Please answer the following questions.

5. Verify that the function y = cosh 5x satisfies the differential equation y" =5\\/25 + (y')2. [Hint: You need to use the identity cosh r - sinh x = 1.] 6. A sector is to be cut from a thin circular metal sheet of radius 1 m and the two straight edges soldered together to form a hollow cone. If the angle of the sector remaining is / then the volume of the cone is given by V = = 127 - 472. Specify the interval where o varies and then determine the angle o so that the cone has maximum volume. Give a reason why it is maximum. You must get from a point A on the straight shore of a lake to a stranded swimmer who is at the point B in the lake. The shortest distance from B to the shore is BC = 30 m where C is a point on the shore, 40 m from you (see figure). Assume you can swim at a speed of 1 m/s and run at a speed of 4 m/s, find the point D along the shore, a meters from C, such that you can reach the swimmer in the minimum time? D (a) Express the running distance and swimming distance in terms of r. 40 (b) Use the result of (a) to find the time T(x) it takes for you to reach B. (c) What is a reasonable interval for a ? (d) Minimize the time T(x) over the interval specified in (c) to locate D and give an argument why it is minimum