the quadratic model $f(x) = -5x^2 + 200$ represents the approximate height, in meters, of a ball $x$ seconds…

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?\n 2.45\n 3.16\n 5.48\n 7.07

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?\n 2.45\n 3.16\n 5.48\n 7.07

Answer

Explanation:

Step1: Set up the equation

We know the height function is ( f(x)= - 5x^{2}+200), and we want to find ( x ) when ( f(x) = 50). So we set up the equation: (50=-5x^{2}+200)

Step2: Solve for (x^{2})

Subtract 200 from both sides of the equation: (50 - 200=-5x^{2}) (- 150=-5x^{2}) Divide both sides by - 5: (x^{2}=\frac{-150}{-5}=30)

Step3: Solve for (x)

Take the square root of both sides. Since (x) represents time (in seconds) and it should be positive, we consider the positive square root: (x = \sqrt{30}\approx5.48) (we ignore the negative root because time cannot be negative in this context)

Answer:

5.48