Please Help Final Tom!! Word Problem

**B1GG13** · November 30th 2007, 05:26 PM

An open box is to be made from a square piece of material 12 inches on a side by cutting equal squares of length x from the corners and turning up the sides.
(a)Write the volume (V) as a function of x.

(b) What is the domain of this function?

(Hint: Solve 0 < 12 – 2 x < 12)

**colby2152** · November 30th 2007, 07:01 PM

$V=x(12 - 2x)^2$

**DivideBy0** · November 30th 2007, 10:41 PM

If you are looking for the practical domain of $V(x) = x(12-2x)^2$ , since $(12-2x)^2$ must always be positive, if we have $x \leq 0$ , then $x(12-2x)^2$ will not be positive, but since Volume is positive, we must have $x> 0$ . So the domain is $x \in R^{+}$

**earboth** · December 1st 2007, 12:24 AM

Originally Posted by DivideBy0

..., since $(12-2x)^2$ must always be positive, ...

Hello,

this statement isn't quite correct. With this problem it is necessary that

$12-2x \geq 0~\wedge~x \geq 0$

Otherwise you cut off more than there exist - and that means you build a box by cutting off parts of the 3-D-space to get a negative space

Thread: Please Help Final Tom!! Word Problem

LinkBack

Thread Tools

Display

Please Help Final Tom!! Word Problem

Similar Math Help Forum Discussions

Final Linear Programming Problem

Final Review word poblem

Final sequence problem!

Please Help Final Tom!! Word Problem

The final problem..

Search Tags