Chapter 3.3, Problem 12CFU

a.

To determine

To write: an absolute value inequality to represent the range of diameters of compact disks.

Answer to Problem 12CFU

  $\left|x-12\right|\le 0.005$

Explanation of Solution

Given information:

Diameter of compact disk = 12 cm

Maximum diameter of the disks = $5\times {10}^{-3}\text{cm}$

Calculation:

Let x be the diameters that are allowable and $\left(x-12\right)$ be the variance which would show the left over. The $\left|x-12\right|$ means it could be either larger or smaller. Thus an absolute value inequality to represent the range of diameters of compact disks is $\left|x-12\right|\le 0.005$ .

b.

To determine

To find: the largest and smallest diameters that are allowable.

Answer to Problem 12CFU

  $11.995\text{ cm to 12}\text{.005 cm}$

Explanation of Solution

Given information:

Diameter of compact disk = 12 cm

Maximum diameter of the disks = $5\times {10}^{-3}\text{cm}$

Calculation:

The inequality evaluated is as follows:

  $\left|x-12\right|\le 0.005$

Solve x to get the allowable diameter of compact disks.

  $\begin{array}{l}\left|x-12\right|\le 0.005\\ x-12\le 0.005\left[\text{If }x\ge 0\right]\\ x\le 0.005+12\\ x\le 12.005\end{array}$

  $\begin{array}{c}-\left(x-12\right)\ge 0.005\left[\text{If }x<0\right]\\ -x+12\ge 0.005\\ -x\ge 0.005-12\\ -x\ge -11.995\\ x\ge \frac{-11.995}{-1}\\ x\ge 11.995\end{array}$

Since $11.9995\le x\le 12.005$ , so the allowable diameter is from 11.995 cm to 12.005cm.