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Sagot :
The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.
A function is defined as a expression containing one or more variables.
Technically speaking, a function is a means of linking a set of inputs to a set of outputs.
The height of the ball at any time t is given by the function:
[tex]h(t)=-16t^2+38t+2[/tex]
Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.
Let us substitute the values:
[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]
This is in the form of a quadratic equation in t.
Solving by using the quadratic formula:
We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Therefore for the above quadratic equation:
[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]
Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.
To learn more about functions:
https://brainly.com/question/12431044
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