The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.) Reaction Braking time distance R B Driver sees Driver applies Car obstacle brakes stops Speed, v 20 40 60 80 100 Reaction Time 8.2 16.7 24.6 Distance, R 33.3 41.9 Braking Time Distance, B 2.0 9. 19.8 35.9 56.2 (a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. R(V) = X (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance time B. B(v) = X (c) Determine the polynomial giving the total stopping distance T. T(V) =(d) Use a graphing utility to graph the functions R, B, and Tin the same viewing window. so an n:- m an an 50 '30 3H0 yin 31' 33 24:- 20 10 10 \"20405030100120 0204061130100120 C9 " 0 " an at- m 7!:- so so an 50 an 3"?! 3! an 30 20 24:- 1o 10 0 020mm301m120 20 40 60 30 100 120 (e) Find the derivative of 7 and the rates of change of the total stopping distance for v = 40, v = 80, and v = 100. T(V) = X