Please see the attached question below

7. (a) The number of atoms, N remaining in a mass of material during radioactive decay after time t seconds, is given by: N = 0.4 e-3t Evaluate the mean number (N) of atoms, for the time t = 0 to t = 1/3. State the answer correct to TWO decimal places. [6 marks] (b) Consider the tank of water in the shape of a cuboid, as shown in Figure 1 with constant dimensions of length L, width W and height H. H Figure 1 The force, F exerted on the wall of the water tank is given by the definite integral: F = So pgW(H - z) dz Page 4 of 5 where p is the density of the water, and g is the constant acceleration due to gravity, taken as 9.8 ms-2 Evaluate the integral F and show clearly with all steps that F = P9WH 2 [Hint: check out the constants first, and integration would be easy!]