# algebra

an open-topped box can be made from a rectangular sheet of aluminum, with dimensions 40 cm by 25 cm, by cutting equal-sized squares from the four corners and folding up the sides.

Declare your variables and write a function to calculate the volume of a box that can be formed.

I figured out this part because the function would be f(x)=x(25-2x)(40-2x)

x being the height
25-2x being the width
40-2x being length

Then it asks what cut lengths to the nearest hundredth are acceptable if the volume of the box must be between 1512 and 2176cm^3.

So you would the write 1512<x(40-2x)(25-2x)<2176

how to you solve the inequality to get the x
Damon you answered this but they cant both equal zero its between those numbers

1. 👍
2. 👎
3. 👁
1. Look at my last reply to you

1. 👍
2. 👎
2. http://www.jiskha.com/display.cgi?id=1395791951#1395791951.1395793571

1. 👍
2. 👎
3. you need to solve two inequalities:

x(40-2x)(25-2x) > 1512
x(40-2x)(25-2x) < 2176

x(40-2x)(25-2x) = 4x^3 - 130x^2 + 1000x

So, you have to solve

4x^3 - 130x^2 + 1000x - 1512 > 0
4x^3 - 130x^2 + 1000x - 2176 < 0

a little synthetic division shows that the first has a root at x=2 and the second has a root at x=4

Now you are just left with two quadratics to solve, and that's easy

There are 3 intervals in the solution, but only two are feasible given positive dimensions.

The two curves are shown here:

http://www.wolframalpha.com/input/?i=plot+y%3D4x^3+-+130x^2+%2B+1000x+-+2176+and+y%3D4x^3+-+130x^2+%2B+1000x+-+1512

1. 👍
2. 👎
4. what do you mean by intervals

1. 👍
2. 👎
5. the solution set to an inequality is not just a number, but a whole range of numbers which satisfy the inequality.

Any x between 2 and 4 is a solution to this problem, as well as in the other intervals. Graphed on the number line, we have

http://www.wolframalpha.com/input/?i=solve+4x^3+-+130x^2+%2B+1000x+-+2176+%3C+0+and+4x^3+-+130x^2+%2B+1000x+-+1512+%3E+0

1. 👍
2. 👎
6. the plate is only 25 cm wide so the big x interval will not work
I got results in the middle of the first two intervals though

1. 👍
2. 👎
7. By intervals he means BETWEEN the zeros of the two functions

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.

2. ### Math

An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must

3. ### Calculus

An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize

4. ### math

a 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard.the sides are folded up to make an open box with a maximum volume.if the perimeter of the base is 50cm,what are the dimensions of the box.

1. ### 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

2. ### Calculus

an open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning up the sides. If the piece of cardboard is 12 cm by 24 cm, what are the dimensions of the box that has the largest

3. ### Calculus 1

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the

4. ### Calc

An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

1. ### Math

From an 8 inch by 10 inch rectangular sheet of paper, squares of equal size will be cut from each corner. The flaps will then be folded up to form an open-topped box. Find the maximum possible volume of the box.

2. ### math

an open rectangular box is to be formed by cutting identical squares, each of side 2 in, one from each corner of a rectangular piece of cardboard, and then turning up the ends. If the area of the piece of cardboard is 160 inĀ² and

3. ### Calculus

An open top box with a square base is to have a volume of exactly 500 cubic inches. Find the dimensions of the box that can be made with the smallest amount of materials.

4. ### Applied Calculus

If an open box is made from a tin sheet 7 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two