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April 21, 2015

April 21, 2015

Posted by **Jeff** on Saturday, July 30, 2011 at 11:08am.

- calculus -
**Reiny**, Saturday, July 30, 2011 at 12:28pmlet each side of the cut-outs be x cm

So the base is 60-2x by 40-2x and the height is x

Volume = x(60-2x)(40-2x)

= 4x^3 - 200x^2 + 2400x

d(volume)/dx = 12x^2 - 400x + 2400

= 0 for a max of volume

3x^2 - 100x + 600 = 0 ----- I divided by 4

x = (100 ± √(2800)/6

= 25.5 or 7.85

but clearly 0 < x < 20 or else the sides make no sense.

so the cut-outs should be 7.85 by 7.85 cm

Plug 7.85 into my volume expression to get the max volume

- calculus -
**Jeff**, Sunday, July 31, 2011 at 7:27am6. A right circular cylinder is to be designed to hold 750 cm3 of processed milk, and to use a minimal amount of material in its construction. Find the dimensions for the container.

- calculus -
**Jeff**, Sunday, July 31, 2011 at 7:27amA right circular cylinder is to be designed to hold 750 cm3 of processed milk, and to use a minimal amount of material in its construction. Find the dimensions for the container.

- calculus -
**Jed**, Tuesday, August 9, 2011 at 8:53amIf you had a device that could record the Earth's population continuously, would you expect the graph of population versus time to be a continuous ( unbroken) curve? Explain what might cause breaks in the curve.

I'm confused. Thanks in advance for any help.

- calculus -
**Jenny**, Monday, April 30, 2012 at 11:57pmTony has a rectangular piece of cardboard which is 60 cm by 40 cm. By cutting squares from each corner of the cardboard and turning up the sides, can he form an open-topped box which will hold (a) 6656 cubic centimeter? (b) 9000 cubic centimeters? (c) what is the maximum amount of space he can obtain?

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