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-9#, when will the tide first be at 6 ft?

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Answer 1 · 2016-12-28T08:42:24

At #8.27# a.m. or #08.27#

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

or,#6 = [- t^2 + 12t - 18]/2#

or, #12 = -t^2 + 12t - 18#

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

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

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

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

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

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

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

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

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

The first time will be #8.449# hours after midnight.

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