A suspension bridge with weight uniformly distributed along its length has twin towers that extend 75 meters above the road surface and are 400 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 100 meters from the center.

Let take the center of bridge as our origin (0,0). Parabola having vertex at origin is represented by y=a.x^2

At the right far end or +ive x-axis side we've x=200 and y=75 , so a=75/(200^2)=0.001875

Y

Parabola equation y=0.001875*x^2

Height of cable from 100m from centre. Y=? ,X=100m

Y=0.001875*(100^2)

Y=18.75 m

Height of ropes at 100m from the center of bridge.

Please don't forget to rate

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

it has the same slope and a different y-intercept

hope this : )