Question

Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipes

may vary by 1%. What is the range of allowable lengths of the pipes?

luat his car it averaqed 28 miles per gallon of gas. Now, the

Answer 1

`21.78\leq x\leq 22.22`

Explanation:

Let x represent the actual length of pipe.

We have been given that Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipes may vary by 1%.

To find the range of allowable lengths of the pipes, we will use tolerance calculation formula.

`|\text{Atual}-\text{Ideal}|\leq \text{Tolerance}`

The variation in the lengths of pipes is 1% of ideal length that is 22.

`22* (1)/(100)=0.22`

Upon substituting, our given values, we will get:

`|x-22|\leq 0.22`

Use absolute value rule: If
`|u|\leq a`, then
`-a\leq u\leq a`

`-0.22\leq x-22\leq 0.22`

Adding 22 on all sides:

`-0.22+22\leq x-22+22\leq 0.22+22`

`21.78\leq x\leq 22.22`

Therefore, the range of allowable lengths of the pipes is
`21.78\leq x\leq 22.22`.