Posted by MUFFY on Thursday, September 24, 2009 at 11:33pm.
An open box is formed by cutting squares out of a piece of cardboard that is 22 ft by 27 ft and folding up the flaps.
What size corner squares should be cut to yield a box that has a volume of less than 235 cubic feet?
I know that the size corner squares are .42 and 9.46. My teacher wants either brackets or parenthesis. I know if it's more than it gets parenthesis and at least gets brackets. I'm not sure what to do if it is less than.
Would it be:
[0,.42]union[.42,9.46]

PreCalc  Reiny, Thursday, September 24, 2009 at 11:53pm
Your equation would be
x(202x)(272x) < 235 or
4x^3  98x^2 + 594x  235 < 0
( I am curious what method you used to solve x = .425 and x = 9.46)
If Volume = 4x^3  98x^2 + 594x  235
we get a cubic, which has Volume = 0 at
x = .425, 9.46, and 14.6
we get a positive Volume for x's between .425 and 9.46, all other values of x produce negative volumes, (which makes no sense)
All this square bracket and round bracket stuff is new to me, in my days we would have simply said:
.425 < x < .946

PreCalc  MUFFY, Friday, September 25, 2009 at 12:07am
I used the same equation you said then put it in the graphing calculator and found the intersection points. I'm thinking that you would put
[.42,9.46) to show that it is more than .42 and less than 9.46.

PreCalc  Reiny, Friday, September 25, 2009 at 12:26am
I believe in the "interval notation"
a [ means you include the number,
while ( excludes the number
so [.42,9.46)
would mean .42 ≤ x < 9.46
are you sure you want to include the .42 ?
It produces a volume of zero.
I know that is less than 235
but so would all negative volumes obtained by x's outside my domain.
I think I would go with (.42 , 9.46)
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