A volleyballis served by a 6-foot player at an initial upward velocity of 33 feet per second. The
situation is modeled by the equation h 16t2 33t + 6 h representing the height in feet
and t representing the time in seconds. Using this equation, define the domain of the ball when
it reaches its maximum height.
○ 1.03 seconds
-1.03 seconds
O122 seconds
23.01 feet
To find the domain of the ball when it reaches its maximum height, we need to find the values of t that make the equation valid.
The height of the ball can be represented by the equation h(t) = 16t^2 + 33t + 6.
To find the maximum height of the ball, we need to find the highest point on the graph of the equation, which occurs at the vertex of the parabolic shape.
The x-coordinate of the vertex is given by the formula t = -b/2a, where a, b, and c are the coefficients of the equation in the form ax^2 + bx + c.
In this case, a = 16 and b = 33. Plugging these values into the formula, we get:
t = -33/(2*16) = -33/32 = -1.03
Therefore, the ball reaches its maximum height at t = -1.03 seconds.
Since time cannot be negative in this context, we can conclude that the domain of the ball when it reaches its maximum height is t = 1.03 seconds.
So, the answer is 1.03 seconds.