the middle span of a bridge is supported by cables from two towers 4200 feet apart. the tops of the towers are 500 feet above the roadway. assuming that the cables are parabolic and are at road level halfway between the towers, find the height of the cables 1000 feet from the center of the bridge, rounded to the nearest foot.
+130466 OK...we have a parabola here, and where it touches the roadway, we can just call that point the "origin," i.e., (0,0)
So...we have this equation
y = ax2
And we know that when x= 2100, y = 500 .... and we need to solve for "a"
So we have
500 = a (2100)2
a = 500 / (2100)2 = 1 / 8820
So we have , when x = 1000
y = (1 / 8820) (1000)2 ≈ 113 ft.
+130466 OK...we have a parabola here, and where it touches the roadway, we can just call that point the "origin," i.e., (0,0)
So...we have this equation
y = ax2
And we know that when x= 2100, y = 500 .... and we need to solve for "a"
So we have
500 = a (2100)2
a = 500 / (2100)2 = 1 / 8820
So we have , when x = 1000
y = (1 / 8820) (1000)2 ≈ 113 ft.
