13. A passenger ship and an oil tanker left the port at any time in the morning. The passenger ship as a former headed north and the latter headed east. At noon, the passenger ship was 40 nautical miles from port and sailing at 30 nautical miles per hour, while the oil tanker was 30 miles from port and sailing at 20 miles per hour. Determine the rate of change of the distance between the two ships with respect to time. (Hint: Use Pythagorean theorem and differentiation).

You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour

What is the slope of the tangent line to y + xy = 12 at the point (1, 3)? A. -¹5 B. 2 233 C. D. -