# How to solve this problem?

Oct 27, 2017

2,439 kw (rounded)

#### Explanation:

"varies directly as the cube of the wind speed S" means that
$P = c {S}^{3}$, where c is some constant you don't know, yet.

But you can derive it, since you are told that when S = 27, P = 750

$750 = c \left({27}^{3}\right) = c \left(19 , 683\right)$
...therefore $c = \frac{750}{19683}$ = .0381 (rounded)
...so then you can plug in 40:

$P = .0381 \left({40}^{3}\right) = .0381 \left(64000\right) = 2 , 439 k w$ (rounded)

GOOD LUCK