2. Practice similar The experimental data in the table below define y as a function of x. y 0 2.9 1 1.8 2 15 3 1.6 4 2.4 5 3.4 (Round your answer to within three decimal places if necessary, but do not round until your final computation.) a. Let P be the point (1, 1.8). Complete the table below by computing the slope of the line PQ when Q is the point of the graph with x-coordinate x1. 1 Slope -1.1 2 -0.3 3 -0.1 4 0.2 5 0.4 b. Draw the graph of the function for yourself and estimate the slope of the line approaches as Q gets closer to P. Slope: ? & APractice similar ( Previous l Next A ball is dropped from a state of rest at time t : 0 seconds. The distance traveled after tseconds is 5(t) : 16t2 ft. (Round your answers to Within three decimal Places if necessary, but do not round until your final computation.) a. How far does the ball travel during the time interval [9, 9.5]? A5 = 148 ft b. Compute the average velocity over [9. 9.5]. 27:: 296 c. Compute the average velocity over the following time intervals. ft sec Time Interval Average Velocity (ft/s) [9, 9.01] ? A [9, 9.001] 7 A [9,9.0001] ? A [8.9999, 9] 7 A [8.999,9] ? A [8.99, 9] "r A Use this to estimate the object's instantaneous velocity at t = 9 seconds, V(9) : ? AL sec 4. Practice similar The point P 1, 3 lies on the curve y = 7+ x ac . (Round your answers to within three decimal places if necessary, but do not round until your final computation.) a. If Q is the point (X, 7+ find the slope of the line PQ for the following values of ac. Slope Slope .5 1.5 2 0.9 A 1.1 2 A 0.99 A 1.01 ? 0.999 ? A 1.001 A b. Guess what the slope of the line approaches as Q gets closer P. Slope: ? A5. Practice similar The graph below shows the distance traveled, D (in miles) as a function of time, t (in hours). (Click on the graph to get a larger version.) a) For each of the intervals, find the values of AD and At between the indicated start and end times. Enter your answers in their respective columns in the table below. Time Interval AD At t = 1.5 to t = 4.5 ? & A ? A t = 1 to t = 3.5 ? & A ? A t = 0.5 to t = 2.5 ? & A ? & A b) Based on your results from (a) it follows that the average rate of change of D is constant, it does not depend over which interval of time you choose. What is the constant rate of change of D? At = ? &. 4 c) Which of the statements below CORRECTLY explains the significance of your answer to part (b)? Select ALL that apply (more than one may apply). O A. It is the total distance the car travels in five hours. O B. It is how far the car will travel in a half-hour. O C. It is the acceleration of the car over the five hour time interval. OD. It is the average velocity of the car over the first two hours. O E. It is the slope of the line. OF. It represents the car's velocity. OG. None of the above6. Practice similar The table below gives the average temperature, T, at a depth d, in a borehole in Belleterre, Quebec. d, depth (m) T, temp (Co) 25 5.50 50 5.20 75 5.10 100 5.10 125 5.30 150 5.50 175 5.75 200 6.00 225 6.25 250 6.50 275 6.75 300 7.00 Evaluate AT/Ad on the following intervals a) 75