Chapter 8.5, Problem 19PPS

To determine

To find the value of $f_2$ .

Answer to Problem 19PPS

the value of $f_2$ is $38$

Explanation of Solution

Given information:

f varies inversely as g

the value of $f_1=-12$ when $g_1=19$

Calculation:

The value of $g_2$ can be obtained as

Use a proportion that relates the values

  $\frac{f_1}{g_2}=\frac{f_2}{g_1}$ [since, inverse variation]

Put the values of $f_1=-12$ , $g_1=19$ and $g_2=-6$ in above equation

  $\begin{array}{l}\frac{-12}{-6}=\frac{f_2}{19}\\ (-12)(19)=f_2(-6)\left[\text{cross multiply}\right]\\ -228=-6f_2\left[\text{simplify}\right]\\ f_2\text{=38 }\left[\text{divide each side by -6}\right]\end{array}$

Hence,

The value of $f_2$ is $38$