Question

Civil engineers are designing a section of road that is going to dip below sea level. The road's curve can be modeled by the equation y = 0.00005x2 - 0.06x, where x is the horizontal distance in feet between the points where the road is at sea level and y is the elevation. The engineers want to put stop signs at the locations where the elevation the road is equal to sea level. At which horizontal distances will they place the stop signs?

Answer 1

1200feet

Explanation:

Given the the road's curve elevation modeled by the equation

y = 0.00005x^2 - 0.06x,

x is the horizontal distance in feet between the points where the road is at sea level and;

y is the elevation

The elevation the road is equal to sea level when y = 0

Substitute y = 0 into the equation and calculate x;

0 = 0.00005x^2 - 0.06x

0.06x = 0.00005x^2

0.06 = 0.00005x

x = 0.06/0.00005

x = 1200 ft

Hence they will place the stop sign at a horizontal distance of 1200feet