Q:

The arch of the Gateshead Millennium Bridge forms a parabola with equation: y= -0.016(x-52.5)²+45 where x is the horizontal distance (in meters) from the arch’s left end and y is the distance (in meters) from the base of the arch. What is the width of the arch?

Accepted Solution

A:
Answer:   about 106 metersStep-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 . . . . metersThe width of the arch at ground level is about 106 meters.