Supplemental Instruction
Iowa State University / Leader: / Anna Steffensmeier
Course: / Math 165
Instructor: / Paul Barloon
Date: / February 28, 2018
Related Rates (3.10)
Mr. Barloon’s Steps
Step 0: Draw a picture of what’s happening and label pictures with variables
Step 1: Write down changing functions of time
Step 2: Related by? Write down equation that relates the changing functions of time. Use picture or equation given to us
Step 3: THE QUESTION ---> translate to math (be specific)
Step 4: Derive equation from step 2 with implicit differentiation
Step 5: Solve at the moment given in problem
Step 6: Check units and end interpret the number you found.
The best thing to do with these problems is to develop a pattern and stick to it. Follow this set of steps or a set you developed on your own. This will help you a lot on the final and on this exam.
1)A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft. from the liftoff point.The moment the range finder’s elevation angle is, the angle is increasing at the rate of .14 rad/min. How fast is the balloon rising at that moment?
2) When a circular plate of metal is heated in an oven, its radius increases at the rate of .01 cm/min. At what rate is the plate’s area increasing when the radius is 50 cm?
3) A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house the base is moving at the rate of 5 ft/sec.
a. How fast is the ladder sliding down the wall then?
b. At what rate is the area of the triangle changing?
c. At what rate is the angle θ between the ladder and the ground changing then?
4) A tank of water in the shape of a cone is leaking water at a constant rate of.The base radius of the tank is 5 ft and the height of the tank is 14 ft.
(a)At what rate is the depth of the water in the tank changing when the depth of the water is 6 ft?
(b)At what rate is the radius of the top of the water in the tank changing when the depth of the water is 6 ft?
FALL FINAL EXAM PROBLEM
3. To help eradicate the new invasive species algebraicusridiculum, four boats set off from the center of a lake each in one of the four cardinal directions (north, south, east, and west). A stretchable rig between the boats makes sure to wipe out all the ridiculum inside the region enclosed by the rig (the shaded region). Suppose that at a particular time we have the following.
•The boat heading north (a) has gone 50 meters and is moving at 2 meters per minute.
•The boat heading south (b) has gone 40 meters and is moving at 3 meters per minute.
•The boat heading east (c) has gone 40 meters and is moving at 1 meter per minute.
•The boat heading west (d) has gone 30 meters and is moving at 4 meters per minute.
Determine the rate at which the total area enclosed by the rig, which is , is changing at this time. (Make sure to include the units for your final answer.)