Answer:
Point A is approximately 4 unit above the ground.
Step-by-step explanation:
A bridge on a river is modeled by the equation h = -0.2d² + 2.25d -------(1)
Where h is the height and d is the horizontal distance.
For cleaning and maintenance purpose a worker wants to tie a taut a rope on two ends of the bridge so that he can slide on the rope.
The rope is at an angle defined by the equation
-d + 6h = 21.77
d - 6h = -21.77
d = 6h - 21.77 -------(2)
Now we have to find the value of h which is the distance from the ground level.
Now we substitute d from equation 2 to equation 1
h = -0.2(6h - 21.77)²+ 2.25(6h - 21.77)
h = -0.2(36h²+ 473.9329 - 261.24h) + 13.5h - 48.9825
h = -(7.2h² + 94.79 - 52.25h) + 13.5h - 48.98
h = -7.2h² - 94.79 + 52.25h + 13.5h - 48.98
h = -7.2h² + 65.75h - 143.77
0 = -7.2h² + 65.75h - h - 143.77
0 = -7.2h² + 64.75h - 143.77
7.2h²- 64.75h + 143.77 = 0
Now we divide the equation by 7.2
h² - 9h + 20 = 0
h² - 5h - 4h + 20 = 0
h(h - 5) - 4(h - 5) = 0
(h - 4)(h - 5) = 0
h = 4 or 5
Therefore, point A is approximately 4 unit above the ground.