00:02
Okay, so i'm not exactly an artist, but i have tried to copy as close as i could a similar graph to what you had.
00:11
And your graph starts somewhere near six, and then it curves down.
00:17
It looks like not quite exponentially, but it takes quite a while.
00:22
You're all the way over at six when it gets down to five, and by the time you get to 12, it's down to two.
00:28
So now, we're asked to divide this up into six, equal rectangles and then find the left rhyme and sums.
00:35
So if we divide 12 by six, we get two, four, six, eight, ten, and twelve.
00:41
So the first thing is to find the left rhyman sums.
00:44
We're going to take the value on the left and draw a rectangle, which is going to be pretty close to exactly on the line.
00:53
And then the second one is going to be a little bit above, but not very much.
01:02
And the third one is going to be significant.
01:04
Above and each one of these after that gets more and more above because this last one would be considerably above the line by the time you got to the right side.
01:16
So then we have to take the height of the rectangle, which the first one is six times the width is two to get the area of each rectangle.
01:24
And this is a judgment call.
01:27
I did my best to read your graphs and to get as close as i could.
01:32
But for part number one, your left rhyme and sums of six rectangles would be a height of six times two would be 12, plus a height of about 5 .9 times two would be 11 .8 for the second one, and then a height of about 5 .5 times two would be 11 for the third one, and a height of 5 times two is going to be exactly 10 for the fourth one.
02:05
And then a height of 4 .2 times 2 would be an area of 8 .4 for the fifth one.
02:13
And then a height of 3 .2 times 2 would be an area of 6 .4 for the last one.
02:21
Now, we could argue back and forth over whether or not this was 5 .9 or 5 .95, or the last one was 3 .2 or 3 .3.
02:31
But you have to use values based on your own judgment.
02:34
Some of them are pretty easy like the third one being exactly on the five well that one is pretty easy to read because it goes right through the crosshairs some of the other ones are judgment calls at any rate if you add these together with the numbers that i've used you get 59 .6 and as long as your number is pretty close to that you're okay now how did you know if it's over or under for the second part of that question.
03:06
Part number two says, is this an overestimate or an underestimate? so if we go back up here, no parts of these triangles are below the function.
03:19
But a small amount of this one is above, and then a bigger amount of this one is above, and each of the ones continuing to the right will be more and more above.
03:29
Of the six of them, all six are going to have at least a small amount, except for maybe the first one that is above.
03:38
So this is definitely an overestimate.
03:43
All right, part three is to do your right rhyme and thumb.
03:49
And i think you're using r6 as your definition.
03:54
So on the right -hand side of the right -hand triangle, it is two units tall times two units wide is four...