Question

In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?

a. r > 4 and r ≤ 4.1
b. r > 4 or r ≤ 4.1
c. r < 4 and r ≥ 4.1
d. r < 4 or r ≥ 4.1

Answer 1

Let

r------> the radius of the gear

we know that

The value of r, must be greater than
`4` cm, but not exceed
`4.1` cm

The compound inequality that represent this situation is

`4\ cm< r \leq 4.1\ cm`

the solution is the interval------->
`(4,4.1]`

all real numbers greater than
`4\ cm` and less than or equal to
`4.1\ cm`

the solution in the attached figure

the answer is the option A

`r > 4` and
`r \leq 4.1`

Answer 2

The correct option is A. r > 4 and r ≤ 4.1

Explanation:

Given that : In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm

Now, the radius of gear is denoted by r and it must be greater than 4 cm

⇒ r > 4

Also, the radius of the gear should not exceed 4.1 cm

So, it can be equal to 4.1 but should not be greater than 4.1

⇒ r ≤ 4.1 cm

Hence, The compound inequality to represent this situation will be :

r > 4 and r ≤ 4.1

Therefore, The correct option is A. r > 4 and r ≤ 4.1