Answer:
about 106 meters
Step-by-step explanation:
The difference in x-values when y=0 is found by solving ...
0 = -0.016(x -52.5)² +45
-45 = -0.016(x -52.5)² . . . . . . subtract 45
45/0.016 = (x -52.5)² . . . . . . . divide by the coefficient of the squared term
±√2812.5 = x -52.5 . . . . . . . . take the square root
x = 52.5 ±√2812.5 . . . . . . . . .add 52.5. These are the x-values where y=0.
So, the difference in x-values at y=0 is ...
(52.5 +√( )) - (52.5 -√( )) = 2√2812.5 ≈ 106.07 . . . . meters
The width of the arch at ground level is about 106 meters.
