Respuesta :
Answer:
The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]Explanation:
The function of the ball's height h (in meters) is given as;
[tex]h=3+30t-5t^2[/tex]the value of time t for which the ball's height is 13 meters, can be derived by substituting h=13 into the function of h.
[tex]\begin{gathered} h=3+30t-5t^2 \\ 13=3+30t-5t^2 \\ 3+30t-5t^2=13 \end{gathered}[/tex]subtract 13 from both sides and solve the quadratic equation;
[tex]\begin{gathered} 3+30t-5t^2-13=13-13 \\ -5t^2+30t-10=0 \end{gathered}[/tex]solving the quadratic equation, using the quadratic formula;
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ t=\frac{-30\pm\sqrt{30^2-4\times-5\times-10}}{2\times-5} \\ t=\frac{-30\pm\sqrt{900-200}}{-10} \\ t=\frac{-30\pm\sqrt{700}}{-10} \\ t=0.3542=0.35 \\ or \\ t=5.64575=5.65 \end{gathered}[/tex]The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]