00:01
All right, so this problem had a bunch of problems within it, but the first part said that there was a ladder leaning against a wall.
00:13
So there's the wall making a right angle, 13 foot ladder, and that whatever the base from the wall to the ladder was, the height was twice the base plus two.
00:30
All right so we can use pythagorean theorem to figure out what the base is so i did 2b 2b plus 2 squared plus b squared equals 13 squared and i squared that first part out i get 4b squared plus 8b plus 4 and then plus b squared equals 169 i put my 4b squared and my b squared together i get 5b squared plus 8b and i subtracted the 169 to have minus 165 equals 0 i couldn't think of what that factored into at first so i did the quadratic formula so i did negative 8 plus or minus square root of b squared minus 4 a c all over to a.
01:45
And i did that out.
01:51
And that was 64.
01:54
Oh, no, inside.
01:58
It came to 3364.
02:06
Over 10.
02:09
The square of that is 58.
02:12
So it did come out nice.
02:18
And so negative 8 minus 58 would give us a negative number.
02:22
So that doesn't make sense for the problem.
02:24
So we'll just focus on the positive answer.
02:26
So negative 8 plus 58.
02:29
Would be 50 over 10 is 5.
02:34
So this piece here would be 5, and then this would be 12.
02:46
All right, second question.
02:54
I told us that we had one number that was three times another number plus one.
03:05
And we also know that their product is third.
03:11
So i set up two equations and now i can use substitution.
03:16
So i'm going to take this 3b plus 1 and substitute it in for a.
03:24
So times b equals 30.
03:28
I'm going to distribute the b in.
03:36
I subtract it 30 to get it to be a factorable problem and that factored into 3b plus 10 times b minus 3.
03:59
And again we're going to have one negative answer and one positive answer.
04:04
This if i said equal to zero would give me a negative answer.
04:08
So again, we'll just focus on the positive and add three.
04:16
So b is three.
04:21
And a would be 10.
04:25
Or the first number.
04:30
And then number three.
04:48
Had a rectangle that said the width was, let's say, w, the length is twice the width.
05:03
Then they cut out squares in each corner that were two by two.
05:19
Okay, so i know that volume is length times width times height...