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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?

Ar > 4 and r ≤ 4.1
Br > 4 or r ≤ 4.1
Cr < 4 and r ≥ 4.1
Dr < 4 or r ≥ 4.1

Verified Answer :

calculista

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 \(r \leq 4.1\)


View image calculista

Answer:

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

Step-by-step 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

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