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1) Let F(x)= f(x^{5}) and G(x)=(f(x))^{5} . You also know that a^{4}=13, f(a)=3,f'(a)=9, f'(a^{5})=12. Find F'(a) and G'(a). 2) Water is leaking out of an inverted conical tank at a rate of 9500.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6.0 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 24.0 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Note: Let “R” be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, \frac{dV}{dt}=R-9500.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by (1/3)pir^2h 3) Let A be the area of a circle with radius r. If dr/dt =2, find dA/dt when r= 2. 4) let xy= 2 and let dy/dt= 3. Find dx/dt when x= 3. 5) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm. (Note the answer is a positive number).

1) Let F(x)= f(x^{5}) and G(x)=(f(x))^{5} . You also know that a^{4}=13, f(a)=3,f'(a)=9, f'(a^{5})=12. Find F'(a) and G'(a).

2) Water is leaking out of an inverted conical tank at a rate of 9500.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6.0 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 24.0 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Note: Let “R” be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, \frac{dV}{dt}=R-9500.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by (1/3)pir^2h

3) Let A be the area of a circle with radius r. If dr/dt =2, find dA/dt when r= 2.

4) let xy= 2 and let dy/dt= 3. Find dx/dt when x= 3.

5) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm. (Note the answer is a positive number).

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