To determine how high above the water the diving board is, we need to evaluate the given equation at the moment when the diver leaves the board. At this initial moment, the time [tex]\( t \)[/tex] is equal to 0.
The given equation modeling the distance [tex]\( d \)[/tex] from the water surface is:
[tex]\[ d = -4.9t^2 + 4t + 5 \][/tex]
To find the height of the diving board, we substitute [tex]\( t = 0 \)[/tex] into the equation:
[tex]\[ d = -4.9(0)^2 + 4(0) + 5 \][/tex]
By simplifying each term:
[tex]\[ d = -4.9 \cdot 0 + 4 \cdot 0 + 5 \][/tex]
[tex]\[ d = 0 + 0 + 5 \][/tex]
[tex]\[ d = 5 \][/tex]
Therefore, the height of the diving board above the water is 5 meters.
