Question

A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.

The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.

Answer 1

Answer:

The swimmer comes back up 9 seconds after the timer was started.

The swimmer dives into the water 3 seconds after the timer was started.

Step-by-step explanation:

Answer 2

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 $t^{2}$ -12t + 27 = 0

by factorizing,

$t^{2}$ -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.

Learn more about maximum and minimum points: brainly.com/question/14993153

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