作业帮一道英文数学题!微积分的!a trough is 6m long and its ends have shape pf isosceles triangles that are 1m accross at the top and have a height of 50cm.if the trough is being filled with water at a rate of 1.2m^3/min,how fast is the water leve
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一道英文数学题!微积分的!
a trough is 6m long and its ends have shape pf isosceles triangles that are 1m accross at the top and have a height of 50cm.if the trough is being filled with water at a rate of 1.2m^3/min,how fast is the water level rising when water is 20cm deep?
Solution :
Let x be the height of water level,L be the width of water level
So,V = (1/2)LX*6 = 3LX
By the similarity :L/x = 100/50 = 2,L = 2x
So,V = 6x^2,dV/dt = 12xdx/dt
When x = 0.2 cm
dV/dt = 2.4dx/dt
dx/dt = (dV/dt)/2.4 = 1.2/2.4 = 0.5 m^3/min
Let l denote the perimeter, a one side (l-2a)/2*a=24, that is la-2a^2=48 differentiate (l-2a)/2*a=24 respect to the time t a*dl
望采纳！
Let l denote the perimeter, a one side (l-2a)/2*a=24, that is la-2a^2=48 differentiate (l-2a)/2*a=24 respect to the time t a*dl