PreCalc
posted by MUFFY .
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]

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 
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. 
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)
Respond to this Question
Similar Questions

PRECALCULUS
AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF CARDBOARD THAT IS 16 FT BY 19 FT AND FOLDING UP THE FLAPS. WHAT SIZE CORNER SQUARES SHOULD BE CUT TO YEILD A BOX THAT HAS A VOLUME OF 175 CUBIC FEET 
PreCalc
I am having a great deal of difficulty with this problem. An open box is formed by cutting squares out of a piece of cardboard that is 16 ft by 19 ft and folding up the flaps. a. what size corner squares should be cut to yield a box … 
math
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions of the box that … 
Calculus
A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must … 
calc
by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the … 
math
An open box is made from a rectangular piece of cardboard, with dimensions of 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. Determine the dimensions of the squares to be cut to create a box … 
calculus
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 14 in. long and 6 in. wide, find the dimensions of the box that … 
calculus optimization problem
by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 30 inches long and 14 inches wide find the dimensions of the box … 
Calculus
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 10 in. wide, find the dimensions of the box that … 
pre calc
An open box is formedby cutting squares out of a peice of cardboard that is 18 feet by 26 feet and folding up the flaps. What size corner squares should be cut to yield a box that has a volume of 250 cubic feet