Question 1181355: The diagram shows a suspension bridge with a center span of 4200 ft. and a tower height of
500 ft. with the lowest part of the suspender 10 ft. above the base of the bridge. Write an
equation to represent the curve of the suspender with h, the tower height from the base of the
bridge, in ft. as a function of d, the horizontal distance from the center of the bridge, in ft.,
assuming that the suspender is symmetrical in shape.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The topic you chose was quadratic equations; in the text of your message you only said that the suspender is symmetrical in shape.
A parabola is symmetrical, so forming a quadratic equation from the given information makes sense.
Note, however, that a suspender hanging freely from two towers does NOT form a parabola -- it forms a catenary. Equations of catenaries are far more complicated than equations of parabolas.
So I will outline a process for finding the equation of a parabola that satisfies the given conditions -- assuming that is what you were asked to do.
The vertex of the parabola is 10 feet above the roadway. 2100 feet either direction from the center of the span, the parabola passes through a point 500 feet above the roadway, which is 490 feet above the vertex.
The equation for the height of the suspender above the roadway, as a function of the distance from the center of the bridge, is then rather simple in vertex form: y = ax^2+10.
Use the point (2100,490) to find the value of the constant a.
I leave it to you to do that little bit of work to finish finding the equation.
|
|
|
