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

Answer:

10

Explanation:

The bridge makes contact with the bank at a height of 4 meters, meaning the contact is made at y= 4; therefore, we have

$-0.1(x-5)^2+12=4$

Subtracting 12 from both sides gives

$-0.1(x-5)^2=-8$

Dividing both sides by -0.1 gives

$(x-5)^2=80^{}$

Taking the square root of both sides gives

$x-5=\pm\sqrt[]{80}$

Adding 5 to both sides gives

$x=\pm\sqrt[]{80}+5$$\begin{gathered} x_1=-\sqrt[]{80}+5 \\ x_2=\sqrt[]{80}+5 \end{gathered}$

The distance between the two banks is, therefore,

$x_2+x_1$$=(\sqrt[]{80}+5)+(-\sqrt[]{80}+5)$$=10.$

Hence, the distance between the two banks is 10m.