NAME MATH 103 Exam 3 version a 24 October 2008 100 points Instructions 1 This exam has 6 pages including this one which contain 8 problems and one bonus problem Please check that you have all of the pages 2 Answer all of the following questions clearly and completely Justify all of your answers 3 You may not use a book or any notes for this exam 4 Give your answer to each problem completely and clearly in the space provided You may use the back of the exam pages for scratch work however if you want this work to be considered make note of it in the space provided for the problem 5 Erase or cross out work you do not wish to be graded 6 Credit partial or full will be given only if sufficient steps leading to the answers are shown 7 You have 50 minutes to complete this exam Page 1 Problem 1 10 points Be sure to show work for both parts of this problem even if you can do them in your head so that I can see that you understand how to do these conversions and that you aren t just using your calculator a 5 points Convert 3 radians to degrees 4 b 5 points Convert 75 to radians Express your answer as a multiple of in other words do not approximate your answer with a decimal Problem 2 12 points Find the exact value of 2 log7 21 log7 9 without using a calculator Page 2 40 Problem 3 12 points Suppose is an acute angle and cos Find the values of the other 41 five trigonometric functions of Problem 4 14 points The function f x and check your answer 4 is one to one Find its inverse function f 1 2 x Page 3 Problem 5 10 points Solve 5 log x 571 15 Problem 6 14 points You have 850 to invest What rate of return r compounded continuously do you need in order to have 1250 after 6 years Page 4 Problem 7 16 points In an electric circuit the voltage across the terminals of a capacitor which is discharging through a resistor decays exponentially In other words the voltage V t at time t is given by V t V0 ekt where V0 is the voltage at time t 0 Suppose this capacitor is charged so that the voltage across its terminals at time t 0 is 25 volts After 10 seconds the voltage is measured and is found to be 8 volts a 8 points Find the value of k in the exponential decay model above b 8 points What will be the voltage across the terminals of the capacitor at time t 15 seconds Page 5 Problem 8 12 points A ladder is leaning against a wall The base of the ladder is 4 feet from the base of the wall and the ladder makes an angle of 70 5 with the floor How long is the ladder Bonus problem 4 points There are a few trigonometric functions which were once common but are now very rarely used One of these is called the versine written versin which is defined as versin 1 cos Find the exact value of 1 sin 68 versin 22 csc2 22 without using a calculator Page 6