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A player throws a basketball toward a hoop. The basketball follows a parabolic path that can be modeled by the equation y = - 0.125x^2 + 1.84x + 6. If the center of the hoop is located at (12, 10), will the ball pass through the hoop?

Respuesta :

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  1. in this exercise you  must substitute the value of  of x = 12  in the equation of the parable given, if the result is 10 then the ball pass through the hoop
  2. Y = (-.125)(12)^2+ (1.84)(12)+6 = -18+22.08+6 = 10.06≅10 , of  this form it is demonstrated, that the ball pass through the  hoop

Answer:

Since [tex]f(12) = 10[/tex], the ball is going to pass through the hoop.

Step-by-step explanation:

We have the following function.

[tex]f(x) = -0.125x^{2} + 1.84x + 6[/tex].

If the center of the hoop is located at (12, 10), will the ball pass through the hoop?

This is going to happen if [tex]f(12) = 10[/tex]. We have to apply f(12) in the equation and verify the result. So:

[tex]f(x) = -0.125x^{2} + 1.84x + 6[/tex].

[tex]f(12) = -0.125*12^{2} + 1.84*12 + 6 = 10[/tex].

Since [tex]f(12) = 10[/tex], the ball is going to pass through the hoop.

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