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NastyAccident
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Homework Statement
A piece of wire 50 cm long is to be cut into two pieces. (X and 50-x)
One piece (X) will form a circle; the other (50-x) will be bent to form a square.
Two students, Max and Min, have different goals. Min wants to minimize the sum of the areas of the circle and square. Max wants to maximize the sume of the areas of the circle and square.
There must only be one (an) equation that will be minimized and maximized.
Hint: You must consider the domain carefully in this situation [D(0,50) ?]
Homework Equations
Circumference:X = 2*pi*R
Area of the Circle:A = pi*R^2
Area of the Square: A = S^2
Length of a side of a square: S = (50-X)/4
The Attempt at a Solution
First, I found the minimum of the problem:
Circle{
Circumference -
X = 2*pi*R
X/(2*pi) = R
A = pi*R^2
A = pi*(x/(2*pi))^2
}
Square{
Length of a side: 4s = (50-x)
s = (50-x)/4
Area = S^2
Area = ((50-x)/(4))^2
}
Total Area (T.A) = A of Circle + A of Square
T.A = pi*(x/(2*pi))^2 + ((50-X)/4)^2
T.A = (4*x^2 + pi*(50-x)^2))/(16*pi)
T.A is approximately 87.52 with x approximately being 22. The answers were obtained by using my graphing calculator and rounding to the hundredths.
The domain I am guessing for this function of T.A is 0<x<50.
But, I haven't got the slightest clue on how to get a maximum from this problem... Any help would be appreciated.