Chapter 12.8, Problem 1ST

To determine

To calculate: A station $40$ KW station can broadcast a distance of $64$ Km. how far could the station broadcast if it produced $70$ KW.

Answer to Problem 1ST

The distance is: $196$ Km.

Explanation of Solution

Given information:

The distance that the signal from a radio station varies directly as the square of the number of kilowatts.

A station $40$ KW station can broadcast a distance of $64$ Km. how far could the station broadcast if it produced $70$ KW.

Formula used:

For varies jointly:

  $d=K{\left(kw\right)}^2$

Calculation:

Consider that, A station $40$ KW station can broadcast a distance of $64$ Km. how far could the station broadcast if it produced $70$ KW.

Recall that for varies jointly:

  $d=K{\left(kw\right)}^2$

The values are:

  $d=64,kw=40$

Therefore, the value of $k$ is,

  $\begin{array}{c}d=K{\left(kw\right)}^2\\ 64=K\times {40}^2\\ K=\frac{64}{40\times 40}\\ K=0.04\end{array}$

Now to find the value of $r$ ,

  $d_2=K{\left(k{w}_2\right)}^2$

The values are:

  $K=0.04,kw=70$

Hence, when:

  $\begin{array}{c}{d}_2=K{\left(k{w}_2\right)}^2\\ d_2=0.04\times {70}^2\\ d_2=0.04\times 70\times 70\\ d_2=196\end{array}$

Thus, the distance is: $196$ Km.