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A certain circle's area is x square units, and its circumference is y units. The value of x+y is 80pi. What is the radius of the circle, in units?

Guest Feb 22, 2017
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I will take a crack at it:

 

Area =Pi x r^2

Circumference =Pi x 2r, since:

x = Area

y = Circumference

[Pi r^2] + [Pi 2r] =80Pi

 

Solve for r:
2 π r + π r^2 = 80 π

Divide both sides by π:
r^2 + 2 r = 80

Add 1 to both sides:
r^2 + 2 r + 1 = 81

Write the left hand side as a square:
(r + 1)^2 = 81

Take the square root of both sides:
r + 1 = 9 or r + 1 = -9

Subtract 1 from both sides:
r = 8 or r + 1 = -9

Subtract 1 from both sides:
Answer: |r = 8                           or                  r = -10(Discard)

Guest Feb 22, 2017

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