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=-1/2t^2+6t-9h=12t2+6t9, when will the tide first be at 6 ft?

1 Answer
Dec 28, 2016

At 8.278.27 a.m. or 08.2708.27

Explanation:

Putting the value of h = 6 in equation h = -1/2t^2 + 6t - 9h=12t2+6t9

or,6 = [- t^2 + 12t - 18]/26=t2+12t182

or, 12 = -t^2 + 12t - 1812=t2+12t18

or, t^2 - 12t + 12 + 18 = 0t212t+12+18=0

or, t^2 - 12t + 30 = 0t212t+30=0

or, t = [-(-12) + sqrt {(-12)^2 - 4*1*30}]/(2*1)t=(12)+(12)2413021 and

[-(-12) - sqrt{(-12)^2 - 4*1*30}]/(2*1)(12)(12)2413021

or, t = [+12 +sqrt{144 - 120}]/2t=+12+1441202 and [+12 - sqrt{144 - 120}]/2+121441202

or, t = [12 +sqrt 24]/2, [12 - sqrt 24]/2 t=12+242,12242

or, #t = [12 + 2 sqrt 6]/2 , [12 - 2 sqrt 6]/2

or, t = 6 +sqrt 6 , 6 - sqrt 6t=6+6,66

The first tide will be at morning 6 +sqrt 66+6 hours.

The first time will be 8.4498.449 hours after midnight.

This give the time as 8 "hours" 27 "minutes"8hours27minutes after midnight.