微积分应用问题Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate.The tank has height 6 m and the diameter at the top is 4 m.If the water level
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![微积分应用问题Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate.The tank has height 6 m and the diameter at the top is 4 m.If the water level](/uploads/image/z/11730874-58-4.jpg?t=%E5%BE%AE%E7%A7%AF%E5%88%86%E5%BA%94%E7%94%A8%E9%97%AE%E9%A2%98Water+is+leaking+out+of+an+inverted+conical+tank+at+a+rate+of+6500+cm3%2Fmin+at+the+same+time+that+water+is+being+pumped+into+the+tank+at+a+constant+rate.The+tank+has+height+6+m+and+the+diameter+at+the+top+is+4+m.If+the+water+level)
微积分应用问题Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate.The tank has height 6 m and the diameter at the top is 4 m.If the water level
微积分应用问题
Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate.The tank has height 6 m and the diameter at the top is 4 m.If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m,find the rate at which water is being pumped into the tank.
微积分应用问题Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate.The tank has height 6 m and the diameter at the top is 4 m.If the water level
圆锥体半径与高的比为4/2/6=1/3
设水高h,则水面半径R=h/3
圆锥体内水的体积V=лR^2h/3=лh^3/27
h=3л^(-1/3)V^(1/3),
h'(t)=л^(-1/3)V^(-2/3)V'(t),
V'(t)= h'(t)л^(1/3)V^(2/3),
V'(t0)=0.2л^(1/3)(л2^3/27)^(2/3)=0.8л/9,
所求注入水流速
v=V'(t0)+6500e-6 (m^3/min)
=0.8л/9+0.0065 (m^3/min)
=0.28575268(m^3/min)
=285752.68(cm^3/min)
555,我也不懂,学历低