A soccer ball is klcked and can be modeled by . When will the ball be at or above 20 feet?

Ask by Rodriquez French. in the United States

Jan 24,2025

Question

A soccer ball is klcked and can be modeled by $$ y=-16 x^{2}+36 x $$. When will the ball be at or above 20 feet? $$ \square] $$

UpStudy AI · Accepted Answer

To find when the soccer ball will be at or above 20 feet, we need to solve the inequality $$ y \geq 20 $$ using the given equation $$ y = -16x^2 + 36x $$.

First, substitute $$ y = 20 $$ into the equation:
$$ 20 = -16x^2 + 36x $$

Now, we need to solve this quadratic inequality. Let's solve it step by step.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$20=-16x^{2}+36x$$
- step1: Swap the sides:
  $$-16x^{2}+36x=20$$
- step2: Move the expression to the left side:
  $$-16x^{2}+36x-20=0$$
- step3: Factor the expression:
  $$-4\left(x-1\right)\left(4x-5\right)=0$$
- step4: Divide the terms:
  $$\left(x-1\right)\left(4x-5\right)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&4x-5=0\&x-1=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&x=\frac{5}{4}\&x=1\end{align}$$
- step7: Rewrite:
  $$x_{1}=1,x_{2}=\frac{5}{4}$$
The solutions to the quadratic equation $$20 = -16x^2 + 36x$$ are $$x = 1$$ and $$x = \frac{5}{4}$$ or $$x = 1.25$$.

Therefore, the soccer ball will be at or above 20 feet when $$x$$ is between 1 and 1.25.

So, the ball will be at or above 20 feet when $$1 \leq x \leq 1.25$$.
The soccer ball will be at or above 20 feet when $$1 \leq x \leq 1.25$$.

A soccer ball is klcked and can be modeled by . When will the ball be at or above 20 feet?

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