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 12 centimeters. the company has decided that a washer whose actual circumference is in the interval 11.8 ≤ c ≤ 12.2 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: Substitute the formula into the inequality

Given $C = 3.14d$ and $11.8\leq C\leq12.2$, we substitute $C$ to get $11.8\leq3.14d\leq12.2$.

Step2: Solve the compound - inequality for $d$

Divide each part of the inequality by 3.14. So, $\frac{11.8}{3.14}\leq\frac{3.14d}{3.14}\leq\frac{12.2}{3.14}$.
Calculating, $\frac{11.8}{3.14}\approx3.758$ and $\frac{12.2}{3.14}\approx3.885$.

Answer:

$3.758\leq d\leq3.885$