標題:
Rate of change
發問:
Water is pumped out at a rate if 3 m^2/min from a hemisphere water tank with radius 13m. When the depth of water is x m, the volume of water inside the tank is (π/3)x^2(39-x) m^3. At what rate is the water level dropping when the depth of water is 8m? Ans: 1/48π m/min
最佳解答:
V=(π/3)x^2(39-x) V=(π/3)(39x^2-x^3) Differentiate both sides w.r.t. t dV/dt=(π/3)(39*2x*(dx/dt)-3x^2*(dx/dt)) dV/dt=(π/3)(78x-3x^2)(dx/dt) -3=(π/3)*432*(dx/dt) dx/dt=-1/48π m/min 2011-01-19 16:08:38 補充： For step3, just sub. x=8 and dV/dt=-3 2011-01-19 20:10:10 補充： Yes........................
Rate of change
發問:
Water is pumped out at a rate if 3 m^2/min from a hemisphere water tank with radius 13m. When the depth of water is x m, the volume of water inside the tank is (π/3)x^2(39-x) m^3. At what rate is the water level dropping when the depth of water is 8m? Ans: 1/48π m/min
最佳解答:
V=(π/3)x^2(39-x) V=(π/3)(39x^2-x^3) Differentiate both sides w.r.t. t dV/dt=(π/3)(39*2x*(dx/dt)-3x^2*(dx/dt)) dV/dt=(π/3)(78x-3x^2)(dx/dt) -3=(π/3)*432*(dx/dt) dx/dt=-1/48π m/min 2011-01-19 16:08:38 補充： For step3, just sub. x=8 and dV/dt=-3 2011-01-19 20:10:10 補充： Yes........................
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