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Bunuel
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area+diameter-circumference=4

pi*r^2+2r=4+2pi*r

isolate r and get r(pi*r+2)=4+2pi*r

r=(4+2pi*r)/(pi*r+2) =>2(2+pi*r)/(pi*r+2)

r=2

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The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/π
B. 2
C. 3
D. 4
E. 5

Area = πr²
Diameter = 2r

Circumference = 2πr

We can write: πr² + 2r - 2πr = 4
Rearrange and set equal to zero to get: πr² - 2πr + 2r - 4 = 0
Factor IN PARTS: πr(r - 2) + 2(r - 2) = 0
Combine to get: (πr + 2)(r - 2) = 0

So, EITHER πr + 2 = 0 OR r - 2 = 0
If πr + 2 = 0, then r = -2/π (not possible)
If r - 2 = 0, then r = 2 (perfect!)
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