Question

An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 4 inches tall and stand 40 inches apart. At some point along the road from the lowest point of the cable, the cable is 0.64 inches above the roadway. Find the distance between that point and the base of the nearest tower.

Answer 1

I might be mistaken, but it looks like there isn't enough information. Based on the information provided--the diagram looks like this.

Answer 2

can someone explain me in words plz

Answer 3

There's enough information. Can more than likely assume the towers are of equal height. Then that's enough to derive the coefficients of the parabola. Then you just take the inverse of it, sort of.

Answer 4

You've got a parabola f(x) = x^2 + ax + b. Where f(40)=f(0)=4, and f(20)=0. Use that to find the coefficients a, b. Now set f(x) = 0.64, and rearrange to find what value of x makes that happen.

Answer 5

a= 4 b=0?

Answer 6

No. f(0) = b = 4.

Answer 7

f(40) = 40^2 + a*40 + b = 40^2 + a*40 + 4 = 4. implies that 1600 + 40 * a = 0. implies that a = -1600 / 40.

Answer 8

the answer I got is -14396