Posted by **red** on Monday, September 7, 2009 at 10:29am.

A manatee swimming 3 feet below the water surface, ascends 2 feet, descends another 5 feet then ascends another 2 feet. Write an expression to find his position relative to the water surface. Then find His position

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**red**, Monday, September 7, 2009 at 11:16am
please help me with this

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**Ms. Sue**, Monday, September 7, 2009 at 11:42am
-3 + 2 - 5 + 2 = ?

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**MathMate**, Monday, September 7, 2009 at 12:00pm
The expression is a step function, which has discontinuities between ascents and descents.

Let the number of movements (ascents or descents) be i, and

h(i) = position relative to the surface after the ith movement.

h(0)=-3 (3 feet below surface)

h(1)=-1 (=-3+2)

h(2)=-6 (=-1-5)

h(3)=-4

h(4)=-9

h(5)=-7

...

So

h(i) = -(i/2)*3 -3 for 2|i (i divisible by 2), and

h(i) = -(i+1)/2*3 +2

= -(3i-1)/2 for 2|(i+1) (i not divisible by 2)

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**MathMate**, Monday, September 7, 2009 at 12:03pm
Ms Sue, you're right. An expression can be all numeric!

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