00:01
I think there's a ton of questions here, but you have a square piece of paper, cardboard, whatever, that is eight by eight.
00:09
And what they decided to do is cut off squares on each side.
00:12
You don't know what the cut is, so we'll just call them x.
00:19
So just to kind of answer a few questions as i go, because i think it's kind of a weird question, the given quantity is eight inches.
00:28
X and for part b, this represents the length of the side.
00:37
For part c, what we're asked to find is the maximum volume.
00:49
Oh, what's part d? what quantity are you asked to maximize? i feel like that's the same question.
01:02
Unless part c, maybe what they wanted on part c, i'm going to put a question mark next to it.
01:08
Because if you're doing volume, you might have to find the length, width, and height of the box.
01:26
Oh, maybe that's what it is.
01:27
Let me put an x through it.
01:29
That part c is asking for the length of the cut.
01:35
And that's what i'm going to solve.
01:36
Just i'm not used to these types of questions.
01:40
And then the variables that i'm using is i'm using x.
01:46
So for part e, you can use any variable you want, though, which kind of confuses me.
01:51
And then part f is actually doing the problem.
01:53
So if you draw out this box now, you can think about how the height of each one of these has to be x.
02:01
Has to be, because you fold it up.
02:03
But then what you have to think about is the length and the width changes.
02:07
And not only are you subtracting one x on one side, but another x on the other.
02:12
So eight minus two x.
02:13
So the volume that we have is eight minus two x times eight minus two x times x.
02:22
So what i would do is simplify that.
02:25
That eight times eight is 64.
02:26
That would be negative 16 with another negative 16.
02:29
That's negative 32 x.
02:31
And then plus, because a negative times a negative is positive.
02:35
Except i messed that one up, because two times two is four.
02:39
And i still have to multiply by that other x...