Chapter 11.4, Problem 54PPS

To determine

Find the number of revolutions the tire completes before it stops spinning?

Answer to Problem 54PPS

1000 revolutions does the tire complete before it stops spinning

Explanation of Solution

Given:

During a maintenance inspection, a tire is removed from a car and spun on a diagnostic machine. When the machine is turned off, the spinning tire completes 20 revolutions the first second and 98% of the revolutions each additional second. How many revolutions does the tire complete before it stops spinning?

Concept Used:

This is a geometric series. $a_1=20\text{and}r=98\%=0.98$

The total number of revolutions done by the tire before it stops spinning is the sum of the series. Because $\left|r\right|=0.98<1$ , we use the formula: $\text{S}=\frac{a_1}{1-r}$

Calculation:

This is a geometric series. $a_1=20\text{and}r=98\%=0.98$

The total number of revolutions done by the tire before it stops spinning is the sum of the series. Because $\left|r\right|=0.98<1$ , we use the formula: $\text{S}=\frac{a_1}{1-r}$

  $\begin{array}{l}{a}_1=20;r=0.98;\text{find}\text{S}\\ \text{S}=\frac{a_1}{1-r}=\frac{20}{1-0.98}=\frac{20}{0.02}=1000\end{array}$

1000 revolutions does the tire complete before it stops spinning

Thus, 1000 revolutions does the tire complete before it stops spinning