cos(4 \times ( - \frac{\pi}{2} ) ) = \\ = - 5 \times ( - 1) + 48 \cos( - 2\pi) = 5 + 48 = 53$

44.4

$S(t) = 2 {t}^{3} - 5t {}^{2} + 4 \\ a(t) = S''(t) = (6 {t}^{2} - 10 t + 0)' = \\ = 12t - 10 \\ \\ a(2) = 12 \times 2 - 10 = 24 - 10 = 14$

Ответ: 14 м/с^2