SOLUTION: A quarter mile running track has the formula for the inside perimeter as P=2πr+2x. a)Solve the perimeter formula for r. b)For a quarter mile track, P=440 yards. Find r when

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Question 895070: A quarter mile running track has the formula for the inside perimeter as P=2πr+2x.
a)Solve the perimeter formula for r.
b)For a quarter mile track, P=440 yards. Find r when x=75 yards, 100 yards, 120 yards, and 150 yards.
c)What are the greatest and least possible values of r if P=440 yards? Explain how you found the values, and sketch the track according to each extreme value.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
To answer (a) and (b), you simply have r as a factor in only one term, so solving for r is simple. For (b), you just substitute the values and evaluate ------ r.

P=2pi%2Ar%2B2x
P-2x=2pi%2Ar
highlight%28%28P-2x%29%2F%282pi%29=r%29

Question part (c) is not complicated. P or r is a linear function of r or P. Same with r and x. Think about the formula given, and you understand that x is the straight length of the track. If the track has NO straight section to length then you simply have a circular track, and x=0. Clear, right? r is what now?
Look again: P=2pi%2Ar%2B2x, and if x becomes zero, then
P=2pi%2Ar%2B2%2A0
P=2pi%2Ar
r=P%2F%282pi%29