Question

You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y  0.000495x 2  0.619x where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? a. The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 625.25 ft b. The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 1250.51 ft c. The bridge is about 1250.51 ft above the river and the length of the bridge above the arch is about 193.52 ft d. The bridge is about 1250.51 ft above the river and the length of the bridge above the arch is about 625.25 ft

Answer 1

Answer:

The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 1250.51 ft

Step-by-step explanation:

  The arch is represented by the equation

y = -  .000495 x² + .619 x where x and y are in ft .

We can write this equation in the form

y = - a x² + bx

The vertex is on the line

x = b / 2a

= .619 / 2 x  .000495

= 625.25

Putting the value in the equation above

y =  -  .000495 ( 625.25)²

= 193.51 ft

This value will give us the depth of river .

To know the width of bridge we shall have to solve the quadratic equation

-  .000495 x² + .619 x = 0

x = [- .619 ± √ ( .619)² - 0] / 2 x .000495

= - .619 + 625.25 and

x = - .619 - 625.25

Difference = 625.25 x 2 = 1250 .51 ft.

So the width of the bridge will be 1250 .51 ft .