= 1 4. (20 points) Consider a bar 30cm long that is made of a material for which a² Assume both the sides and the ends of the bar are insulated. Suppose that the initial temperature is given by f(x) = 4 cos (7x) - ½ cos (1) for x = (0,30). (a) (5 points) According to the description in the problem, set up the corresponding heat equation of the temperature u = u(x,t) with suitable initial and boundary conditions. (b) (15 points) Solve the heat equation to find the temperature u.

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.