The formula in factored form is (t - 3)(t - 9) and the swimmer dives into the water 3 seconds after the timer was started also, the swimmer comes back up 9 seconds after the timer was started.
Analysis:
at h(t) = 0 that is when the diver has not dived or at height 0 foot
the equation becomes [tex]t^{2}[/tex] -12t + 27 = 0
by factorizing,
[tex]t^{2}[/tex] -9t -3t + 27 = 0
(t-9)(t-3) = 0, this is the equation in factored form.
t = 3 or 9
These are the times, the height h(t) = 0
Which means the swimmer dived 3 seconds later or got to the top of water after 9 seconds in which case h(t) = 0
In conclusion, the swimmer dives 3 seconds later after the timer was started and the swimmer comes back up after 9 seconds are the true statements for this problem.
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