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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

How much do they overlap? Look at the little circle that is what they overlap. So minus the barn we get 3 / 4 (10^2) π

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi

Post 21 looks familiar.

zee-f had this question too and eventually got 10/10 for doing it that way.

The last area is expected to be approximate.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

To me it looks as if each side is over lapping by 3 blocks, each side overlapping by a green and two reds. Would that mean they are overlapping by 30? (3 blocks, each block = 10, 3 x 10 = 30)

*Last edited by demha (2013-09-11 09:03:47)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

The green circle is the overlap of the two circles because going right or left you have the same center.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Yes I understand that. The E-circle represents the entire range, the F-circle and G-circle represent the both ways the goat can go, and the H-circle (green) represents where they overlap. So would this just be considered as one area, as in just 10? Making the equation:

1/4 x 10^2 x PI

Am I following the right path here?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

No, remember you can not use the barn, so it is 3 / 4 of the circle.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

3/4 x 10^2 x PI

This would be the equation for #9?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

Yes, that is what I would put down as the answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Cool! So it would be:

3/4 x 10^2 x PI

3/4 x 100 x PI

75 (PI) is the final answer or 235.619

And #7 and #8 are literally asking for the same thing. So the equation for them both would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) is the final answer or 706.858 - is this correct?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

That is what I would put also but the solution I have is 300 π. Let's go with your answer.

But take a look at this thread that bob bundy worked on

http://www.mathisfunforum.com/viewtopic … =18391&p=6

before and after post 117. This problem has been worked on in this forum. I also posted the exact answer for 10) in the computer math thread.

It does agree with Bob's work there.

Am going offline for a bit.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Ok, so redoing #7 - #9:

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI)

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: (this would be the same as #7)

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI)

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

Answer:

3/4 x 10^2 x PI

3/4 x 100 x PI

75 (PI)

---

If these are right, shall we move on to #10?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

What do you want to do about 10, as you can see the expression is very complicated. Bob suggests you might submit an approximation.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Ok here is the "redo" for #7 - #10:

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: The new radius is 30. It can make up to ¼. So the area would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) = 706.858

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: The radius is 30. It can make up to ¼. So the area would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) = 706.858

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

Answer: I would say that the area is 75. It looks like it almost makes a square shape.

10. What is the total grazing area the goat can reach?

Answer: To get this answer, I added up the ansers of #6, #7 and #8 then subtracted the answer from #9:

1875(PI) + 225(PI) + 225(PI) 75

2325(PI) 75

7304.202 75

7229.202 is the final answer.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

That is very close to the exact answer of 7213.3.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

So I'm guessing I went wrong some where, but where?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

You did not go wrong anywhere. Your answer is just an approximation. The exact answer requires calculus.

Check the drawing out. The black are is what is impossible for the goat to reach.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Finished with this lesson! Thank you very much Bobbym for your help. Much appreciated!!

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

How did you do?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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