Chapter 3.7, Problem 75PPE

To determine

To find: The range for the acceptable diameters for the piston.

Answer to Problem 75PPE

Acceptable diameter of the piston is between $89.992\text{ and }90.008$ .

Explanation of Solution

Given:

The ideal diameter of piston for one type of car engine is $90\text{mm}$ and the actual diameter vary from ideal by at most $0.008\text{mm}$ .

Concept used:

The difference is that a solution to the inequality is not the drawn line but area of the coordinate plane that satisfy the inequality.

The common area is the solution of inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

The ideal diameter of piston for one type of car engine is $90\text{mm}$ and the actual diameter vary from ideal by at most $0.008\text{mm}$ .

Let $D$ denotes the acceptable diameter of the piston.

This means the value of $D$ is $0.008$ from $90$ on a number line.

The inequality that models this situation is:

  $\left|D-90\right|\le 0.008$ .

Solving further, this inequality can be written as:

  $\begin{array}{l}-0.008\le D-90\le \mathrm{0.008.}\\ \Rightarrow -0.008+90\le D\le 0.008+90.\\ \Rightarrow 89.992\le \mathrm{90.008.}\end{array}$

Hence, the acceptable diameter of the piston is between $89.992\text{ and }90.008$ .