University of Georgia Department of Mathematics Math 1113 Final Exam Fall 2022 By providing my signature below I acknowledge that I abide by the University s academic honesty policy This is my work and I did not get any help from anyone else Name sign Student Number Instructor s Name Name print Class Time Problem Number Points Possible Points Made 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 20 20 17 20 15 10 10 10 10 10 10 11 10 If you need extra space use the last page Do not tear o the last page Please show your work An unjusti ed answer may receive little or no credit If you make use of a theorem to jus tify a conclusion then state the theo rem used by name Your work must be neat If we can t read it or cannot nd it we cannot grade it The total number of possible points that is assigned for each problem is shown here The number of points for each subproblem is shown within the exam Please turn o your mobile phone You are only allowed to use a TI 30 cal culator No other calculators are per mitted A calculator is not necessary but nu merical answers should be given in a form that can be directly entered into a calculator Common identities Total 173 cos cos cos sin sin sin sin cos cos sin 1 2 Bonus Common Knowledge What will Marianne Vos have to do to beat Fem Van Empel this cross season A Page 1 of 17 Math 1113 Final Exam Fall 2022 2 Determine all values of x that satisfy each equation below a 5 pts 2x2 5x 7 0 b 5 pts log cid 0 4x2 3 cid 1 5 A Page 2 of 17 10 points Math 1113 Final Exam Fall 2022 c 5 pts 4 5x 7 d 5 pts 2 8x 1 7 63 2x A Page 3 of 17 10 points Math 1113 Final Exam Fall 2022 3 Determine the value of each of the requested quantities in each question below Numerical values should be to within 0 01 of the true value All angles are given in radians and should be expressed in radians if you have to determine their value a 5 pts Determine the cosine sine and tangent of the angle in the diagram below 5 12 b 5 pts Determine the cosine sine and tangent of the angle in the diagram below The radius of the circle in the diagram is 6 y x 5 x A Page 4 of 17 10 points Math 1113 Final Exam Fall 2022 c 5 pts Determine the radian measure of the angle in the diagram below The point shown is on the unit circle x 0 6 y y y x d 5 pts Determine the radian measure of the angle in the diagram below The circle has a radius of two and the arclength of the shaded sector is 10 A Page 5 of 17 10 points Math 1113 Final Exam Fall 2022 4 Three functions k x w x and g x are given below Use the functions to answer each cid 26 x g x x 0 x 3 x 0 of the questions below y 5 4 3 2 1 k x x w x 0 2 3 1 0 2 1 3 2 4 5 3 3 2 1 1 2 3 x a 5 pts Determine the value of w k 1 b 5 pts Determine the value of w g 5 c 4 pts Determine the average rate of change of g x from x 2 to x 4 d 3 pts For what values of x is the function g k x increasing A Page 6 of 17 17 points Math 1113 Final Exam Fall 2022 5 For each description below determine a formula for an equation that matches the require ments a 10 pts A parabola that is increasing if x 4 and decreasing if x 4 The parabola has a maximum value of 1 The y intercept of the parabola is at y 10 b 10 pts A linear function that goes through the point 2 5 and the line is parallel to the line 3x 8y 7 A Page 7 of 17 20 points Math 1113 Final Exam Fall 2022 6 For each scenario below circle the phrase that will best describe the kind of function that will best approximate the phenomena under consideration a 5 pts Money is deposited into a back account that o ers compounded interest and no money is withdrawn The amount of money in the bank account as a function of time Linear Function Quadratic Function Exponential Function Trigonometric Function b 5 pts A bird lands on the end of the blade of a windmill and remains in place The bird s height as a function of time Linear Function Quadratic Function Exponential Function Trigonometric Function c 5 pts A Coast Guard ship is sent to look for a person who was swept o of a boat The captain of the ship speci es a search area that is a square whose sides grow at a constant rate in time The area in square meters of the search area as a function of time Linear Function Quadratic Function Exponential Function Trigonometric Function A Page 8 of 17 15 points Math 1113 Final Exam Fall 2022 7 10 pts An object is raised along a wall The height of the object increases at a constant rate Initially the object is 10 meters above the ground and after 120 seconds the object is 30 meters above the ground Determine the height of the object above the ground as a function of time for any time between 0 and 120 seconds A Page 9 of 17 10 points Math 1113 Final Exam Fall 2022 8 10 pts A eld has a rectangular shape and one of its dimensions is 40 meters A cord will be stretched across the diagonal between two opposite corners of the eld Determine the length of the cord given the area A of the eld Your answer should be a function of A A Page 10 of 17 10 points Math 1113 Final Exam Fall 2022 9 10 pts Determine the value of cos arctan 2 3 arccos 0 2 Express the exact value so that no trigonometric functions occur in the expression Do not use a calculator and you do not need to simplify your expressions A Page 11 of 17 10 points Math 1113 Final Exam Fall 2022 10 10 pts Determine a formula for the function whose graph is shown below expressed as a sine function The values of A b and c should be positive numbers p x A sin bx c d y 4 3 2 1 1 2 3 2 1 1 2 3 x p x A b c d A Page 12 of 17 10 points Math 1113 Final Exam Fall 2022 11 The amount of mercury in parts per million ppm that will accumulate in …