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*girlie*
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#1
Report Thread starter 16 years ago
#1
A rectangular sheet of metal measures 50 cm by 40 cm. Squares of side x cm are cut from each corner of the sheet and the remainder is folded along the dotted lines to make an open tray.

Show that the volume, V cm^3, of the tray is give by: V=4x(x^2-45x+500). State the range of possible values of x and find the value of x for which V is a maximum.
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Feria
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Report 16 years ago
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Once the sides are cut off and the box is folded, the sides then become x, 40-2x and 50-2x.

x(50-2x)(40-2x)
4x(25-x)(20-x)
4x(x^2-45x+500)

V=max at dV/dx=0

V=4x^3 - 180x^2 + 2000x
dV/dx=12x^2-360x+2000
0=3x^2-90x+500
x= 22.637...
x=7.3623...

x=7.3623... as x<20 (since otherwise x will have chopped all and more of the 40cm side of the card)
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Feria
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#3
Report 16 years ago
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Oh, and range of values is probably 0<x<20 since x cant be negative either.
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