solve it the function h(t)= - 2.5t² + 24t + 6 represents the height, in meters, of the stomp rocket t…

solve it the function h(t)= - 2.5t² + 24t + 6 represents the height, in meters, of the stomp rocket t seconds after it has been launched. when will the rocket reach its maximum height of 63.6 meters? round to three decimal places if necessary. 4.5 seconds edit my response

solve it the function h(t)= - 2.5t² + 24t + 6 represents the height, in meters, of the stomp rocket t seconds after it has been launched. when will the rocket reach its maximum height of 63.6 meters? round to three decimal places if necessary. 4.5 seconds edit my response

Answer

Explanation:

Step1: Identify the function type

The height - function $h(t)=-2.5t^{2}+24t + 6$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-2.5$, $b = 24$, and $c = 6$. The vertex of a quadratic function $y=ax^{2}+bx + c$ gives the maximum (when $a<0$) or minimum (when $a>0$) value. The $t$ - coordinate of the vertex of a quadratic function is given by the formula $t=-\frac{b}{2a}$.

Step2: Substitute the values of $a$ and $b$ into the formula

Substitute $a=-2.5$ and $b = 24$ into $t=-\frac{b}{2a}$. [t=-\frac{24}{2\times(-2.5)}=\frac{24}{5}=4.8]

Answer:

$4.800$ seconds