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December 21, 2014

December 21, 2014

Posted by **Becky** on Monday, January 28, 2013 at 6:59pm.

Use three decimal places in all intermediate calculations.

(a) What is the period of the tides in hours?

Round your answer to three decimal places.

(b) If the boat leaves the bay at midday, what is the latest time it can return before the water becomes too shallow?

Round your answer to three decimal places.

- Pre-Calculus -
**Reiny**, Monday, January 28, 2013 at 7:49pma) period = 2pi/.5 = 12.663 hrs

so we need the height to be 2.5

5 + 4.6sin(.5t)= 2.5

sin(.5t) = (2.5-5)/4.6 = -.543478

make sure your calculator is set to radians and take

inverse sine(+ .543478)

to get .574575 radians

But, the sine was negative so the "angle" must have been in quadr III or quadrant IV

so .5t = pi + .574575 or .5t = 2pi - .574575

t = 7.432336 or t = 11.41722

or t = 7:26 am or t = 11:25 am

remember that midnight was t=0

so the water was below 2.5 m between

7:25 am and 11:25 am

and the period was 12.663 hrs or 12:40 hrs

so the next time the water will go below 2.5 m

= 7:25 + 12:40 = 17:65 = 18:05 or 6:05 pm

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