# math

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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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-3 + 2 - 5 + 2 = ?

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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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Ms Sue, you're right. An expression can be all numeric!

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