Question

1. the height ( h ), in metres, of a diver relative to the water level is described by ( h = \frac{1}{2}t^2 - 6t + 10 ) where ( t ) represents the elapsed time, in seconds, since the start. how long did the diver remain underwater?

Explanation:

Step1: Set height to 0 (underwater)

$\frac{1}{2}t^2 - 6t + 10 = 0$

Step2: Eliminate fraction, multiply by 2

$t^2 - 12t + 20 = 0$

Step3: Factor quadratic equation

$(t-2)(t-10) = 0$

Step4: Solve for t values

$t=2$ or $t=10$

Step5: Calculate time underwater

$10 - 2 = 8$

Answer:

8 seconds