NAME Math 103 Exam 3 retake 12 December 2008 100 points Instructions 1 This exam has 7 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 4 radians to degrees 3 b 5 points Convert 165 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 log3 45 log3 25 without using a calculator Page 2 28 Problem 3 12 points Suppose is an acute angle and cos Find the values of the other 53 five trigonometric functions of Problem 4 14 points The function f x and check your answer 3 is one to one Find its inverse function f 1 x 10 Page 3 Problem 5 14 points A horizontal awning 10 feet wide is to be attached to the side of a building A supporting chain will run from the outer edge of the awning to the side of the building above the point the awning is attached The angle between the awning and the chain must be at least 37 in order to support the weight of the awning The builder wants to use the least possible amount of chain a 7 points How long should the chain be b 7 points How far above the awning should the chain be attached to the building Page 4 Problem 6 16 points Remember that radioactive decay follows an exponential decay model so the amount A t of a radioactive substance at time t is given by A t A0 ekt where A0 is the amount of the substance at time t 0 A sample of 100 grams of radioactive rhenium 182 is produced in a reaction After 22 hours there are 78 80 grams of rhenium 182 remaining a 8 points Find the value of k in the exponential decay model above b 8 points What is the half life of rhenium 182 Page 5 Problem 7 12 points a 6 points What is the domain of f x ln x b 6 points The graph of a function g x is shown below Based on this graph what is the domain of the function h x ln g x Why y 5 4 y g x 3 2 1 5 4 3 2 1 1 1 2 3 4 5 Page 6 2 3 4 5 x Problem 8 10 points Solve log 3x 157 log 100 5 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 85 versin 5 csc2 5 without using a calculator Page 7