微积分数学题。。。求教

来源：百度知道 编辑：UC知道 时间：2024/05/05 00:27:15
a water trough is 10m long and a cross-section has the shape of an isosceles triangle that is 1m across at the top and is 50cm high. the trough is being filled with water at a rate of 0.4m3/min. how fast will the water level rise when the water is 40cm deep?

Solution:

Let the height water be h, the width be x
volume of the water be V
x/h = 1/0.5, x = 2h
V = ½ xh×10 = 5xh = 10h²
dV/dt = 20hdh/dt
when h = 0.4,
dh/dt = 0.4/20×0.4 = 1/20 = 0.05 m/min

我靠，用英语搞微积分问题，本来英语都没学好，更别提微积分了...

agree with 安克鲁