Asked by jon
A wire along 1 meter is divided into three parts . The first part is formed into a circle , the second part is formed into an equilateral triangle , and the third part is formed into a square . Determine the size of each section so that the total area of the three wake formed the maximum possible
Answers
Answered by
Steve
If the radius of the circle is x, the side of the triangle is y, and the side of the square is z, then we have
2πx+3y+4z = 1
a = πx^2 + √3/4 y^2 + z^2
da/dx = 2πx
da/dy = √3/2 y = √3/2 (1-2πx-4z)
da/dz = 2z
a will have a maximum where all the partial derivatives are zero.
2πx+3y+4z = 1
a = πx^2 + √3/4 y^2 + z^2
da/dx = 2πx
da/dy = √3/2 y = √3/2 (1-2πx-4z)
da/dz = 2z
a will have a maximum where all the partial derivatives are zero.
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