Can someone help me with this problem?

[moronatmath]

An open box is to be made from a flat square piece of material 8 inches in length and width by cutting equal squares of length x from the corners and folding up the sides.

Write the volume V of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors.

V =

If we write the domain of the box as an open interval in the form (a,b), then what is a?

a =

and what is b?

b =

 

[tkhunny]

For me, personally, it just seems like a waste of time to help someone who calls himself "moronatmath".

mo·ron n.

1) A stupid person; a dolt.

2) Psychology. A person of mild mental retardation having a mental age of from 7 to 12 years and generally having communication and social skills enabling some degree of academic or vocational education. The term belongs to a classification system no longer in use and is now considered offensive.

Get a little self concept, will you!?

 

[Mrspi]

An open box is to be made from a flat square piece of material 8 inches in length and width by cutting equal squares of length x from the corners and folding up the sides.

Write the volume V of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors.

V =

If we write the domain of the box as an open interval in the form (a,b), then what is a?

a =

and what is b?

b =

You're starting with a square with side 8 inches. If you remove an x-by-x square from each corner, then the bottom of the box will be a square with sides of 8 - 2x inches, and the height of the box will be x inches.

Volume = length * width * height

Fill in the length, width and height.....

For your interval, consider what the smallest and largest possible values are for x, the length of the side of the square you cut from each corner.

I hope this helps you.

 

[soroban]

Hello, moronatmath!

An open box is to be made from a flat square piece of material 8 inches in length and width
by cutting equal squares of length x from the corners and folding up the sides.

Write the volume V of the box as a function of x.
Leave it as a product of factors; you do not have to multiply out the factors.

If we write the domain of the box as an open interval in the form (a,b),
then what is a? \(\displaystyle \;\) and what is b?

From an 8-by-8 inch square, four congruent corners squares are removed.

      : x : 8-2x  : x :
      *---+-------+---*
      |::::       ::::| x
      + - * - - - * - +
      |   :       :   |
      |   :       :   | 8-2x
      |   :       :   |
      + - * - - - * - +
      |::::       ::::| x
      *---+-------+---*
      * x : 8-2x  : x *

The sides are folded up and an open-top box is formed:

              *-------------*
            / |           / | x
          /   *---------/   *
        /   /         /   /
      *-------------*   / 8-2x
    x |             | /
      *-------------*
           8-2x

The volume of a box is, of course: \(\displaystyle \:V\;=\;L\,\times\,W\,\times\,H\)

So we have: \(\displaystyle \:V\;=\;(8\,-\,2x)(8\,-\,2x)x \:=\:x(8\,-\,2x)^2\)


The domain of \(\displaystyle x\) is: \(\displaystyle (0,\,4)\)

If \(\displaystyle x\) (side of the removed square) is 0, no squares are removed.
\(\displaystyle \;\;\)There are no "sides" to fold up.
\(\displaystyle \;\;\)The volume of the so-called box would be 0.

If \(\displaystyle x\,=\,4\), we have removed all of the original square.
\(\displaystyle \;\;\)There is no material to form the box, so its volume is 0.

Hence, the value of \(\displaystyle x\) must lie between 0 and 4.

 

[moronatmath]

Thank you for the people that took the time to explain this to me.
So a=0 and b=4?

I am sorry but how are you getting x=0 and x=4?

 

[stapel]

I am sorry but how are you getting x=0 and x=4?

The reasoning is completely explained in the fully-worked solution presented in the post immediately above yours. At which point did you get lost?

Please reply with specifics.

Thank you.

Eliz.