Question

The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 4 centimeters. The company has decided that a washer whose actual circumference is in the interval 3.9≤C≤4.2 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.

Answer 1

Answer: 1.2 ≤ d ≤ 1.3

Work Shown:

3.9 ≤ C ≤ 4.2

3.9 ≤ 3.14d ≤ 4.2

3.9/3.14 ≤ 3.14d/3.14 ≤ 4.2/3.14

1.242038 ≤ d ≤ 1.337580

1.2 ≤ d ≤ 1.3

Round the decimal values however your teacher instructs. I rounded to one decimal place because 3.9 and 4.2 have the same level of precision.

Therefore, the diameters are roughly between 1.2 cm and 1.3 cm