A diver diving into a pool can be modeled by the function h = -16t2 + 16t + 12 where h is the
height in feet above the water after t seconds.When will the diver enter the water? Round to the nearest tenth, if necessary.
AAAaannndd the bot gets it wrong yet again!
it was ok to here: t = (4 ± 8) / 8
but then it botched it.
-16t^2 + 16t + 12 = -4(2t+1)(2t-3)
t = -1/2 or 3/2
To find when the diver enters the water, we need to find when h is equal to zero, since that represents the height of the water.
0 = -16t^2 + 16t + 12
Dividing both sides by -4:
0 = 4t^2 - 4t - 3
Using the quadratic formula:
t = (4 ± sqrt(16 + 48)) / 8
t = (4 ± sqrt(64)) / 8
t = (4 ± 8) / 8
The two solutions are:
t = 1/2 and t = -3/4
Since time cannot be negative, the answer is t = 1/2 seconds.
Therefore, the diver will enter the water after half a second.