Respuesta :
Answer:
The ball's height is 11 feet at t = 0.19s and t = 1.31s
Step-by-step explanation:
The ball's height h (in feet) after seconds is given by the following function:
[tex]h(t) = 7 + 24t - 16t^{2}[/tex]
Find all values of t for which the ball's height is 11 feet.
This is t when [tex]h(t) = 11[/tex].
We will need to solve a quadratic equation for this.
Solving a quadratic equation
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this problem:
[tex]h(t) = 11[/tex]
[tex]7 + 24t - 16t^{2} = 11[/tex]
[tex]16t^{2} - 24t + 4 = 0[/tex]
Simplifying by 4
[tex]4t^{2} - 6t + 1 = 0[/tex]
So [tex]a = 4, b = -6, c = 1[/tex]
[tex]\bigtriangleup = (-6)^{2} - 4*(4)*1 = 20[/tex]
[tex]x_{1} = \frac{-(-6) + \sqrt{20}}{2*4} = 1.31[/tex]
[tex]x_{2} = \frac{-(-6) - \sqrt{20}}{2*4} = 0.19[/tex]
The ball's height is 11 feet at t = 0.19s and t = 1.31s
