If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter.
Height:???
Width:???
更新1:
Determine the dimensions of the window which minimize the perimeter?
determine the dimensions of the window which minimize the perimeter.?
2017-11-14 3:01 pm
Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height T that is 0.9 times the width w of the rectangle (as shown in the figure below).
If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter.
Height:???
Width:???
If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter.
Height:???
Width:???
回答 (1)
2017-11-17 11:17 pm
area, A = h*w + wT/2 = hw + 0.45 w^2
=>
h=(A - 0.45*w^2)/w
perimeter=(w+2h)+2*w*(0.5^2+0.9^2)^(1/2)
=2w+ (A-0.45*w^2)/w + 2*w*(0.5^2+0.9^2)^(1/2)
=[2-0.45+ 2*(0.5^2+0.9^2)^(1/2)] w + A/w >= 2√{A[2-0.45+ 2*(0.5^2+0.9^2)^(1/2)]}
when [1.55+ 2*(0.5^2+0.9^2)^(1/2)] w = A/w
w =√{A/ [1.55+ 2*(0.5^2+0.9^2)^(1/2)]} ~0.526 √A
=>
h=(A - 0.45*w^2)/w
perimeter=(w+2h)+2*w*(0.5^2+0.9^2)^(1/2)
=2w+ (A-0.45*w^2)/w + 2*w*(0.5^2+0.9^2)^(1/2)
=[2-0.45+ 2*(0.5^2+0.9^2)^(1/2)] w + A/w >= 2√{A[2-0.45+ 2*(0.5^2+0.9^2)^(1/2)]}
when [1.55+ 2*(0.5^2+0.9^2)^(1/2)] w = A/w
w =√{A/ [1.55+ 2*(0.5^2+0.9^2)^(1/2)]} ~0.526 √A
收錄日期: 2021-04-18 17:58:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20171114070125AArIqbc