9. The descent of a roller coaster starts at the maximum point of a parabola whose...

  

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9. The descent of a roller coaster starts at the maximum point of a parabola whose equation is y = 100 - 1x and ends along the horizontal line y = 0. In order to make the ride smooth, a section of track following the graph of the function y = a(x - 40) is added as a transition from the parabola to the line. 100 a. b 20 40 Determine the value for a which makes the ride from the top to the end along the horizontal line smooth, that is, continuous and differentiable at the transition point x = b. b. At what point do the two parabolas meet? What is the slope at this point? 9. The descent of a roller coaster starts at the maximum point of a parabola whose equation is y = 100 - 1x and ends along the horizontal line y = 0. In order to make the ride smooth, a section of track following the graph of the function y = a(x - 40) is added as a transition from the parabola to the line. 100 a. b 20 40 Determine the value for a which makes the ride from the top to the end along the horizontal line smooth, that is, continuous and differentiable at the transition point x = b. b. At what point do the two parabolas meet? What is the slope at this point?