Mathematical Analysis Of Pool Table Geometry And Tangent/Normal Line Calculations

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Mathematical Analysis of Pool Table Geometry and Tangent/Normal LineCalculations1)Since the pool table is 3.8 feet wide, the pocket to the right of the origin is located at thepoint (1.9,0).From the first diagram, it is easily determined thatthe pocket above the origin is located atthe point (0,1.6)This gives us two equations that we can solve for a and b.0 = b–a(1.9)21.6 = b–a(0)2The second equation immediately yields the result b = 1.6.Solving the first equation for a gives0 = 1.6–a(1.9)2a = 0.4432The equation of the parabola is then:y = 1.6–0.4432x22)The slope of the line is defined as change in y divided by change in x. This becomes:(1.6–0.4432p2–0) / (p–0)(1/p)(1.6–0.4432p2)3)To find the slope of thetangentline, take the derivative of the function.slopetangent line= y’ =-0.8864p

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