Chapter 11.3, Problem 17PPS

To determine

To Find: The ratio, simplify it and state the excluded values of the variable.

Answer to Problem 17PPS

  $\frac{2}{5t}$ , $t\ne 0$

Explanation of Solution

Given:Ratio= $\frac{\text{circumference}}{\text{area}}$

  

Given: $\frac{\text{circumference}}{\text{area}}$

Radius of the circle= $5t$

Then

Circumference= $2\pi r=2\pi (5t)$

Area= $\pi r^2=\pi {(5t)}^2=25\pi t^2$

Then

  $\frac{\text{circumference}}{\text{area}}=\frac{10\pi t}{25\pi t^2}=\frac{2}{5t}$

The denominator cannot be zero thus

  $\begin{array}{l}5t=0\\ t=0\end{array}$

Thus

The value of $t$ cannot be $0$

i.e.

  $t\ne 0$