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Math Help - Word problem about a road closing time..

  1. #1
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    Word problem about a road closing time..

    The road to an island close to the shore is sometimes covered by the tide. When the water rises to the level of the road, the road is closed. On a particular day, the water at high tide is a height 4.6m above mean sea level. The height, h meters, of the tide is modeled by using the equation h = 4.6coskt, where ti s the time in hours from high tide; it is also assumed that high tides occur every 12 hours.

    (a) Determine the value of k
    The value of k should be 360 / 12 = 30

    (b) On the same, a notice says the the road will be closed for 3 hours. Assuming that this notice is correct, find the height of the road above sea level, giving your answer correct to two decimal places.
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  2. #2
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    (a) Good.

    (b) If the road must be closed for 3 hours, then the water creeps up on the road and rises for half of that time (1.5 hours) before high tide hits and the tide begins to recede...which it must do for the second half of the 3 hours. (We can make this assumption because the function used to represent the tide is vertically symmetric with respect to any maximum, or minimum for that matter). At any rate, what you have to do to find the height above sea level of the road is figure out the y-value of your function at the moment the water first creeps up onto the road. That should do it.
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