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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2013-09-14 01:02:39

How did you do?

demha
2013-09-14 00:59:48

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

bobbym
2013-09-13 05:44:32

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.

http://www.mathisfunforum.com/showimage.php?pid=239899&filename=Fig+4.gif

demha
2013-09-13 05:32:13

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

bobbym
2013-09-13 03:20:21

That is very close to the exact answer of 7213.3.

demha
2013-09-13 03:13:38

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 . 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 . 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.

bobbym
2013-09-13 02:01:51

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

demha
2013-09-13 00:52:47

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?

bobbym
2013-09-12 22:34:04

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 … 91&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.

demha
2013-09-12 22:28:00

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?

bobbym
2013-09-12 21:58:02

Hi;

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

demha
2013-09-12 12:15:39

3/4 x 10^2 x PI

This would be the equation for #9?

bobbym
2013-09-12 09:37:24

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

demha
2013-09-12 09:35:17

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?

bobbym
2013-09-12 09:21:08

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

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