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 leve
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?
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
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