Question

The formula Upper C equals 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 99 centimeters. The company has decided that a washer whose actual circumference is in the interval 8.88≤C≤9.1 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.

The corresponding interval for diameters of the washers is
_________
​(Type an inequality or a compound inequality using d as the variable. Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

The corresponding interval for diameters of washers with an acceptable circumference interval of 8.88 to 9.1 centimeters is 2.830 to 2.898 centimeters when using the formula C = πd with π approximated as 3.14.

Step-by-step explanation:

The formula C = πd is used to approximate the circumference of a circle given its diameter (d). To find the acceptable range of diameters for the washers based on the acceptable circumference, we use the boundaries of the interval 8.88 ≤ C ≤ 9.1 centimeters and substitute them into the formula (where π is approximately 3.14).

• For the lower bound of the circumference, 8.88 = 3.14d, dividing both sides by 3.14 gives d ≤ 2.830 centimeters (rounded to three decimal places).
• For the upper bound of the circumference, 9.1 = 3.14d, dividing both sides by 3.14 gives d ≤ 2.898 centimeters (rounded to three decimal places).

Therefore, the corresponding interval for diameters of these washers is 2.830 ≤ d ≤ 2.898 centimeters.