Chapter A.1, Problem 145AYU

To determine

To find:

a. Is a ball bearing of radius $x=2.999$ acceptable?

Answer to Problem 145AYU

a. Yes.

Explanation of Solution

Given:

The Fire Ball Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within $0.01$ cm of this stated radius are acceptable. If $x$ is the radius of a ball bearing, a formula describing this situation is $\left|x-3\right|\le 0.01$.

Calculation:

$\left|x-3\right|\le 0.01$

a. $\left|2.999-3\right|\le 0.01$

$\left|-0.001\right|\le 0.01$

$0.001\le 0.01$

Yes, ball bearing of radius $x=2.999$ acceptable.

To determine

To find:

b. Is a ball bearing of radius $x=2.89$ acceptable?

Answer to Problem 145AYU

b. No.

Explanation of Solution

Given:

The Fire Ball Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within $0.01$ cm of this stated radius are acceptable. If $x$ is the radius of a ball bearing, a formula describing this situation is $\left|x-3\right|\le 0.01$.

Calculation:

$\left|x-3\right|\le 0.01$

b. $\left|2.89-3\right|\le 0.01$

$\left|0.11\right|\le 0.01$

$0.11\nleqq 0.01$

$0.11>0.01$

No, ball bearing of radius $x=2.89$ is not acceptable.