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 9 centimeters. the company has decided that a washer whose actual circumference is in the interval 8.8 ≤ c ≤ 9.2 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: Start with the circumference - diameter formula

Given $C = 3.14d$. We know that $8.8\leq C\leq9.2$.

Step2: Substitute $C$ in the inequality

Substitute $C = 3.14d$ into the inequality $8.8\leq C\leq9.2$, we get $8.8\leq3.14d\leq9.2$.

Step3: Solve the compound - inequality for $d$

Divide each part of the compound - inequality by $3.14$. So, $\frac{8.8}{3.14}\leq d\leq\frac{9.2}{3.14}$.

Step4: Calculate the values

$\frac{8.8}{3.14}\approx2.8025$ and $\frac{9.2}{3.14}\approx2.930$.

Answer:

$2.803\leq d\leq2.930$