Stuffed Figure
Help with calculation problems, optimization trivial to find out?
Hey guys please help me this problem. Also please describe clearly the steps and how the solution reacher. Thanks A piece of wire 75 m in length is divided into two parts. One Piece is used to form a circle. The other used to make a square. Find the lengths of the pieces that minimize the total area of the circle and square. I think I am, supposed to start with the realization (75-x) for one of the two forms x for the other. Thank you very much for your help.
x = part that form a square 75 – = x piece that forms a circle, but x is the perimeter of the square. Therefore x / 4 is the side of the square and (x / 4) ² is the area of the same thing square with the circle C = 2πr 75-x = 2πr r = (75-x) / (2π) A = π r ² A = [π (75-x) / (2π)] ² A = π (75-x) ² / (4π ²) A = (75-x ) ² / (4π) so that the total area formed by the two forms is: TA = (X / 4) ² + (75 x) ² / (4π) normally we set TA '= 0 and solve for x, but why not plot the equation and solve for x? so x = ~ 42.00m 42m for the 33 square to the circle hope it helps:)
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