Question

Abrocket isnlaunched 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 the equation, find out the time at which yhe rocket will reach its max, to the nearest 100th of a second y=-16x² + 163x + 138

Answer 1

The rocket reaches its maximum height at approximately 5.09 seconds, which is found by calculating the vertex of the parabolic equation representing the rocket's height over time.

Step-by-step explanation:

To find the time at which the rocket will reach its maximum height, we consider the quadratic equation that represents the height y of the rocket as a function of the time x after launch, which is y = -16x² + 163x + 138. The time at which the rocket reaches its maximum height corresponds to the vertex of the parabola represented by this equation. The vertex of a parabola in the form of y = ax² + bx + c is located at the time x = -b/(2a). Substituting the values from our equation, we get x = -163/(2(-16)) which equals 5.09375 seconds. Therefore, the rocket reaches its maximum height at approximately 5.09 seconds to the nearest hundredth of a second.