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A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after t seconds is given by the following.

h=7+23t-16t^2

Find all values of t for which the ball's height is 15 feet.

Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Respuesta :

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0.85 and 0.59:

You get the quadratic equation: [tex]-16t^2+23t-8[/tex]

You can solve it with the quadratic equation: [tex] \frac{-b+ \sqrt{b^2-4ac}}{2a} and \frac{-b- \sqrt{b^2-4ac}}{2a}[/tex]

From here you solve and get the given numbers as your answers!

As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).

What is a quadratic equation?

"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."

Given, [tex]h = 15[/tex] feet.

Therefore, the quadratic equation for [tex]h = 15[/tex] will be:

A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.

The ball's height h (in feet) after t seconds is:

[tex]h = 7+23t-16t^{2}[/tex]

[tex]15 = 7+23t-16t^{2}[/tex]

⇒ [tex]15-7-23t+16t^{2} = 0[/tex]

⇒ [tex]16t^{2} -23t - 8 = 0[/tex]

⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)

⇒ [tex]t =[/tex] [23 ± 1041]/32

⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32

⇒ [tex]t =[/tex] 33.25, - 31.813

Learn more about a quadratic equation here: https://brainly.com/question/2263981

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