Question

An open box is formed from a square piece of cardboard, by removing squares of side 4 in. from each corner and folding up the sides. If the volume of the carton is then 32 in3, what was the length of a side of the original square of cardboard?

Answer 1

with or without lagrange multipliers? lol

Answer 2

:)

Answer 3

lolol

Answer 4

joemath look at previous sanasaj post

Answer 5

Haha satellite.

Answer 6

put length of paper at x, then
\[(x-8)(x-8)x=32\] solve for x

Answer 7

As a mathematician, you're obsessed with lagrange multipliers; as a computer scientist, I'm obsessed with genetic algorithms; both of these techniques can solve this problem XD

Answer 8

actually this is not a max min problem, just an algebra one

Answer 9

Or his previous problem, let's say. :P

Answer 10

algebra is fine :)

Answer 11

by the way this cubic is a bear to solve. set up of problem is straightforward, solution is not

Answer 12

whats the equation?

Answer 13

(as i dont feel like setting it up lol)

Answer 14

\[(x-8)(x-8)x=32\]

Answer 15

i think. maybe i am wrong

Answer 16

that sounds right.

Answer 17

v=4 x^2
32=4 ^2
x=2(sqrt 2)
s=2(sqrt 2)+8

Answer 18

Sorryt, 32=4 x^2

Answer 19

oh damn that is not right! it is just
\[(x-8)(x-8)4=32\] ho ho h0

Answer 20

wait...shouldnt it be (x-8)(x-8)(4)?

Answer 21

the height is 4, not x.

Answer 22

i forgot to read it as a "square" :)

Answer 23

ah ok,.you got it lol

Answer 24

i have seen the problem so many times as "find x to maximize..." i wasn't paying attention

Answer 25

yeah, i saw what you posted and was like, "yeah thats it" without really thinking lol

Answer 26

\begin{array}l\color{red}{\normalsize\text{T}}\color{orange}{\normalsize\text{h}}\color{#9c9a2e}{\normalsize\text{e}}\color{green}{\normalsize\text{y}}\color{blue}{\normalsize\text{ }}\color{purple}{\normalsize\text{n}}\color{purple}{\normalsize\text{e}}\color{red}{\normalsize\text{e}}\color{orange}{\normalsize\text{d}}\color{#9c9a2e}{\normalsize\text{ }}\color{green}{\normalsize\text{t}}\color{blue}{\normalsize\text{o}}\color{purple}{\normalsize\text{ }}\color{purple}{\normalsize\text{a}}\color{red}{\normalsize\text{d}}\color{orange}{\normalsize\text{d}}\color{#9c9a2e}{\normalsize\text{ }}\color{green}{\normalsize\text{s}}\color{blue}{\normalsize\text{o}}\color{purple}{\normalsize\text{m}}\color{purple}{\normalsize\text{e}}\color{red}{\normalsize\text{ }}\color{orange}{\normalsize\text{c}}\color{#9c9a2e}{\normalsize\text{o}}\color{green}{\normalsize\text{l}}\color{blue}{\normalsize\text{o}}\color{purple}{\normalsize\text{r}}\color{purple}{\normalsize\text{ }}\color{red}{\normalsize\text{t}}\color{orange}{\normalsize\text{o}}\color{#9c9a2e}{\normalsize\text{ }}\color{green}{\normalsize\text{i}}\color{blue}{\normalsize\text{t}}\color{purple}{\normalsize\text{ }}\color{purple}{\normalsize\text{s}}\color{red}{\normalsize\text{o}}\color{orange}{\normalsize\text{ }}\color{#9c9a2e}{\normalsize\text{t}}\color{green}{\normalsize\text{h}}\color{blue}{\normalsize\text{a}}\color{purple}{\normalsize\text{t}}\color{purple}{\normalsize\text{ }}\color{red}{\normalsize\text{i}}\color{orange}{\normalsize\text{t}}\color{#9c9a2e}{\normalsize\text{ }}\color{green}{\normalsize\text{i}}\color{blue}{\normalsize\text{s}}\color{purple}{\normalsize\text{ }}\color{purple}{\normalsize\text{r}}\color{red}{\normalsize\text{e}}\color{orange}{\normalsize\text{a}}\color{#9c9a2e}{\normalsize\text{d}}\color{green}{\normalsize\text{a}}\color{blue}{\normalsize\text{b}}\color{purple}{\normalsize\text{l}}\color{purple}{\normalsize\text{e}}\color{red}{\normalsize\text{ }}\color{orange}{\normalsize\text{;}}\color{#9c9a2e}{\normalsize\text{)}}\color{green}{\normalsize\text{}}\end{array}

Answer 27

answer is
\[x=4+2\sqrt{2}\]

Answer 28

i can bearly read that >.< lolol

Answer 29

damn still wrong. it is
\[8+2\sqrt{2}\]

Answer 30

robtoby did it in like two seconds. good work!

Answer 31

Thank you.