Question

The quadratic model f(x)=-5x^2 +200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds
2.45
3.16
5.48
7.07

Answer 1

Answer:

Third option: 5.48

Step-by-step explanation:

Given the quadratic  model that represents the approximate height in meters of the ball $f(x)=-5x^2 +200$. the time in seconds x, when the ball is 50 meters from the ground can be calculated by substituting $f(x)=50$ and solving for x.

Then:

$50=-5x^2 +200$

Subtract 200 from both sides:

$-200+50=-5x^2 +200-200\\-150=-5x^2$

Divide both sides by -5:

$\frac{-150}{-5}=\frac{-5x^2}{-5}\\30=x^2$

Apply square root to both sides:

$\sqrt{30}=\sqrt{x^2}\\\sqrt{30}=x\\5.48=x$

The ball is 50 meters from the ground after about 5.48 seconds.