Chapter 9.5, Problem 18PPS

To determine

To find the value of $f_2$ .

Answer to Problem 18PPS

the value of $f_2$ is $-\frac{56}{3}$

Explanation of Solution

Given information:

f varies inversely as g

the value of $f_1=4$ when $g_1=28$

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 $f_1=4$ , $g_1=28$ and $g_2=-6$ in above equation

  $\begin{array}{l}\frac{4}{-6}=\frac{f_2}{28}\\ (4)(28)=f_2(-6)\left[\text{cross multiply}\right]\\ 112=-6f_2\left[\text{simplify}\right]\\ f_2=-\frac{112}{6}\\ f_2\text{=}-\frac{56}{3}\left[\text{divide numerator and denominator by 2}\right]\end{array}$

Hence,

The value of $f_2$ is $-\frac{56}{3}$