Question

The quadratic function d= -4x+1,100 models a snowboarder's distance, in feet, from the bottom of a hill x seconds after the snowboarder starts moving down the hill. After how many seconds is the snowboarder 100 ft from the bottom of the hill?

Answer 1

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:

$d=-4x^2+1100$

Final position of the snowboarder is $d=100\ ft$

Now, plugging in 100 for 'd' and solving for 'x', we get:

$100=-4x^2+1100$

Adding -1100 both sides, we get:

$100-1100=-4x^2+1100-1100\\-1000=-4x^2$

Dividing both sides by -4, we get:

$\frac{4x^2}{4}=\frac{1000}{4}\\x^2=250$

Taking square root and neglecting the negative root as time can't be negative. So,

$\sqrt{x^2}=\sqrt{250}\\x=5\sqrt{10}=15.8\ s\approx 16\ s$

Therefore, after 16 seconds, the snowboarder will be at a distance of 100 ft from bottom of hill.