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 4 centimeters. the company has decided that a washer whose actual circumference is in the interval 3.9 ≤ c ≤ 4.1 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: Isolate the diameter in the circumference formula

Given $C = 3.14d$, we can solve for $d$ by dividing both sides of the equation by $3.14$, so $d=\frac{C}{3.14}$.

Step2: Substitute the lower - bound of the circumference

When $C = 3.9$, $d_1=\frac{3.9}{3.14}\approx1.242$.

Step3: Substitute the upper - bound of the circumference

When $C = 4.1$, $d_2=\frac{4.1}{3.14}\approx1.306$.

Answer:

$1.242\leq d\leq1.306$