微積分應用問題
微積分應用問題
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.
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.
英語人氣：341 ℃時間：2020-05-11 12:23:45
優(yōu)質解答
圓錐體半徑與高的比為4/2/6=1/3設水高h,則水面半徑R=h/3圓錐體內水的體積V=лR^2h/3=лh^3/27h=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...
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