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Concentric circles on steroids


Best Answer Yoruichi-san, 09 March 2013 - 09:24 AM

Spoiler for Yeah...

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10 replies to this topic

#1 bonanova

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Posted 09 March 2013 - 12:59 AM

A goat is tethered to a circular silo of radius r = 29 yd that is centered in a circular grassy field of radius R. The goat is just able to keep the silo wall clear of grass. He is also able to eat half of the grass in the annular field.

 

How big must that field be?


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#2 Rob_Gandy

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Posted 09 March 2013 - 02:01 AM

Spoiler for I got


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#3 bonanova

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Posted 09 March 2013 - 03:36 AM

Spoiler for I got

 

Smaller than the silo footprint.

To clarify:

goat.gif


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#4 Prime

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Posted 09 March 2013 - 06:13 AM

The goat in the picture is about 50 yards long and 40 yards tall. I would not like to meet it in a dark alley.

 

Spoiler for seems like calculus


Edited by Prime, 09 March 2013 - 06:15 AM.

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Past prime, actually.


#5 Yoruichi-san

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Posted 09 March 2013 - 07:18 AM

Spoiler for I get...


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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

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#6 bonanova

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Posted 09 March 2013 - 09:03 AM

I am wondering whether my analysis is off a bit.


I get a slightly smaller R than Y-San does.
But RG's answer gives exactly twice hers, meaning he may have given diameter instead of radius.
So there is the possibility they are both correct (with a misplaced factor 2 in RG's case - a typo more or less.)

Anyone else want to give it a shot, I'll go back over my equations meantime.

Nice going, both, in any event. ;)

Prime is correct, it involves an a messy integral.

And to be clear, the area the goat covers is half the annular field of grass.


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#7 Yoruichi-san

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Posted 09 March 2013 - 09:24 AM   Best Answer

Spoiler for Yeah...


Edited by Yoruichi-san, 09 March 2013 - 09:27 AM.

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#8 bonanova

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Posted 09 March 2013 - 09:30 AM

Nice going. bona_gold_star.gif


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#9 dark_magician_92

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Posted 09 March 2013 - 03:44 PM

If i got the question right, then

Spoiler for
 


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#10 bonanova

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Posted 10 March 2013 - 10:58 PM

If i got the question right, then

Spoiler for
 

 

dm92 your answer answer agrees with that of several others.

 

Y-san and I get a slightly smaller number.

It puzzles me (npi) what is the difference in solving this that leads to two different solutions.

Maybe the wording of the OP is ambiguous.

 

Spoiler for For the record I get


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