Answer:
The horizontal location, from the starting point at which the ball first bounces = 7.5
Step-by-step explanation:
The equation representing LaToya's throw y = -0.6·x² + 4·x + 11
The equation that represent the path of the bridge y = -0.1·x + 8
Where;
x = The horizontal location
y = The vertical location
The location where the ball bounces is given by the common solution of both equations as follows;
-0.6·x² + 4·x + 11 = -0.1·x + 8
-0.6·x² + 4·x + 11 - (-0.1·x + 8) = 0
-0.6·x² + 4·x + 11 + 0.1·x - 8 = 0
-0.6·x² + 4.1·x + 3 = 0
Which gives;
-0.6/(-0.6)·x² + 4.1/(-0.6)·x + 3/(-0.6) = 0
Which gives;
x² - 41/6·x - 5 = 0
By the quadratic formula, we have;
x = (41/6 ± √((-41/6)² - 4× 1 × (-5)))/(2 × 1)
x = 7.5 or x = -2/3
Therefore;
The horizontal location, from the starting point at which the ball first bounces, x = 7.5.
