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pshichka [43]
2 years ago
6

1. The height of a missile t seconds after it has been fired is given by h=4.9t^2+44.1t. How many seconds will it take for the r

ocket to reach its greatest height?​
Mathematics
1 answer:
asambeis [7]2 years ago
7 0

Answer:

The rocket will take 4.5 seconds to reach its maximum height.

Step-by-step explanation:

The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t

This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0

To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply: x=\frac{-b}{2*a}. The y coordinate of the vertex corresponds to the function evaluated at that point.

In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:

t=\frac{44.1}{2*(-4.9)}

t=4.5

<u><em>The rocket will take 4.5 seconds to reach its maximum height.</em></u>

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