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Brainliest is given to the correct answer!

A high school race track is composed of a rectangle and two semicircles.

a. If the length "l" of the rectangle is twice as long as the diameter of the semicircles, write a formula for "p," the distance around the track, in terms of the radius "r" of the semicircles.

b. Rewrite the formula from a so the radius of the semicircles is given in terms of the distance around the track. Show your work.

Brainliest is given to the correct answer A high school race track is composed of a rectangle and two semicircles a If the length l of the rectangle is twice as class=

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akposevictor

Answer:

a. [tex] p = 2\pi r + 8r [/tex]

b. [tex] r = \frac{p}{2\pi + 8} [/tex]

Step-by-step explanation:

a. Radius of semicircle (r) = r

Diameter of semicircle (d) = 2r

Length of rectangle (l) = 2*diameter of semicircle = 2*2r = 4r

Distance around the track (p) = circumference of circle + 2(l)

Note: the two semicircles of the track = 1 full circle

Circumference of full circle = πd = π*2r = 2πr

Distance around the track:

p = 2πr + 2(4r)

p = 2πr + 8r

b. Rewriting the formula to make radius, r, the subject of the formula in terms of distance around the track.

[tex] p = 2\pi r + 8r [/tex]

Factor out r

[tex] p = r(2\pi + 8) [/tex]

Divide both sides by (2π + 8)

[tex] \frac{p}{2\pi + 8} = \frac{r(2\pi + 8)}{2\pi + 8} [/tex]

[tex] \frac{p}{2\pi + 8} = r [/tex]

[tex] r = \frac{p}{2\pi + 8} [/tex]

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