Use Units If units are given in the problem, make sure you give them in your answer. Answer the Question Be very careful to answer the question asked. If you're asked to find the points of intersection between y=x2 and y =cosx, then {x = .82413, -.82413} is the wrong answer! The correct answer is: points (-.82413, .67919) and (.82413, .67919). Formulas Here is a short list of area and volume formulas that you might need: . . 2 . For a circle of radius r: Area = nr , Circumference =2nr. 4 For a sphere of radius r: Volume = []m'3, Surface Area = 4mg. For a right circular cylinder with radius r and height h: Volume = nrzh, Surface Area = 2m + 2mg. For a right circular cone with radius r and height h: Volume =[%]nr2k. For a 2-liter bottle of cola: Volume=2 liters. Free-Response Question 1 (with calculator) You may use your calculator for this question. (When you nish this question, if your test is proctored, ask your proctor for the next section. If you're ta king the unproctored version of the test, continue with the next question.) 1 1. The region R is bounded by the x-axis, x = 1, x = 3, and y = 3. x A. Find the area of R. B. Find the value of h, such that the vertical line X = h divides the region R into two regions of equal area. C. Find the volume of the solid generated when R is revolved about the X-axis. D. The vertical line x = k divides the region R into two regions such that when these two regions are revolved about the x-axis, they generate solids with equal volumes. Find the value of k. Free-Response Question 2 (no calculator) You may not use your calculator for this question. 2. River currents (miles per hour) at a certain location are given below. The current direction at this location was "from the north" during the time interval shown, and the current did not exhibit any severe fluctuations other than those shown in the chart. Time of Day 6:00 AM 6:10 AM 6:20 AM 6:30 AM |6:40 AM Speed (mph) 17 20 22 21 17 A. Using trapezoids, estimate the average river current speed from the north from 6:00 AM until 6:40 AM. B. At approximately what time between 6:00 AM and 6:40 AM would you estimate that the river current had the average velocity?C. A message in a bottle near this location is released at 6:00 AM. Assuming that the bottle travels along with the river's current, approximately how far south will the bottle be at 6:40 AM? D. What is the average acceleration of this bottle from 6:00 AM to 6:40 AM