Question

Suppose f varies directly as g, and f varies inversely as h. Find g when f = 10 and h = –12, if g = 56 when h = –2 and f = –7. Round your answer to the nearest hundredth, if necessary.

Answer 1

Answer:

-480

Step-by-step explanation:

If f varies directly as g, and inversely as h, then we can write the variation equation:

$f=\frac{kg}{h}$, where k is the constant of variation.

If g=56 when h=-2 and f=-7, then we substitute these values into the formula to find the value of k.

$-7=\frac{k(56)}{-2}$

$-7\times -2=56k$

$k=\frac{14}{56}=\frac{1}{4}$

The equation now becomes:

$f=\frac{g}{4h}$

if f=10 and h=-12, then;

$10=\frac{g}{-48}$

$g=-48\times 10=-480$

The correct answer is B.