If the square has side s and the circle has radius r, then
A = s^2 + πr^2
But, 4s+2πr = 77, so s = (77-2πr)/4
A(r) = (77-2πr)^2/16 + πr^2 = (π62/4 + π)r^2 - 77π/4 r + 5929/16
The vertex of that parabola is at r = 77/(8+2π)
C = 2πr = 77π/(4+π)
You have a wire that is 77 cm long. You wish to cut it into two pieces. One-piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?
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