Suppose you deposit 6000 at 7 interest compounded

Question

1. Determine the volume of the solid generated by rotating function f(x) = √(64 - x²) about the x-axis on [6, 8].

2. Find the volume of the solid formed by rotating the region enclosed by y = e^3x + 1, y = 0, x = 0, x = 0.4 about the x-axis.

3. Find the average value of the function f(x) = 5x² on the interval 0 ≤ x ≤ 4.

4. Suppose you deposit $6000 at 7% interest compounded continuously. Find the average value of your account during the first 2 years.

5. If a cup of coffee has temperature 100^oC in a room where the ambient air temperature is 24^oC, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 24 + 76e-^t/50.  What is the average temperature of the coffee during the first 28 minutes?