Finding the a, b, and c of this function?

[voidflux]

Hello everyone, Anyone have any idea's on how I would get started on this problem.

The main span of a certain suspension bridge is horizontal and 1000 feet long. It is suspended
from two main cables hanging between two 400 foot towers, so that these cables just touch the
roadway in the center of the span. The main cables each form a parabolic arc going from the top
of one tower down to the roadway and up to the top of the other tower.
(a) Choose an x-coordinate starting at the left-hand tower and measured in feet along the roadway.
The height of one of the main cables above the roadway is given by a function of the
form ax2 +bx+c (since the curve is a parabola). Find the a, b and c which fit this problem.
(b) The roadway is suspended from the main cables by secondary, vertical cables spaced every
10 feet. Use a definite integral to approximate the total length of the secondary cables on
each side of the bridge.
(c) Estimate the error in this approximation. Do you have any way of getting the exact answer?
(d) Estimate how much cable would be saved on each side of the bridge by putting the secondary
cables every 12.5 feet instead.


Thanks

[da_silvy]

For a

You know it touches the bridge at +500 and it must go thru the point (0, 400)

So:

y = a(x-500)^2

400 = a (-500)^2

.'. y = 1/625(x-500)^2

will give you a graph for the main cables

bbl

gtg

[voidflux]

Thanks alot!

[da_silvy]

For the other parts,

you would antidifferentiate the function describing the wires

then you would calculate the area occupied by one wire in half of one of the support wires

i.e. you would approximate the width of a wire, then use an integral for say [10 to 10.1] or whatever, assuming the wire is .1 feet wide


then you could multiply the result by 4
;o

should work