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?\n2.45\n3.16\n5.48\n7.07

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?\n2.45\n3.16\n5.48\n7.07

Answer

Explanation:

Step1: Set up the equation

We know that $f(x)=50$, so we set $-5x^{2}+200 = 50$.

Step2: Rearrange the equation

Subtract 200 from both sides: $-5x^{2}=50 - 200=-150$.

Step3: Solve for $x^{2}$

Divide both sides by - 5: $x^{2}=\frac{-150}{-5}=30$.

Step4: Solve for $x$

Take the square - root of both sides. Since $x$ represents time, we consider the positive root only. So $x=\sqrt{30}\approx5.48$.

Answer:

5.48