help! -tethered cow problem.
 

[QUOTE=drew]Read post number 48. Assuming the expression you provided is correct (5/6 pi L[sup]2[/sup]), that's the ratio I had determined for one answer over the other if the ropes were equal length. But since one rope is 11/10 as long as the first, the area for that rope is 121/100 as large as it would be. 121% / 120% = 1.00833.

Drew[/QUOTE]
:smile: Fair enough Andy, as long as you establish that the expression is mine.
The rest a school boy coud work out. Thanks
Mally :coffee:
P.S. BTW the curve we discussed is NOT a Cartoid in your spelling but a CARDIOID.

[QUOTE=Wacky]Mally,
Your reasoning is faulty. Just because you found something in some book does not necessarily imply that the information is correct. Even the best of authors have, on occasion, been found to have made a mistake.

Therefore, finding the exact problem in the book may support a particular answer, but it cannot be considered a "final authority" as you imply. It still remains for each individual to examine the evidence, including your latest reference, and attempt to resolve, for themself, the correct answer.[/QUOTE]
:smile: Well Richard, how do you feel about the problem now?
As an expert do you still say the reasoning is faulty? Have you bothered to test out the solution or are you only interested in giving totally negative comments?
Mally :coffee:

[QUOTE=mfgoode]Well Richard, how do you feel about the problem now?
As an expert do you still say the reasoning is faulty? Have you bothered to test out the solution or are you only interested in giving totally negative comments?[/QUOTE]

I am only pointing out that your "argument" for the correctness (that it is published somewhere) is lacking from a mathematical perspective. Had you given the publication as a reference which shows the derivation of the answer, then said publication might well be of some value. However, I reitterate that it is not proper math, or debate, to simply state that someone else said so, and therefore it MUST be so.

help! -tethered cow problem.
 

[QUOTE=Wacky]I am only pointing out that your "argument" for the correctness (that it is published somewhere) is lacking from a mathematical perspective. Had you given the publication as a reference which shows the derivation of the answer, then said publication might well be of some value. However, I reitterate that it is not proper math, or debate, to simply state that someone else said so, and therefore it MUST be so.[/QUOTE]
:sad: Von wackerbarth there is no 'argument' about the matter. You simply want to make one out of it.
I have clearly stated the author and the name of the book and can give the publishers name if required. I have also lucidly given the solution STRAIGHT from the book albeit a diagram which any high school student can follow.
And still you stubbornly refuse to accept it simply because it is from Mally??? :censored:
Your post analysis is that you are terribly confused within your self. And by the way I have not come across a single post of yours with a correct solution to ANY of the puzzles. :furious:
You simply hitch your wagon to the side which has the fastest horses!!!! :confused:
Mally :coffee:

[QUOTE=mfgoode]:smile: Fair enough Andy, as long as you establish that the expression is mine.
The rest a school boy coud work out. Thanks
Mally :coffee:
P.S. BTW the curve we discussed is NOT a Cartoid in your spelling but a CARDIOID.[/QUOTE]

Call it what you want. Neither cardioid nor cartioid is a solution to this problem. :wink:

help! -tethered cow problem.
 

[QUOTE=drew]Call it what you want. Neither cardioid nor cartioid is a solution to this problem. :wink:[/QUOTE]
:surprised Well, Well, quite a nonchalant attitude in mathematics!
You know that Mathematical symbolism is very important and there is no dearth of it in our world today. BY adding one more like Cartoid will confuse the issue as this is a medical term familiar to doctors.
FYI: when calculus was jointly invented by Newton and Leibnitz at much the same time, Germany and France stole an advance over England mainly because of the symbol for differentiation. Leibnitz's was simpler and more clear on understanding infinitesimals. Not to sound partial they also had the better Mathematicians, at the time, who took up the challenge!
The nearest I could get to cartoid was this
"Did you mean: carotid
Cartoid
Cartoid, Carotid artery stenosis angiogram. Cartoid, Carotid body tumour (angiogram).
Cartoid, Carotid body tumour (MRA)
[url]www.freevas.demon.co.uk/cartoid.htm[/url] - 2k - Cached - Similar pages
Cartoid angioplasty and stenting"
Mally :coffee:

[QUOTE=mfgoode]:surprised Well, Well, quite a nonchalant attitude in mathematics!
You know that Mathematical symbolism is very important and there is no dearth of it in our world today. BY adding one more like Cartoid will confuse the issue as this is a medical term familiar to doctors.
FYI: when calculus was jointly invented by Newton and Leibnitz at much the same time, Germany and France stole an advance over England mainly because of the symbol for differentiation. Leibnitz's was simpler and more clear on understanding infinitesimals. Not to sound partial they also had the better Mathematicians, at the time, who took up the challenge!
The nearest I could get to cartoid was this
"Did you mean: carotid
Cartoid
Cartoid, Carotid artery stenosis angiogram. Cartoid, Carotid body tumour (angiogram).
Cartoid, Carotid body tumour (MRA)
[url]www.freevas.demon.co.uk/cartoid.htm[/url] - 2k - Cached - Similar pages
Cartoid angioplasty and stenting"
Mally :coffee:[/QUOTE]
Well Mally, I was just pointing out your Red Herring. Rather than admit you were wrong about something, you criticize my spelling. It's a very transparent tactic.

FWIW, I spelled it 'cartioid', not 'cartoid'. With that correction you'll be relieved to find that Google returns "Did you mean cardioid?". And I later realized my error and began spelling it correctly, which you'll see if you read subsequent posts in this thread. I'm not sure how you pronounce English words over in India, but in the U.S. we'd pronounce them both the same. It's a simple mistake and absolutely irrelevant to the discussion at hand.

Drew

help! -tethered cow problem.
 

[QUOTE=drew]Well Mally, I was just pointing out your Red Herring. Rather than admit you were wrong about something, you criticize my spelling. It's a very transparent tactic.

FWIW, I spelled it 'cartioid', not 'cartoid'. With that correction you'll be relieved to find that Google returns "Did you mean cardioid?". And I later realized my error and began spelling it correctly, which you'll see if you read subsequent posts in this thread. I'm not sure how you pronounce English words over in India, but in the U.S. we'd pronounce them both the same. It's a simple mistake and absolutely irrelevant to the discussion at hand.

Drew[/QUOTE]
:smile: Well Drew we in India follow the 'Queen's English' with BBC accents.
Pronunciation: 'kär-dE-"oid Function: noun Date: 1753
Mally :coffee:

help! -tethered cow problem.
 

[QUOTE=mfgoode]Drew[/QUOTE]

:redface:
Im sorry that I gave some misinformation in my post to the silo problem.

Actually he gives two goats one (George) tethered to the silo,at half circumference length ( call it L) This rope is 11 feet long. The other goat (Bill) grazes freely in the field tied with a rope of 10' length.

I will give a partial solution restricted to my presentation of no diagram.
The Integral of one side of the curve is of [(pi*x^2 dx)/2L] from 0 to L.
The one side area is thus (pi*l^2)/6

So for both sides, which are equal in this case, the area is twice the single area. i.e.(2Pi*L^2)/6. So the total of George's grazing area is the area of the 2 symetrical curves on either side of the ring attached to the silo. plus the area of the semi circle which is (pi*l^2)/2.

Adding these up we get (5 Pi*l^2)/6 which if compared to Bills area of 100*pi gives the fraction 121/120 as much, or just 0.833% greater
Mally :coffee:[/QUOTE]

:rolleyes:
I have now established that the grazing area is definitely not a cardioid, the area of which is (3*Pi *l^2)/2
Mally :coffee: