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 8 centimeters. the company has decided that a washer whose actual circumference is in the interval 7.9 ≤ c ≤ 8.1 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.)

Explanation:

Step1: Substitute \(C = 3.14d\) into the compound inequality

We have \(7.9\leq C\leq8.1\). Substituting \(C = 3.14d\) gives \(7.9\leq3.14d\leq8.1\).

Step2: Solve the compound inequality for \(d\)

Divide each part of the inequality by \(3.14\).
For the left - hand side: \(\frac{7.9}{3.14}\approx2.516\)
For the right - hand side: \(\frac{8.1}{3.14}\approx2.580\)

So the compound inequality for \(d\) is \(2.516\leq d\leq2.580\)

Answer:

\(2.516\leq d\leq2.580\)