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 11.9 ≤ 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: Start with the circumference - diameter formula

We know that $C = 3.14d$.

Step2: Substitute the lower - bound of the circumference

When $C = 11.9$, we solve for $d$: $d=\frac{C}{3.14}=\frac{11.9}{3.14}\approx3.79$.

Step3: Substitute the upper - bound of the circumference

When $C = 12.2$, we solve for $d$: $d=\frac{C}{3.14}=\frac{12.2}{3.14}\approx3.89$.

Answer:

$3.79\leq d\leq3.89$