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 10 centimeters. the actual circumference is in the interval 9.9 ≤ c ≤ 10.1 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: Recall the circumference - diameter formula

The formula for the circumference of a circle is $C = 3.14d$.

Step2: Solve the inequality for $d$ when $C$ is in the given interval

We have the inequality $9.9\leq C\leq10.1$. Substitute $C = 3.14d$ into the inequality:
$9.9\leq3.14d\leq10.1$.
First, solve the left - hand side of the inequality $9.9\leq3.14d$ for $d$. Divide both sides by $3.14$: $d\geq\frac{9.9}{3.14}\approx3.153$.
Then, solve the right - hand side of the inequality $3.14d\leq10.1$ for $d$. Divide both sides by $3.14$: $d\leq\frac{10.1}{3.14}\approx3.216$.

Answer:

$3.153\leq d\leq3.216$