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Alice was sitting on a dock looking at a lake. She picked up a stone and through it in the air and out

toward the lake. It seemed like it was in the air for a long time. The equation that can be used to

model the height of the stone (in feet) as it relates to the time in the air in seconds) is given by

h(t) = 5 + 50 - 16t2. In order to solve for how long the stone was in the air, Alice will need to use the

quadratic equation which is:

|-bb4ac

2a

X

Respuesta :

A quadratic equation is in the form of ax²+bx+c. The time for which the stone was in the air is 3.526.

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.

As the height of the stone will be zero or can say that the stone will be at the ground in only two conditions. When the stone will be just thrown and when the stone will complete its flight. Therefore, we can substitute the value of heigh h in the function as 0 to get those two timings.

[tex]h(t) = 5 + 50t - 16t^2\\\\0 = 5+50t - 16t^2[/tex]

Substitute the quadratic equation in the formula of the root of the quadratic function,

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-50\pm\sqrt{(50)^2-4(-16)(5)}}{2(-16)}\\\\t= -0.089, 3.526[/tex]

Hence, the time for which the stone was in the air is 3.526.

Learn more about Quadratic Equations:

https://brainly.com/question/2263981

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