Question

this question has two parts. first, answer part a. then, answer part b. part a track a 400 - meter olympic - size track can be modeled with a rectangle and two semicircles. a. if an athlete runs around the track once, how far has the athlete traveled to the nearest meter? m part b b. what assumption can be used to explain the difference between your answer in part a and the actual length around the track? in part a, i assumed that there was no space between the field and the select choice of the track. i also assumed that the athletes body was select choice of the track select choice to the left of the border to the right of the border centered on the border

Explanation:

Step1: Analyze track composition

The track is composed of two - straight parts and two semi - circles (which form a full circle). The length of the two straight parts is \(2\times84.39\) meters, and the diameter of the circle formed by the two semi - circles is \(73\) meters.

Step2: Calculate circle circumference

The formula for the circumference of a circle is \(C = \pi d\), where \(d = 73\) meters. So \(C=\pi\times73\approx3.14\times73 = 229.22\) meters.

Step3: Calculate length of straight parts

The length of the two straight parts is \(2\times84.39=168.78\) meters.

Step4: Calculate total track length

The total length of the track \(L = 229.22+168.78 = 398\) meters.

Answer:

a. 398
b. In part a, I assumed that there was no space between the field and the inner - most of the track. I also assumed that the athlete's body was centered on the border of the track.