1.

Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads due west at 16 kilometers per hour. After 2.5 hours, how fast is the distance between the boats increasing? O A. V89 kilometers per hour O B. 2v89 kilometers per hour O C. 3V89 kilometers per hour O D. 4V89 kilometers per hour O E. 5V89 kilometers per hourThis question has two parts. First, answer Part A. Then, answer Part B. Part A The height y of an object falling from rest from a height of 2,000 m is given by the equation y = 2250 - 50t - 250e-, where t is in seconds. What is the object's velocity at t = 6 s? Round your answer to the nearest whole number. O A. -27 m/s O B. -29 m/s O c. -31m/s O D. -33 m/s O E. -35 m/sPart B Which of the following best represents the magnitude of the object's acceleration at t = 2.5 s? Round your answer to the nearest tenth. O A. 3.7 m/s O B. 6.1 m/s O C. 6.7 m/s O D. 9.0 m/s O E. 9.5 m/sThis question has two parts. First, answer Part A. Then, answer Part B. Part A The position of an object bobbing up and down on a spring is given by the function s = 5 sin(3t + 2) cm/s, where s is in cm and t is in seconds. Which of the following best represents the object's velocity at time t = 2 s? O A. -14.4 cm/s O B. -2.2 cm/s O C. 2.2 cm/s O D. 4.8 cm/s O E. 14.4 cm/sPart B What is the object's acceleration at time t = 2 s? O A. -44.5 cm/s O B. -43.2 cm/s O C. -14.8 cm/s O D. 6.5 cm/s O E. 12.6 cm/sGia has just purchased a car whose value in dollars, because of depreciation, will be worth 6' = 25, OBOE\"Mt aftert months have passed. At the same time, she is saving $112": per month. (Interest on her savings can be ignored.) Which of the following best represents when the combined value of her car and savings will start to increase wtth time? 2K A. 28.3 months B. 40.2 months G. 5?.6 months D. 3'43 months E. 115.1 months Find two positive numbers whose product is 192 and whose sum is a minimum. O A. 3 and 64 O B. 4V3 and 16:3 O C. 8 and 24 O D. 8V3 and 8v/3 O E. 12 and 16Find the value of c that satisfies the Mean Value Theorem for f (@) = In (@ ) on the interval [1, e]. O A. c= e - 2 O B. c=e- 1 O C. c= 2e - 2 O D. c= 2e - 1 O E. c= e+1This question has two parts. First. answer Part A. Then, answer Part B. Part A At time t = 1 an object moving along a straight line with a constant acceleration of 3111fr s2 is located at s (1} = 5 and has a velocity of u (1) = 10. What is the equation for the velocity as a function of time? 3' A. t) = 7 + 1-5t :3 a. 1.16) = 7+3: .:3. G. \"(t) = 10 1.5: D. o) = 10 + 1-5: E. o) = 10 + 3: Part B What is the equation for the location as a function of time? O A. s (t) = -2.75 + 7t + 0.75t2 O B. s (t) = -3.5 + 7t + 1.5t2 O C. s (t) = 5 + 10t - 0.75t2 O D. s (t) = 5 + 10t + 0.75t2 O E. s (t) = 5 + 10t + 1.5t2