题目

微积分 应用题
A rain gutter is to be constructed from a length of sheet metal that is 24cm wide.To form the gutter,the width is folded along its
length,in three equal sections,so that both ends form an angle @ with the middle section (horizontal).Find the angle that will
maximize the capacity of the rain gutter.
a) Since the capacity is proportional to the cross-sectional area created by the folds,find the cross-sectional area as a function of
the angle.
b) Give a reasonable explanation of why the set of possible angles should be a clased set.
c) Carry out the optimization to find the angle that maximizes the capacity of the gutter.

提问时间：2021-03-29

答案

翻译一下好了：
水槽是由一个金属板材的长度是24厘米宽建造.形成了排水沟,宽折沿其长度路段,在三个平等,使两端形成一个角度@与中间部分（水平）.寻找角度,将最大限度地水槽容量的雨水.1）由于能力是成正比的横截面积倍创造的,找到一个函数的角度交叉的截面面积.二）作出合理的解释为什么一套可行的角度应该是clased设置.三）开展了优化,以最大化的角度找到了水沟的容量.