Question

As a decoration for a school dance, the student council creates a parabolic arch with balloons attached to it. The shape of the arch is modeled by the equation y=|5 xl.Can a student who is 6 feet 6 inches tall walk through the arch without ducking?

Answer 1

Yes, a student who is 6 feet 6 inches tall can walk through the arch without ducking.

Step-by-step explanation:

The shape of the arch is modeled by the equation y=|5x|. To determine if a student who is 6 feet 6 inches tall can walk through the arch without ducking, we need to substitute the student's height into the equation and check if it exceeds the height of the arch at any point.

First, convert the student's height to inches: 6 feet 6 inches = 78 inches. Substitute x=78 into the equation: y=|5(78)|=|390|=390.

Since the maximum height of the arch is 390 inches, which is greater than the student's height of 78 inches, the student can indeed walk through the arch without ducking.