Pease help! I don't understand this problem: 20 inche wide aluminum sheet, sides turned up 90 degrees....etc
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Pease help! I don't understand this problem: 20 inche wide aluminum sheet, sides turned up 90 degrees....etc

[From: ] [author: ] [Date: 12-08-02] [Hit: ]
-if you fold up the left and the right sides just to let water flows through it,and you dont fold both end, otherwise water cant flow.since it is quadratic and x² term is negative,take derivativem let it=0 , is where the tangent =0 or its maximum point,......
1) What depth will allow the most cross sectional area, for water to flow?
2) What depths will allow 42 square inches of water to flow?

Please help! I have no idea how to do this.

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if you fold up the left and the right sides just to let water flows through it,
let x = depth of the fold
both sides = 2x
bottom = 20- 2x
and you dont fold both end, otherwise water can't flow.
You still need to find its volume
V= sectional area timeA length of material L
L=20
A= (20-2x)x

V= (20-2x)(x)*20= (20x-2x²)(20)
or
V= 40*(10x-x²)
since it is quadratic and x² term is negative, its graph is a downward parabola
take derivativem let it=0 , is where the tangent =0 or its maximum point, solve for x

-
Hint: Turn up a depth of x units. This will result in 4 squares of side x at each corner.
1
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