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What is the right choice for question 23) ? http://postimg.org/image/fuc1r5e75/

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jayson94 | Salutatorian

Posted August 19, 2013 at 2:05 AM via web

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What is the right choice for question 23) ?

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llltkl | College Teacher | Valedictorian

Posted August 19, 2013 at 3:11 AM (Answer #1)

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The water level in a coastal inlet has a maximum depth of 4 meters above the mean level at 8 am, and has a period of 12.4 hrs. The trigonometric equation for  modelling the tidal depth has to be found.

The given equations are all cosine graphs. The general formula for a cosine graph is:

`y=Acos(Bx-C)+D`

[where A=amplitude of the function = (max.-min.)/2 (vertical stretch of the graph), B=stretch/shrink on the x-axis, it is related to period as: `B=(2pi)/P` , C/B is the phase shift of the graph, and V=vertical shift of the graph]

Here, maximum depth of water is 4 meters above the mean level. So, minimum depth should be 4 meters below mean level.

Therefore, A=(4-(-4))/2=4

Here only option C) has A=4,  hence it is the correct answer.

Other constants, i.e. B, C and D can also be checked from the given relationships.

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