Question

The arch of the Gateshead Millennium Bridge forms a parabola with equation:

Answer 1

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.