Answer :
The time interval between which the ball will be 15 feet above the ground is from 0.4594 seconds to 2.04 seconds.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The solutions of a quadratic equation can be found using the formula,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Given that the height of a tennis ball tossed into the air is modelled by h(x)=40x – 16x², where x is elapsed time in seconds.
Now, the time interval will the tennis ball be at least 15 feet above the ground is,
h(x) = 40x – 16x²
Substitute the height of the ball as 15 feet,
h(x) = 40x – 16x²
16x² - 40x + 15 = 0
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2 - 4(16)(15)}}{2(16)}\\\\[/tex]
x = 2.04056, 0.4594
Therefore, the time interval between which the ball will be 15 feet above the ground is from 0.4594 seconds to 2.04 seconds.
Learn more about Solutions of a Quadratic Equation:
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