Would a truck that is 12 feet tall and 9 feet wide fit through a parabolic arch that is 15 feet high at the high point and 16 feet wide?
let the vertex be (0,15)
then the equation is
y = ax^2 + 15
the x-intercept is (8,0)
0 = 64a + 15
a = -15/64
y = (-15/64)x^2 + 15
so when x = 4.5 , assuming the truck goes down the middle of the road
y = (-15/64)(4.5^2) + 15
= 10.25
but the truck is 12 ft tall, so it can't pass through the arch
To determine if the truck could fit through the parabolic arch, we need to compare the dimensions of the truck to the dimensions of the arch.
The height of the truck is 12 feet, so we need to check if it can pass through the 15-feet high point of the arch. Since 12 feet is less than 15 feet, the truck should be able to fit in terms of height.
Next, we need to consider the width of the truck, which is 9 feet. The arch is 16 feet wide, so we need to verify if the truck can fit through this width. In this case, since 9 feet is less than 16 feet, the truck should be able to fit in terms of width as well.
Therefore, based on the given dimensions, the truck should fit through the parabolic arch without any issues.