Two cars leave central square. the first car drives north at 35 miles per hour (mph), and its distance to central square is a (here a is actually a function of time). the second car drives east at 50 mph and its distance from central square is b (here b is also a function of time). the distance between the two cars is d. at a certain time, a = 20 miles and b = 40 miles.

a) sketch the general picture of what the cars and central square look like. be sure to label the diagram with a, b, and d, representing the distances mentioned in the stem of the problem.

b) give a general formula for d in terms of a and b.

c) find a formula for d', the derivative of d, with respect to time in terms of a, a', b, and b'.

d) are the two cars getting closer or farther away from each other at the certain time? how fast is the distance between them changing at that time?