Answer:
16 seconds (Approximately)
Step-by-step explanation:
Given:
The function that gives the distance of snowboarder from the bottom of hill with time 'x' is:
[tex]d=-4x^2+1100[/tex]
Final position of the snowboarder is [tex]d=100\ ft[/tex]
Now, plugging in 100 for 'd' and solving for 'x', we get:
[tex]100=-4x^2+1100[/tex]
Adding -1100 both sides, we get:
[tex]100-1100=-4x^2+1100-1100\\-1000=-4x^2[/tex]
Dividing both sides by -4, we get:
[tex]\frac{4x^2}{4}=\frac{1000}{4}\\x^2=250[/tex]
Taking square root and neglecting the negative root as time can't be negative. So,
[tex]\sqrt{x^2}=\sqrt{250}\\x=5\sqrt{10}=15.8\ s\approx 16\ s[/tex]
Therefore, after 16 seconds, the snowboarder will be at a distance of 100 ft from bottom of hill.
