The parabolic arch of a bridge over a one-way road can be described by the equation y = -x^2 + 6, where x and y ar emeasured in metres. A transpor truck is 3m wide and 3.5m high. What is the maximum clearance of the truck's top corners if it passes under the bridge?

Question

anonymous · Answer

This is an Optimization problem.

dumbcow · Answer

so you want the max distance from the top corner of truck to arch ??

dumbcow · Answer

distance from top center of arch to top corner of truck is 2.915 m

anonymous · Answer

Yes
How were you able to work that out?

dumbcow · Answer

d^2 = 2.5^2 + 1.5^2

anonymous · Answer

How did you come to this equation?

dumbcow · Answer

truck is 3.5m so vertical distance from top is (6-3.5) = 2.5
truck is 3m wide, 1.5m on either side of center line
imagine a triangle formed from right side of top of truck to top center of arch
d is hypotenuse and is the longest distance from arch to truck top corner