Answer:
6 ft
Step-by-step explanation:
Since the shape of the cables on the bridge are to open up, the standard equation of the parabola produced is given as:
(x - h)² = 4p(y - k)
Where (h, k) is the vertex and focus is at (h, k+p)
From the question, the point (0, 2) is the vertex and point (50, 27) lie on the parabola. Hence:
(x - 0)² = 4p(y - 2)
x² = 4p(y - 2).
Sinc the tower is 100 ft apart and 27 ft height, hence the point 100/2 = 50 ft and 27 ft lie on the parabola
To find p, use (50, 27)
50² = 4p(27 - 2)
2500 = 4p(25)
100p = 2500
p = 25
hence:
x² = 4(25)(y - 2)
x² = 100(y - 2)
At a point of 20 feet (i.e x = 20), y is the height of the cable, hence:
20²=100(y-2)
400 = 100y - 200
100y = 600
y = 6
The height is 6 ft at a point of 20 ft
