Four exponentials conjecture - Revision history

en>Rjwilmsi: /* References */Added 1 dois to journal cites using AWB (10090)

2014-05-01T20:11:43Z

References: Added 1 dois to journal cites using AWB (10090)

← Older revision		Revision as of 22:11, 1 May 2014
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	~~{{Multiple issues\|orphan = April 2011\|refimprove = October 2009}}~~		Hi, everybody! <br>I'm Turkish female ;=). <br>I really love Seaglass collecting!<br><br>Also visit my web site :: [http://www.imariogames.net/profile/roi59.html wordpress backup]

	~~In [[algebra]]~~, ~~'''componendo and dividendo''' (or '''componendo et dividendo''') is a method of [[simplification]] based on fractions provided that they are in proportion. It states that~~<~~ref~~>~~Bhamra,~~ '~~'Partial Differential Equations''. PHI Learning Pvt. Ltd. ISBN 978-81-203-3917-0~~
	~~</ref>~~
	~~<ref>~~
	~~http://www.qc.edu.hk/math/Junior%20Secondary/Componendo%20et%20Dividendo.htm~~
	~~</ref>~~

	~~:<math> \text{If } \frac{a}{b}~~ = ~~\frac{c}{d} \text{ and } a \neq b \text{, then } \frac{a+b}{a-b} = \frac{\frac{a}{b} + 1}{\frac{a}{b} - 1} = \frac{\frac{c}{d} + 1}{\frac{c}{d} - 1} = \frac{c+d}{c-d}~~. <~~/math>~~

	~~==Comment on the proof==~~
	~~We can similarly deduce the much more general fact that the value of any fraction~~

	~~:<math>\frac{x_0 + \cdots + x_n}{y_0 + \cdots +y_n}</math>~~

	~~in which <math>x_0</math~~> ~~and~~ <~~math~~>~~y_0~~<~~/math~~> ~~are nonzero and can be expressed in terms of the values of~~

	:~~<math>\frac{x_1}{x_0}, \ldots, \frac{x_n}{x_0}, \frac{y_1}{y_0}, \ldots, \frac{y_n}{y_0} </math>~~

	~~and the value of <math>\frac{x_0}{y_0}</math>, and so depends only on the values of those 2''n'' + 1 fractions~~:

	:~~<math> \frac{x_0 + \cdots + x_n}{y_0 + \cdots +y_n}~~
	~~= \frac{x_0}{y_0} \left(\frac{1 + \frac{x_1}{x_0} + \cdots + \frac{x_n}{x_0}}{1 + \frac{y_1}{y_0} + \cdots + \frac{y_n}{y_0}}\right)<~~/~~math>~~

	~~The original result is essentially a special case of this fact, because~~

	~~:<math>\frac{x+y}{x-y} = \frac{x+y}{x+(-y)}<~~/~~math>~~

	~~can be regarded as a fraction of the above form~~.

	~~==Example==~~
	~~This method can be used in various situations~~.

	~~For instance :~~

	~~:<math>\frac{\sqrt{3} + x}{\sqrt{3} - x} = 2<~~/~~math>~~

	~~Find the value of ''x''~~.

	~~Solution :~~

	~~Applying C and D~~

	~~: <math>\frac{(\sqrt{3} + x) + (\sqrt{3} - x)}{(\sqrt{3} + x) - (\sqrt{3} - x)} = \frac{2 + 1}{2 - 1}</math>~~
	~~: <math>=> \frac{2 \sqrt{3}}{2 x} = \frac{3}{1}</math>~~
	~~: <math>=> \frac{\sqrt{3}}{x} = 3</math>~~
	~~: <math>=> x = \frac{1}{\sqrt{3}}</math>~~

	~~==References==~~
	~~<references/>~~

	~~==See also==~~
	* [[Reduction (mathematics)]]
	* [[Fraction (mathematics)]]

	~~{{DEFAULTSORT:Componendo And Dividendo}}~~
	~~[[Category:Fractions]]~~
	~~[[Category:Algebra]~~]


	~~{{algebra-stub}}~~

en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9832)

2014-01-05T15:59:50Z

fixed CS1 errors: dates & General fixes using AWB (9832)

← Older revision		Revision as of 17:59, 5 January 2014
Line 1:		Line 1:
	Real estate planning takes a very special type of legal professional, individual who is aware the financial markets and tendencies, along with the way that they pertain to your specific situation. However it might be tempting to draw in your very own programs and targets, you would be wise to experience a legitimate consultant to assist you as you go along. Read through in this article about what to look for in a great estate attorney.<br><br>		{{Multiple issues\|orphan = April 2011\|refimprove = October 2009}}

	~~There~~ is a ~~directly to count~~ on ~~very clear~~, ~~consistent communication with the legal professional~~. The individual should be able to supply you with a common summery of what you can anticipate in terms of your situation, as well as what possible issues might occur and what is done to remedy these problems.<br><br>~~Examine online to discover what type of fees~~ http://~~youtube~~.~~com~~/~~watch?v=qWZomlaZgCI ([http:~~//~~www~~.~~youtube.com~~/~~watch?v~~=~~qWZomlaZgCI More hints]) are standard for your personal legal issues. This can help you prevent getting ripped off later on. Pick~~ a ~~legal professional who may have~~ a ~~good reputation and significant amounts of experience to make sure that they don't overcharge you for individual time~~-~~throwing away mistakes~~.<br>~~<br>Wait to sign a binding agreement having an attorney before you have~~ the ~~condition is proper. Request a quote from~~ the ~~lawyer so you are aware approximately~~ the ~~amount~~ of ~~several hours he or she intends on putting~~ in ~~to the scenario. In case the legal representative refuses, proceed. A array is appropriate, but it is not acceptable in case you have little idea what you really are engaging in.~~<br><br>~~Often~~ be ~~mindful~~ of ~~methods properly you happen to be conveyed with by~~ the legal professional. If this usually takes days as well as days to acquire replies to telephone calls or e-mails, then two possibilities can be found. Sometimes your attorney will not look at you with a top priority, or they are over-worked. Neither of ~~them circumstance is good for you.~~<br><br>~~Be sure to recognize how much you are going to commit before you engage a legal professional. Attorneys can be quite pricey. Their by~~ the hour costs can break your financial budget prior to they can begin to assist you. Ensure you understand the costs advance and if you cannot afford a specific legal professional, seek out one that one could afford to pay for.<br><br>~~When getting together with using a would-be lawyer or attorney~~, ~~ask her or him~~ the ~~person you will generally be talking to concerning your case. In certain situations, lawyers give part~~ of their caseload to your junior affiliate. If you believe you actually interact with a definite lawyer, instantly determining you will end up working with another person might be very disconcerting. These thoughts could be exacerbated should you don'~~t get in addition to the other person, way too.~~<br><br>~~Observe how possible lawyers react to your own personal needs.~~ The ~~real key to some great attorney~~ is ~~now being prepared to accomodate the needs and wants with their customers. If you come across~~ a ~~legal professional which is not considering satisfying~~ this, ~~then you definitely have been presented ample warning that you ought to find a person else to handle your case.~~<br><br>~~Whenever you believe that you could have got a lawsuit, it~~ can be ~~appealing to phone one~~ of ~~those particular legal representatives inside~~ the ~~tv commercials on television~~. ~~Even though these attorneys are qualified, [http://www.youtube.com/watch?v~~=~~ORuh1Dr9rcs richard schwartz] they will not~~ be ~~capable to [http~~:/~~/Www~~.~~Adobe.com~~/~~cfusion~~/~~search/index.cfm?term~~=~~&training+law&loc=en_us&siteSection~~=~~home training law] in your state, based on where by they had taken the Pub examination. It is always good to check out this and study the fine print.~~<br><br>If you discover a breakup attorney and they also seem extremely enthusiastic about producing your ex lover "spend" for everything they already have carried out to you, try to find somebody else. Although you might have vengeance within your coronary heart, your attorney should certainly think direct constantly. Getting biased is just not a great job ethic, even if it is inside your favor.<br><br>~~Now you recognize much more about how residence preparation operates and how legal counsel can help, you can move ahead with a properly~~-~~knowledgeable strategy. Look for testimonials, shop around and get your brand new lawyer or attorney on board once you can.It is by no means past too far to plan your future.~~		In [[algebra]], '''componendo and dividendo''' (or '''componendo et dividendo''') is a method of [[simplification]] based on fractions provided that they are in proportion. It states that<ref>Bhamra, ''Partial Differential Equations''. PHI Learning Pvt. Ltd. ISBN 978-81-203-3917-0
			</ref>
			<ref>
			http://www.qc.edu.hk/math/Junior%20Secondary/Componendo%20et%20Dividendo.htm
			</ref>

			:<math> \text{If } \frac{a}{b} = \frac{c}{d} \text{ and } a \neq b \text{, then } \frac{a+b}{a-b} = \frac{\frac{a}{b} + 1}{\frac{a}{b} - 1} = \frac{\frac{c}{d} + 1}{\frac{c}{d} - 1} = \frac{c+d}{c-d}. </math>

			==Comment on the proof==
			We can similarly deduce the much more general fact that the value of any fraction

			:<math>\frac{x_0 + \cdots + x_n}{y_0 + \cdots +y_n}</math>

			in which <math>x_0</math> and <math>y_0</math> are nonzero and can be expressed in terms of the values of

			:<math>\frac{x_1}{x_0}, \ldots, \frac{x_n}{x_0}, \frac{y_1}{y_0}, \ldots, \frac{y_n}{y_0} </math>

			and the value of <math>\frac{x_0}{y_0}</math>, and so depends only on the values of those 2''n'' + 1 fractions:

			:<math> \frac{x_0 + \cdots + x_n}{y_0 + \cdots +y_n}
			= \frac{x_0}{y_0} \left(\frac{1 + \frac{x_1}{x_0} + \cdots + \frac{x_n}{x_0}}{1 + \frac{y_1}{y_0} + \cdots + \frac{y_n}{y_0}}\right)</math>

			The original result is essentially a special case of this fact, because

			:<math>\frac{x+y}{x-y} = \frac{x+y}{x+(-y)}</math>

			can be regarded as a fraction of the above form.

			==Example==
			This method can be used in various situations.

			For instance :

			:<math>\frac{\sqrt{3} + x}{\sqrt{3} - x} = 2</math>

			Find the value of ''x''.

			Solution :

			Applying C and D

			: <math>\frac{(\sqrt{3} + x) + (\sqrt{3} - x)}{(\sqrt{3} + x) - (\sqrt{3} - x)} = \frac{2 + 1}{2 - 1}</math>
			: <math>=> \frac{2 \sqrt{3}}{2 x} = \frac{3}{1}</math>
			: <math>=> \frac{\sqrt{3}}{x} = 3</math>
			: <math>=> x = \frac{1}{\sqrt{3}}</math>

			==References==
			<references/>

			==See also==
			* [[Reduction (mathematics)]]
			* [[Fraction (mathematics)]]

			{{DEFAULTSORT:Componendo And Dividendo}}
			[[Category:Fractions]]
			[[Category:Algebra]]


			{{algebra-stub}}

en>Helpful Pixie Bot: ISBNs (Build KG)

2012-05-11T10:24:19Z

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Real estate planning takes a very special type of legal professional, individual who is aware the financial markets and tendencies, along with the way that they pertain to your specific situation. However it might be tempting to draw in your very own programs and targets, you would be wise to experience a legitimate consultant to assist you as you go along. Read through in this article about what to look for in a great estate attorney. 

There is a directly to count on very clear, consistent communication with the legal professional. The individual should be able to supply you with a common summery of what you can anticipate in terms of your situation, as well as what possible issues might occur and what is done to remedy these problems. Examine online to discover what type of fees http://youtube.com/watch?v=qWZomlaZgCI ([http://www.youtube.com/watch?v=qWZomlaZgCI More hints]) are standard for your personal legal issues. This can help you prevent getting ripped off later on. Pick a legal professional who may have a good reputation and significant amounts of experience to make sure that they don't overcharge you for individual time-throwing away mistakes. Wait to sign a binding agreement having an attorney before you have the condition is proper. Request a quote from the lawyer so you are aware approximately the amount of several hours he or she intends on putting in to the scenario. In case the legal representative refuses, proceed. A array is appropriate, but it is not acceptable in case you have little idea what you really are engaging in. Often be mindful of methods properly you happen to be conveyed with by the legal professional. If this usually takes days as well as days to acquire replies to telephone calls or e-mails, then two possibilities can be found. Sometimes your attorney will not look at you with a top priority, or they are over-worked. Neither of them circumstance is good for you. Be sure to recognize how much you are going to commit before you engage a legal professional. Attorneys can be quite pricey. Their by the hour costs can break your financial budget prior to they can begin to assist you. Ensure you understand the costs advance and if you cannot afford a specific legal professional, seek out one that one could afford to pay for. When getting together with using a would-be lawyer or attorney, ask her or him the person you will generally be talking to concerning your case. In certain situations, lawyers give part of their caseload to your junior affiliate. If you believe you actually interact with a definite lawyer, instantly determining you will end up working with another person might be very disconcerting. These thoughts could be exacerbated should you don't get in addition to the other person, way too. Observe how possible lawyers react to your own personal needs. The real key to some great attorney is now being prepared to accomodate the needs and wants with their customers. If you come across a legal professional which is not considering satisfying this, then you definitely have been presented ample warning that you ought to find a person else to handle your case. Whenever you believe that you could have got a lawsuit, it can be appealing to phone one of those particular legal representatives inside the tv commercials on television. Even though these attorneys are qualified, [http://www.youtube.com/watch?v=ORuh1Dr9rcs richard schwartz] they will not be capable to [http://Www.Adobe.com/cfusion/search/index.cfm?term=&training+law&loc=en_us&siteSection=home training law] in your state, based on where by they had taken the Pub examination. It is always good to check out this and study the fine print. If you discover a breakup attorney and they also seem extremely enthusiastic about producing your ex lover "spend" for everything they already have carried out to you, try to find somebody else. Although you might have vengeance within your coronary heart, your attorney should certainly think direct constantly. Getting biased is just not a great job ethic, even if it is inside your favor. Now you recognize much more about how residence preparation operates and how legal counsel can help, you can move ahead with a properly-knowledgeable strategy. Look for testimonials, shop around and get your brand new lawyer or attorney on board once you can.It is by no means past too far to plan your future.