Find all subgroups of .Z6; /.

2.1 – Tangent and Velocity Problems Tangent line at (2,8) 1. Start from secant lines – (2.5, 2.5 ), (2.1, 2.1 ), (2.01, 2.01 ) 3 2. Find the slope using the slope formula – y -y / x 2x 1 2 1 a. 2.5 – 8 / 2.5 – 2 = 15.25 3 b. 2.1 – 8 / 2.1 – 2 = 12.61 c. 2.01 – 8 / 2.01 – 2 = 12.0601 3. The slopes of the secant lines tend to get closer to 12 as the line get closer to the point (2, 8). a. Tangent line = y – 8 = 12 (x – 2) -> y = 12x – 16 2 A rock is thrown up; the height is given as y = 40t – 16t . (y = feet, t = seconds) 1. Find the Average Velocity Average Velocity -> displacement / time Displacement -> end height – initial height [2, 2.5] [2, 2.1] [2, 2.05] [2, 2.01] y (2.5) – y (2) y (2.1) – y (2) y (2.05) – y (2) y (2.01) -y (2) 2.5 – 2 2.1 – 2 2.05 – 2 2.01 - 2 = -32 ft/s = -25.6 ft/s = -24.18 ft/s = -24.16 ft/s With each set of times I plugged each into the height formula. After that I used the slope formula to determine the displacement. 2. Based on the answers from 1, we may guess the instantaneous velocity at t=2 is -24 ft/s.