Question

The height of the tide measured at a seaside community varies according to the number of hours t after midnight. If the height h, in feet, is currently given by the equation h=-1/2 t^2+6t-9, when will the tide first be at 6 ft?

Answer 1

Explanation:

Given that, the height of the tide measured at a seaside community varies according to the number of hours t after midnight. The height is given by the equation as :

$h=-\dfrac{1}{2}t^2+6t-9$

When the tide first be at 6 ft, put h = 6 ft in above equation as :

$-\dfrac{1}{2}t^2+6t-9=6$

$-t^2+12t-18=0$

On solving the above equation to find the value of t. It is equal to :

t = 3.551 seconds

or

t = 8.449 seconds

So, the tide of 6 ft is at  3.551 seconds and 8.449 seconds. Hence, this is the required solution.