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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.

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abidemiokin abidemiokin · Answer 1 · 2022-06-07T14:17:29+02:00

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the point where the velocity the body is zero.

Given the function that represent the height of the swimmer as h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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