Chapter 4.2, Problem 44HP

a.

To determine

To write: An equation involving an absolute value that represents the number of people that can hear natural voices at Red Rocks Amphitheater.

Answer to Problem 44HP

The equation is $\left|x-20000\right|=1000$ .

Explanation of Solution

Given Information: Maximum number of people is $20000$ with a variation of $1000$ .

Calculation:

Due to the intricacies involved in the acoustic qualities, maximum number of people that can hear natural voices clearly is $20000$ , plus or minus $1000$ . This implies that the absolute value of difference of number of people and $20000$ will always be $1000$ . Mathematically, $\left|x-20000\right|=1000$ .

Thus, the equation is $\left|x-20000\right|=1000$ .

b.

To determine

To find: The maximum and minimum number of people that can hear natural voices clearly in the amphitheater.

Answer to Problem 44HP

Maximum number is $21000$ and minimum number is $19000$ .

Explanation of Solution

Given Information: Maximum number of people is $20000$ with a variation of $1000$ .

Calculation:

Due to the intricacies involved in the acoustic qualities, maximum number of people that can hear natural voices clearly is $20000$ , plus or minus $1000$ . Mathematically, maximum number of people can be $20000\pm 1000$ .

Maximum number of people: $20000+1000=21000$

Minimum number of people: $20000-1000=19000$

Thus, maximum number is $21000$ and minimum number is $19000$ .

c.

To determine

To find: The range of people in part $b$ .

Answer to Problem 44HP

The range is $2000$ .

Explanation of Solution

Given Information: Maximum number is $21000$ and minimum number is $19000$ .

Calculation:

  $\begin{array}{l}Range=MaximumNo.-MinimumNo.\\ =21000-19000\\ =2000\end{array}$

Thus, the range is $2000$ .