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 ≤ 12.1 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: Start with the circumference - diameter formula

Given $C = 3.14d$. We want to find the interval for $d$ when $11.8\leq C\leq12.1$.

Step2: Solve the left - hand side of the inequality for $d$

Substitute $C = 11.8$ into $C = 3.14d$. Then $d=\frac{C}{3.14}$, so $d_1=\frac{11.8}{3.14}\approx3.758$.

Step3: Solve the right - hand side of the inequality for $d$

Substitute $C = 12.1$ into $C = 3.14d$. Then $d=\frac{C}{3.14}$, so $d_2=\frac{12.1}{3.14}\approx3.854$.

Answer:

$3.758\leq d\leq3.854$