SOLUTION: a suspension has two towers that rise 500 feet above the road and connected by cable that hang in the shape of the parabola that can be represented by y=1/8960(x-2100)^2+8, where x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a suspension has two towers that rise 500 feet above the road and connected by cable that hang in the shape of the parabola that can be represented by y=1/8960(x-2100)^2+8, where x      Log On


   

Question 970721: a suspension has two towers that rise 500 feet above the road and connected by cable that hang in the shape of the parabola that can be represented by y=1/8960(x-2100)^2+8, where x and y are measured in feet and x is the distance from the left tower in the direction of the right tower. what is the distance between the two towers?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=500 at two different values of x.

y=%281%2F8960%29%28x-2100%29%5E2%2B8=500

%28x-2100%29%5E2=%28-8%2B500%29%2A8960

%28x-2100%29%5E2=492%2A8960

%28x-2100%29%5E2=+2%5E2%2A3%2A41%2A2%5E8%2A5%2A7

%28x-2100%29%5E2=2%5E10%2A3%2A5%2A7%2A41

x-2100=0%2B-+2%5E5%2Asqrt%283%2A5%2A7%2A41%29

x-2100=0%2B-+32sqrt%284305%29

x=2100%2B-+32sqrt%284305%29
Distance between these two x values:
%282100%2B32sqrt%284305%29%29-%282100-32sqrt%284305%29%29
highlight%2864%2Asqrt%284305%29%29

further computing, 64%2A65.6125=highlight%284199.2%29 depending on the accuracy you are allowed.