Question

Engineers built an arch bridge across a river. The arch bridge makes a parabola shape that has the equation y = -0.1(x - 5)' + 12 where I and y are measured in meters. If the bridge makes contact with both banks at a height of 4 meters, how long is the distance between the two banks of the river where the bridge is? Round your answer to the nearest whole number. meters

Answer 1

The distance between the two banks of the river where the bridge is is approximately 9 meters.

Step-by-step explanation:

The equation of the parabolic shape of the arch bridge is y = -0.1(x - 5)² + 12. We know that the bridge makes contact with both banks at a height of 4 meters. To find the distance between the two banks of the river, we need to determine the horizontal distance where the bridge is at a height of 4 meters.

Setting y equal to 4 in the equation, we get 4 = -0.1(x - 5)² + 12. Solving for x, we have:

4 = -0.1(x - 5)² + 12

-8 = -0.1(x - 5)²

80 = (x - 5)²

(x - 5)² = 80

x - 5 = ±√80

x = 5 ± √80

x ≈ 9.24, 0.76

The distance between the two banks of the river where the bridge is is approximately 9 meters.