The length of a football field is 120 yards (100 yards plus 10 yards for each end zone).
To encompass a football field with a track that is at least 440 yards around and has straightaways
of 120 yards on the sides and a semicircle on each end, what must the minimum radius of the
semicircles be (to the nearest yard)?

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Now, given that he length of a football field is 120 yards (100 yards plus 10 yards for each end zone) and to encompass a football field with a track that is at least 440 yards around and has straightaways of 120 yards on the sides and a semicircle on each end.

Let

L = length of sides of football field = 120 ft,
r = radius of semi-circular part and
D = length of track round field.

Given that we have two sides of the field and two semi-circles at both ends of the field,

the length of both sides is 2L and
the length of both semi-circles is 2πr

So, the length of track D = length of both sides + length of semi-circles

L = 2L + 2πr

Now, since L ≥ 440 ft, we have that

2L + 2πr ≥ 440

L + πr ≥ 220

What is the minimum value of the radius of the semi-circle?

So, r ≥ (220 - L)/π

Substituting the values of L and π into the equation, we have

r ≥ (200 - L)/π

r ≥ (220 - 120)/3.1416

r ≥ 100/3.1416

r ≥ 31.83

r ≥ 32 yards (to the earest yard)

So, the minimum value of the radius of the semi-circle r is r = 32 yards

Learn more about radius of semi-circle here:

brainly.com/question/25581473

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