Chapter 3.8, Problem 40PPS

a.

To determine

In how many minutes will the car reach the sensor

Answer to Problem 40PPS

The car will reach the sensor in 5 minutes.

Explanation of Solution

Given:

The function $f(x)=|4.5-0.9x|$ models the car’s distance in miles from a sensor, where x represents the number of minutes since timing began.

Calculation:

The car will reach the sensor when $f(x)=0$

  $\begin{array}{l}=>|4.5-0.9x|=0\\ =>4.5-0.9x=0[\because |x|=0=>x=0]\\ =>0.9x=4.5\\ =>x=\frac{4.5}{0.9}\\ =>x=5\end{array}$

Therefore, the car will reach the sensor in 5 minutes.

b.

To determine

Will the sensor indicate that the car is speeding?

Answer to Problem 40PPS

Yes the sensor will not indicate

Explanation of Solution

Given:

The speed limit on the highway is 55mi/hr.

Calculation:

Putting $x=0inf(x)=|4.5-0.9x|$

  $=>f(0)=4.5$

Therefore, initially when time is 0, (i.e., $x=0$ ) the car is 4.5 miles away from the sensor.

In the previous question we have found that the car reaches the sensor in 5 minutes, i.e., $\frac{1}{12}hrs$ .

Therefore, the car must have a speed of $\frac{4.5}{\left(\frac{1}{12}\right)}=54mi/hr[\because Speed=\frac{distance}{time}]$

Hence, if the car reaches the sensor before 5mins, it must have been speeding.