Question

The shape of a dome can be modeled by the equation h=2dsquared +100 when h issue height (in feet) of the dome from the floor d feet from its center. How far from the center of the domes is the height 50 feet?

Answer 1

Given that,

The shape of a dome can be modeled by the equation :

$h=2d^2+100$ ....(1)

h is the height of the dome

d is distance from its center

We need to find the distance from the center of the dome if the height is 50 feet. Put h = 50 in equation (1)

$50=2d^2+100\\\\2d^2=100-50\\\\2d^2=50\\\\d^2=25\\\\d=5\ \text{feet}$, neglecting d = -5 feet (as height can't be negative)

So, at a distance of 5 feet from the center of domes the height is 50 feet.