12/09 Practice FinalSupplemental InstructionIowa State UniversityLeader: Matt ECourse: Math 165 Instructor: KramerDate: 12/09/10Part 1 – For the first part of the test, do not use a calculator. 1) Find a. b. c. Supplemental Instruction1060 Hixson-Lied Student Success Center v 294-6624 v www.si.iastate.edu2. Evaluate and simplify (without using a calculator). Don’t rationalize denominator.3. Find the particular solution to the differential equation: that satisfies when 4. Evaluate the following integrals:Part 2 – You may now use a calculator on this part, but don’t go back and use it on Part 1. Show the work that leads to all answers. 1. Find the volume of the largest right circular cylinder that will fit inside a sphere of radius 3ft. 2. Water is draining from a large conical tank at a rate of 3 m3/s. The cone is 10m tall and has a radius of 5m at the top. i) At what rate is the water level dropping when there is 1m (depth) of water left? ii) How long would it take to completely drain the tank if it were full?a. On what (closed) intervals is f increasing? b. Find all critical points c. Use the second derivative test (if possible) to classify each critical point as a max or min. If the second derivative test fails, use the first derivative test. 5. A radioactive substance has a half-life of 2000 years, and there are initially 50 grams. Let y(t) represent the amount (in grams) of the substance remaining after t years. i) Write a differential equation to describe this situation. ii) Solve your differential equation, using the half-life to find a particular solution: y(t)iii) How much of this substance is left after 9000 years? Round to 3 decimal
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