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December 19, 2014

December 19, 2014

Posted by **Remmy** on Wednesday, November 28, 2012 at 1:25am.

2) A running track 4 m wide goes around a soccer field that is twice as long as it is wide. At each end of the soccer field the track is a semi-circle with inner radius r. Find a formula for the area of the track in terms of *pi and r.

3a) Suppose that you plan to run once around the track described in the problem above. If you stay 0.5 m from the inner edge of the track, how far will you run? (Hint: The circumference of a circle is *2pir. Your answer will be in terms of *pi and r.)

3b) Suppose that a friend stays 0.5 m from the outer edge of the track. How much farther does your friend run than you do?

*pi = 3.14 or 22/7

- Algebra -
**Reiny**, Wednesday, November 28, 2012 at 10:49amoriginal square ---- > let each side be x

new sides are x-3 and x-5

so x^2 - (x-3)(x-5) = 185

x^2 - (x^2 - 8x + 15) = 185

8x - 15 = 185

x = 200/8 = 25

check:

original square was 25 by 25 , area = 625

new rectangle was 22 by 20 , area = 440

difference = 625-440 = 185

All looks good

2. I will let you do this one.

Hint: let the width of the soccer field be 2r, that way you can label the radius of the ends as r

The two semi-circular ends will constitute one whole circle. So the circular part of the track will be the "ring" formed by two circles, one of radius r, the other of radius (r-4)

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