calc help!!!!!!!!!!!?

Wire: 28 m

Therefore,

Piece #1 = w

Piece #2 = 28 - w

Minimize area of circle + area of square.

If square uses piece #1, then

A = (w/4)^2 = w^2/16 = (1/16)w^2

If circle uses piece #2, then

A = pi r^2

But 28 - w = pi*diameter

28 - w = pi * 2r

28 - w = 2pi r

(28 - w)/(2pi) = r

Therefore,

A = pi ( (28 - w)/(2pi) )^2

A = pi (28 - w)^2 / (4pi^2)

A = (28 - w)^2 / (4pi)

A = (1/4)(1/pi) (28 - w)^2

Since we want to minimize the area of both pieces, the formula to calculate the sum of their areas is

A = (1/16)w^2 + (1/4)(1/pi) (28 - w)^2

So this is our area function, A(w).

A(w)=(1/16)w^2 + (1/4)(1/pi) (28 - w)^2

Minimize the area of this by solving for the first derivative.

A'(w) = (1/8)w + (1/4)(1/pi)(2)(28 - w)(-1)

A'(w) = (1/8)w - (1/2)(1/pi)(28 - w)

Make A'(w) = 0, to get

0 = (1/8)w - (1/2)(1/pi)(28 - w)

Multiply both sides by 8pi to cancel all denominators.

0 = pi(w) - (4)(28 - w)

0 = pi(w) - 112 + 4w

112 = pi(w) + 4w

112 = w(pi + 4)

112/(pi + 4) = w

So w = 112/(pi + 4).

w represents what should be allocated to the square, so

28 - w represents what should be allocated to the circle.

28 - w = 28 - 112/(pi + 4)

= [ 28(pi + 4) - 112 ] / (pi + 4)

= [ 28pi + 112 - 112 ] / (pi + 4)

= 28pi/(pi + 4)

28pi/(pi + 4) meters of wire should be allocated to the circle.

This is approximately equal to 12.317223701676393474506598486384.