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.
2) What depths will allow 42 square inches of water to flow?
Please help! I have no idea how to do this.
-
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
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.