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NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=-4.9t2+64t+136.
The rocket will reach its peak height of 345 meters above sea level at _____ second

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Using the vertex of the quadratic equation, it is found that:

The rocket will reach its peak height of 345 meters above sea level at 6.53 seconds.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$$y = ax^2 + bx + c$$

The vertex is given by:

$$(x_v, y_v)$$

In which:

$$x_v = -\frac{b}{2a}$$

$$y_v = -\frac{b^2 - 4ac}{4a}$$

Considering the coefficient a, we have that:

- If a < 0, the vertex is a maximum point.

- If a > 0, the vertex is a minimum point.

In this problem, the equation is given by:

h(t) = -4.9t² + 64t + 136.

The coefficients are a = -4.9 < 0, b = 64, c = 136, hence the instant of the maximum height is given by, in seconds:

$$t_v = -\frac{64}{2(-4.9)} = 6.53$$

More can be learned about the vertex of a quadratic equation at

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