maths,help!
2009-07-19 5:02 am
A piece of wire of length L is cut into two pieces,and each piece is bent to form a square.Find the minimum total area of the two squares.
回答 (1)
2009-07-19 5:59 am
✔ 最佳答案
Let one piece of the wire is x so the other is L - xSide of each square = x/4 and (L-x)/4 respectively
Total area A = (x/4)2 + [(L-x)/4]2
=(1/16)(x2 + L2 -2xL +x2]
=(1/16)(2x2 - 2xL + L2)
dA/dx = (1/16)(4x - 2L)
d2A/dx2 = 1/4 > 0 => min
Equate dA/dx = 0
4x - 2L = 0 => x = L/2
Therefore min total area = (1/16)[2(L/2)2 - 2(L/2)L + L2]
= (1/16)(L2/2 - L2 + L2)
= (1/32)L2
收錄日期: 2021-04-23 23:20:17
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