Cable Vertex
Cable Vertex
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if a bridge rises about 650 feet above the cener of the road bed. The length of the main span is 4260 feet. Cables are attached to for a parabola whos vertex is at its height. The vertex is a t the origin.
give the equation of the parabola
I will give you ten points if you can give me an answer
This is a tenth grade problem
by the way Andy C if i knew how to do it i wouldn't be asking
In Cartesian coordinates, a parabola with an axis parallel to the y axis with vertex (h, k), focus (h, k + p), and directrix y = k - p, with p being the distance from the vertex to the focus, has the equation with axis parallel to the y-axis
4p(y-k) = (x-h)^2
We know that the vertex is at the origin so h and k are zero
4py=x^2
Assuming you mean that the top of the cables are 650' above the road then y=650
x would be half the span or 2130 feet.
So the coordinates of the cable ends would be
(-2130,650) and (2130,650)
solve for p
p=2130^2/4*650
p=1745 ( nearest foot)
The equation of the parabola is
x^2=4py
x^2=6980y for a cable supported bridge. Vetex at the lowest point of the cables.
If as you say the vetex is at the bridge height, then you can't use cables but the equation would be
x^2= -6980y
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kx125 2003 sound check & walk around
