1. Newton's Law of Cooling. I have noticed that when my hot coffee sets in my 75 degree kitchen, it cools from 200 degrees to 175 degrees in 2 minutes. If I add milk to the 200 degree coffee, it immediately cools to 192 degrees but if I wait 6 minutes to add the milk after it has cooled a bit, the temperature only drops 5 degrees. Find the temperature of the coffee after 6 minutes in the following two cases: 1) I add the milk immediately and then let it cool for 6 minutes, or 2) I add the milk after the coffee has cooled for 6 minutes. Hint: The constant k is the same in both cases.

2. Related Rate. At midnight, a car leaves an intersection heading due east at a constant speed of 62 mph. At the same time, a bicycle leaves the intersection on a second road at a constant speed of 20 mph. At 1:00 AM it is observed that the distance between the bicycle and car is increasing at the rate of 49 mph. Find the angle of intersection, to the nearest degree, between the two roads. Hint: Use the law of cosines.