A 3m piece of wire is cut into two pieces and bent around to form a square and a circle. Find the size of the two lengths, correct to 2 decimal places, that will make the total area of the square and circle a minimum.
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let the length for the circle = x
then length for the square = 3-x
Total area = pi *(x/ (2*pi))^2 + ((3-x)/4)^2
Differentiate that with respect to x and put result = 0, then solve for x
then length for the square = 3-x
Total area = pi *(x/ (2*pi))^2 + ((3-x)/4)^2
Differentiate that with respect to x and put result = 0, then solve for x
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differentiate with respect to x and equate the resulting equation to 0
y = (3-x)^2 + pi * x^2
where ^2 means squared, * means multiply
y = (3-x)^2 + pi * x^2
where ^2 means squared, * means multiply