x = 3
-2 | 2.2(3) - 3.3 | = -6.6
-2 | 6.6 - 3.3 | = -6.6
-2 | 3.3 | = -6.6
-2 * 3.3 = -6.6
-6.6 = -6.6
We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.
The given road capacity is 3,500 vehicles per hour, and the expected number of vehicles arriving is 14,000. To calculate the time required for these vehicles to access the arena:
14,000 vehicles divided by 3,500 vehicles per hour equals 4 hours.
If the event is scheduled to commence at 7 p.m., the roads should close at: 7 p.m. minus 4 hours, which results in 3 p.m.
