Question

Polygonal convex set? I don't know how to find the area of the closed figure.

http://puu.sh/6Ao2e.png

Answer 1

Probably easiest way is to draw it out...u got 1 horizontal n 1 vertical line there so just need to plot the other two.,..

Answer 2

Sorry i would have drawn it out but the drawing tool in OS is not working :(

Answer 3

Can you attach a picture of what the plot would look like?

Answer 4

Hmmmm i got 3 out of the 4 lines for u here :)

Answer 5

Would I use the normal 1/2bh to find the area?

Answer 6

Well thats three lines so I can't use that.. Hm

Answer 7

Add the fourth lines there n i suspect u can divide the area into different triangles which will allow u to use 1/2bh to calculate the smaller areas. Just add them up to get the total!

Answer 8

does that last line break down to y >= 3?

Answer 9

No, the last line is 2x+3y=6...rearrange n simplify will give u: y=-2/3x+2
Also note that this is only good for x between -6 and -12

Answer 10

I'm lost.

Answer 11

OK take a step back - do u understand what is shown in the picture I posted?

Answer 12

Yes

Answer 13

Then can you re-draw the picture but add the line y=-2/3x+6 there plz?

Answer 14

To add the line, I decided to use my graphing calculator and shows that it would be drawn at an angle starting at y = 6 and moving downward to the right, but you said that it should be between -6 and -12 on the x-axis.

Answer 15

yup yup good - u add the right line there :)
so all u need to do is to extend it for x<0, that will give u the part between -6 and -12

Answer 16

so, something like this?
http://puu.sh/6Aru1.png

Answer 17

Hahahaaa sorry for my poor drawing to begin w :)

Almost but not quite right: u got an extra vertical line there...the only vertical line should be x=0 which is the y-axis right?

Answer 18

ah, right. my mistake. so it should look like this

http://puu.sh/6ArJb.png

Answer 19

yup yup....nice calcuator btw :P

ok - remember the Q separates the two slanting lines and tell u to use one for x between 0 to -6 and the other between -6 to -12? now u need to figure which areas those represent...

Answer 20

Both of the slanted lines go through 0 to -6, but only the -x line goes beyond -6

Answer 21

While staying under y = 10, anyway

Answer 22

Check ur lines again plz? sorry i didnt notice it but when u put in y=10 into 2x+3y=6, x should be equal to -12

Answer 23

My mistake, lol. My calculator only takes equations in the form of y=, so I put in -2/3x + 6. Was that incorrect?

Answer 24

Ahh u forgot to divide both sides by 3 ;)

Answer 25

So the 2x+3y=6 line should move down lower....