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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
maximum height reached by the rocket, to the nearest tenth of a foot.
y = -16x2 + 119x + 73

Respuesta :

mhanifa

Answer:

  • 294.3 ft

Step-by-step explanation:

Given function

  • y = -16x^2 + 119x + 73

This is quadratic function  

It reaches the maximum value at vertex, which is calculated by the formula:

  • x = -b/2a

Substituting values

  • x = -119/2*(-16) = 3.71875

y-value of same point is

  • y = -16*3.71875^2 + 119*3.71875 + 73 = 294.265625  ≈ 294.3 ft

So maximum height is 294.3 ft

DarlinEsteves

The equation we have is:

[tex]y = { - 16x}^{2 } + 119x + 73[/tex]

This is equation of a parabola that opens down.

To find the maximum point or the maximum height, we need to find the vertex of the parabola.

First, let's define variables:

A will be the coefficient of the x squared.

b is the coefficient of the x and

C is the independent term:

[tex]a = - 16 \\ b = 119 \\ c = 73[/tex]

The vertex of will have the following x coordinate:

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

Substituting the values of a and b:

[tex]x = - \frac{119}{2( - 16)} [/tex]

Solving the operations:

[tex]x = - \frac{119}{ - 32 } \\ x = 3.71875[/tex]

The next step is to substitute this x value into our equation to find the maximum height y:

[tex]y = { - 16x}^{2} + 119x + 73 \\ \\ substituting \: x = 3.71875 \\ \\ y = - 16(3.71875)^{2} + 119(3.71875) + 73[/tex]

Solving the operations:

[tex]y = - 16(13.8291) + 442.49555 + 73 \\ \\ y = 294.23[/tex]

Rounding to the nearest tenth (1 decimal place)

y=294.2

Answer: 294.2 feet.

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