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flagitious-t
2005-07-24 08:39:45

uhh... both?

Zach
2005-07-24 08:23:17

MathsIsFun
2005-07-24 08:01:15

#### flagitious-t wrote:

wow, really complicated.

flagitious-t
2005-07-24 03:57:14

thanks!

wow, really complicated.

ganesh
2005-07-23 20:29:02

Thanks, Mathsisfun,
I am on the verge of post # 200
and this an occassion for me to celebrate,
I shall take a big chunk of thhat

MathsIsFun
2005-07-23 20:21:34

These look particularly yummy.

Mathsy gets first choice.

ganesh
2005-07-23 19:58:25

mathsyperson
2005-07-23 19:39:24

My fault again! "Haha!"

I got the sectors the wrong way around.
Length x sector's angle: cos-¹(1-x²/1800)
Length 30 sector's angle: cos-¹(x/60)

So, the latest formula is =900*PI()*ACOS(1-B8*B8/1800)/(2*PI())+B8*B8*PI()*ACOS(B8/60)/(2*PI())-SQRT((30+B8/2)*(B8/2)*(B8/2)*(30-B8/2))

Edit: And it works perfectly! Cookies for everyone!
To the nearest cm, the goat's leash is 34.76m long.

MathsIsFun
2005-07-23 19:14:34

Oh, rats ... I mean goats. Well, the answer is somewhere in there. Maybe flagitious can take it from here.

mathsyperson
2005-07-23 19:03:54

We still haven't cracked it though. When the goat's leash has length 0m, it can apparantly eat around 700m² of grass. It must have a long neck...

MathsIsFun
2005-07-23 18:51:09

See? My turn to be foolish. I have already had my flash of brilliance for today - it is all downhill now

mathsyperson
2005-07-23 18:34:10

And then it would just be strange: "Math Is      Forum"

All I can see is that you haven't divided the sector areas by the number of whatever you're measuring by. Excel works with radians by default so try this:
=900*PI()*ACOS(B8/60)/(2*pi()) + B8*B8*PI() *ACOS(1-B8*B8/1800)/(2*pi()) - SQRT((30+B8/2) * (B8/2)* (B8/2) * (30-B8/2))

MathsIsFun
2005-07-23 18:20:02

"Sorry"? Try "Haha"!

( Gee, if we all have to be worried about making mistakes then we may as well take the "Fun" off the forum name. )

Still not quite there ... maybe i am not getting my formula right.

=900*PI()*ACOS(B8/60) + B8*B8*PI() *ACOS(1-B8*B8/1800) - SQRT((30+B8/2) * (B8/2)* (B8/2) * (30-B8/2))

If you have a chance, see if you can get it working, then just delete the last two or three posts and show the world how neat and perfect we are!

mathsyperson
2005-07-23 18:05:14

Sorry, I've given you a duff formula. The two sectors 'areas' are actually just their angles. *Feels stupid*

The real area: 900Π*cos-¹(x/60)/360 + x²Π*cos-¹(1-x²/1800)/360 - √((30+x/2)(x/2)²(30-x/2))
Sorry again!

MathsIsFun
2005-07-23 18:00:54

ACOS() ?

Pi is there, it just looks weird: Π

By the way, I tried that formula in excel with "30" for x and got -387.617, have we somehow created anti-grass?

Formula: =ACOS(B8/60) + ACOS(1-B8*B8/1800) - SQRT((30+B8/2) * (B8/2)* (B8/2) * (30-B8/2))