Answer:
5 feet
Step-by-step explanation:
We are told that the height of the dome can be modelled by the equation:
[tex]\boxed{h = -2d^2 + 100}[/tex]
The question is essentially asking us: for what value of d will the value of h be 50 feet?
To solve this, we have to substitute h in the equation with 50 and then solve for d.
∴ [tex]50 = -2d^2 + 100[/tex]
⇒ [tex]50 + 2d^2 + 100[/tex]
⇒ [tex]2d^2 = 100 - 50[/tex]
⇒ [tex]d^2 = \frac{100 - 50}{2}[/tex]
⇒ [tex]d^2 = 25[/tex]
⇒ [tex]d = \sqrt{25}[/tex]
⇒ [tex]d = \bf 5[/tex]
This means that 5 feet from the center of the dome, the height of the dome is 50 feet.
