4.46
1) Note that this quadratic model describes a parabola that opens down.
We need to find the zeroes of this quadratic equation.
2) So, we can write down the following:
[tex]\begin{gathered} -13x^2+65x=0 \\ \\ -13x^2+65-65=0-65 \\ \\ -13x^2=-65 \\ \\ \frac{-13x^2}{-13}=\frac{-65}{-13} \\ \\ x^2=5 \\ \\ x=\pm\sqrt{5} \end{gathered}[/tex]
Note that the square root of five is approximately 2.23. We can pick the second root and subtract from that the first root
[tex]\begin{gathered} t=|-2.23-2.23| \\ t=|4.46| \\ t=4.46 \end{gathered}[/tex]
3) Thus, we can tell that the ball has been flying for approximately 4.46 seconds.
