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 7 centimeters. the actual circumference is in the interval 6.8 ≤ c ≤ 7.2 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 $C = 3.14d$. Given $6.8\leq C\leq7.2$.

Step2: Substitute $C$ in the inequality

Substitute $C$ in the inequality: $6.8\leq3.14d\leq7.2$.

Step3: Solve the compound - inequality for $d$

Divide each part of the inequality by $3.14$. For the left - hand side: $\frac{6.8}{3.14}\approx2.166$. For the right - hand side: $\frac{7.2}{3.14}\approx2.293$. So, $2.166\leq d\leq2.293$.

Answer:

$2.166\leq d\leq2.293$