Posted by Ashley V on Thursday, November 8, 2007 at 10:25pm.
an 18 inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company.
a. write a polynomial funtion to model the volume of the box.
how can i graph this?
c. the company wants the box to have a volume of 224 cubic inches. write an equation to model this situation.
d. find a positibe integer for x.
Math Calculus Word Problem - Reiny, Thursday, November 8, 2007 at 11:34pm
I will asssume that you are going to cut equal squares from each of the four corners to do this.
Let each side of a square be x inches.
then the length of the box will be 20-2x
its width will be 18-2x in
and its height will be x in
since Vol = length x width x height
Vol = x(20-2x)(18-2x)
make a table of values, noting there are zeros at x=0, x=10 and x=9
b) x(20-2x)(18-2x) = 224
c) expanding this and simplifying I got
x^3 - 19x^2 + 90x - 56=0
I ran this through the following cubic equation solver
and got x=6.529, the other two answers are extraneous.
(check my work, I tend to get careless at this time of night)
Answer This Question
More Related Questions
- Math - From a 10-inch-by-19-inch piece of cardboard, 3-inch-square corners are ...
- Math - From an 8 inch by 10 inch rectangular sheet of paper, squares of equal ...
- Calculus - You are given a 60 inch by 30 inch piece of cardboad and asked to ...
- Calculus - An open top box is made by cutting congruent squares from the corners...
- Maths- Calculus - a sheet of cardboard is to be folded up to make a closed box. ...
- math - Identical square are cut from each corner of an 8 inch by 11.75inch ...
- Algebra 1 (Reiny!) - A piece of 8.5-by-11-inch cardboard has identical squares ...
- MATH help - A box with no top is to be constructed from a piece of cardboard ...
- Calculus - Equal squares of side length x are removed from each corner of a 20 ...
- Algebra - A box with a lid is to be cut out of a 12 inch by 24 inch sheet of ...