contestada

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 15 yards, 30 yards away from the player. A second kick is modeled by $f\left(x\right)=-0.032x\left(x-50\right)$ , where $f$ is the height (in yards) and $x$ is the horizontal distance (in yards). Compare the distances that the footballs travel before hitting the ground.

Respuesta :

Answer:

kick 1 has travelled 15 + 15 = 30 yards before hitting the ground

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

Step-by-step explanation:

1st kick travelled 15 yards to reach maximum height of 8 yards

so, it has travelled 15 + 15 = 30 yards before hitting the ground

2nd kick is given by the equation

y (x) = -0.032x(x - 50)

[tex]y = 1.6 x - 0.032x^2[/tex]

we know that maximum height occurs is given as

[tex] x = -\frac{b}{2a}[/tex]

[tex]y = - \frac{1.6}{2( - 0.032)} = 25[/tex]

and maximum height is

[tex]y = 1.6(25) - 0.032 (25)^2[/tex]

y = 20

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

MrRoyal

The maximum point of a quadratic function is its vertex.

By comparison, the first kick traveled farther than the second kick.

The given parameter is:

[tex]\mathbf{f(x) = - 0.032x(x - 50)}[/tex]

Expand the bracket

[tex]\mathbf{f(x) = - 0.032x^2 + 1.6x}[/tex]

Differentiate the above function

[tex]\mathbf{f'(x) = - 0.064x + 1.6}[/tex]

Equate to 0

[tex]\mathbf{- 0.064x + 1.6 = 0}[/tex]

Collect like terms

[tex]\mathbf{- 0.064x =- 1.6 }[/tex]

Divide both sides by -0.064

[tex]\mathbf{x =25}[/tex]

The above means that: the ball in the second kick traveled 25 yards before hitting the ground

Hence, the first kick traveled farther than the second kick.

Read more about quadratic functions at:

https://brainly.com/question/23094373

Otras preguntas

Q&A Education