Linear equation and Talk:Carnival Corporation & plc: Difference between pages

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==Name==

A '''linear equation''' is an [[equation]] involving only the sum of [[constant]]s or products of constants and the first power of a [[variable]]. Such an equation is equivalent to equating a [[Degree of a polynomial|first-degree polynomial]] to zero. These equations are called "linear" because they represent [[Line (mathematics)|straight line]]s in [[Cartesian coordinate system|Cartesian coordinates]]. A common form of a linear equation in two variables is

"Carnival Corporation & Plc", is that a UK subsidiary?--[[User:Jerryseinfeld|Jerryseinfeld]] 00:19, 1 Jan 2005 (UTC)

*No it's a [[dual listed company]]. [[User:Carina22|Carina22]] 5 July 2005 03:21 (UTC)

== Merger and the Surviving Corporate Name==

:<math>y = mx + b \,</math>

In regards to a statement made in [[Carnival Corporation & Plc]] by [[User:Carina22]] stating that Carnival Corporation & Plc was formerly known as P&O Princess is incorrect! Carnival Corporation was a separate independently operated cruise line owned by Micky Arison and his family for nearly 40 years and P&O Princess was a United Kingdom publicly traded cruise line to which Mr. Arison and his family had absolutely '''NO''' affiliation with until the Carnival-P&O Princess merger occurred. So basically after the merger was completed P&O Princess became a subsidary of Carnival and the P&O name was dropped in favor of the Carnival name but the way you wrote it, it made it look like Carnival was always called P&O Princess which as stated before is an incorrect statement to make. [[User:Misterrick]] 05:10, 05 July 2005 (UTC).

In this form, the value <math>m</math> will determine the [[slope]] or gradient of the line; and the value '''<math>b</math>''' will determine the point at which the line crosses the ''y''-axis. Equations involving terms such as ''x''², ''y''^1/3, and ''xy'' are "non-linear".

:No it isn't a subsidiary, it is a [[dual listed company]]. This is an unusual arrangement, so read the article if you don't know what it means. So far as I know Carnival is the only major "American" dual listed company, but we have several in the UK so we are more familiar with the concept. [[User:Carina22|Carina22]] 06:37, 12 July 2005 (UTC)

Again, In accurate statements being made by [[User:Carina22|Carina22]]. Yes, P&O Princess did become a subsidary under the new dual listed company and again Carnival was never formerly known as P&O Princess, As stated before P&O Princess was a separate company that mergered with Carnival, In fact Carnival was started 40 years before Princess even existed so how can Carnival have been formerly known as P&O Princess when P&O Princess didn't even exist when Carnival was first started by Micky Arison's father? Additionally on the Carnival Corporation & Plc website it states, "On April 17, 2003, Carnival Corporation (NYSE: CCL) and P&O Princess Cruises plc (LSE: POC) merged via a dual listed company structure (DLC). Subsequently, P&O Princess Cruises plc has changed its name to Carnival plc." so there is no way that Carnival could ever have been formerly known as P&O Princess. [[User:Misterrick|Misterrick]] 19:52, 12 July 2005 (UTC).

==Examples==

::No, Carnival '''plc''' ''was'' formerly P&O Princess Cruises. The problem is that you still don't understand what a [[dual listed company]] is. The quotation you give does '''not''' state or imply that P&O Princess Cruises plc became a subsidiary of Carnival Corporation, because it didn't. They both became holding companies of a dual listed company. Carnival Corporation was never called P&O Princess, but Carnival '''Plc''' was. This is possible because Carnival Corporation and Carnival Plc are '''two''' ''separate'', independently quoted companies. Carnival plc is the '''same''' legal entity as P&O Princess Cruises with the same shareholder body but a different name, just the same as if Ford changed its name to Detroit Motors it would be the same legal entity with the same shareholder body. The only difference is that now Carnival Plc is one of the two holding companies of Carnival Corporation & Plc. Corporation and Plc are '''two''' companies with separate shareholder bodies and ''neither owns the other'', which is a what being a [[dual listed company]] is about.

Examples of linear equations in two variables:

::Deleting a paragraph and marking that as a minor edit is not appropriate.

::And finally P&O is a lot older than Carnival Corporation. The Peninsular and Oriental Steam Navigation Company was founded in 1837, and P&O Princess Cruises demerged from it on 23 October 2000.[[User:Carina22|Carina22]] 09:46, 21 July 2005 (UTC)

You know Carina22, I'll let you have it because your being such an a--hole, I do know what a dual listed company is but you can't get it through your head what I am trying to tell you and by the way P&O doesn't stand for Princess and Orient, it's Pacific and Orient and P&O didn't found Princess they acquired it in the 60s or 70s so Carnival Cruise Lines is older. [[User:Misterrick|Misterrick]] 21:15, 28 July 2005 (UTC)

:<math>x + y = 3,</math>

:<math>3a + 472b = 10b + 37\,</math>

I have to disagree with Carina22 on this one as well. This demerger thing is giving me a headache.

:<math>3x + y -5 = -7x + 4y +3\,.</math>

From what I understand using my own knowledge:

*Carnival Cruise Lines is formed by Arison

*P&O Princess Cruises is formed later by P&O

*Carnival Corp/PLC is formed after Carnival gobbles up a bunch of other cruise lines. The Corp/PLC puts all of the lines (Carnival/HAL/Costa) under one umbrella)

*Princess Cruises demerges from the main P&O and becomes it's own company dealing only with cruises (The company has several cruise brands under its umbrella)

*Carnival and Princess merge, or perhaps Princess is bought out. Anyway, Princess becomes another cruise brand under the umbrella of Carnival Corp/PLC

I don't think Carnival was ever called P&O BEFORE the two companies merged. They had no relations with each other until the merger.

== Forms for 2D linear equations ==

Here is the company history website: [[http://phx.corporate-ir.net/phoenix.zhtml?c=200767&p=irol-history]]

Complicated linear equations, such as the ones above, can be rewritten using the laws of [[elementary algebra]] into several simpler forms. In what follows, capital letters represent [[constant]]s (unspecified but fixed numbers), while ''x'' and ''y'' are the variables.

*It says that in 2003, Carnival Corp (including brands Carnival/HAL etc) merged with P&O Princess Cruises plc (consisting of Princess, P&O, and AIDA cruises). Perhaps the names were merged to become Carnival Corporation & plc

After further research, I found this confusing text from cruisecritic.com about Princess:

===General form===

*Princess is now part of the industry's giant Carnival Corporation a move that occurred when Carnival acquired the cruise line's parent company -- U.K.-based P&O Cruises.

:: <math>Ax + By + C = 0\,</math>

: Here ''A'' and ''B'' are not both equal to zero. The equation is usually written so that ''A'' ≥ 0, by convention. The [[Cartesian coordinate system|graph]] of the equation is a [[Line (mathematics)|straight line]], and every straight line can be represented by an equation in the above form. If ''A'' is nonzero, then the ''x''-intercept, that is the ''x''-[[coordinate]] of the point where the graph crosses the ''x''-axis (y is zero), is &minus;''C''/''A''. If ''B'' is nonzero, then the ''y''-intercept, that is the ''y''-coordinate of the point where the graph crosses the ''y''-axis (x is zero), is &minus;''C''/''B'', and the [[slope]] of the line is &minus;''A''/''B''.

And regarding P&O Cruises ...

===Normal Form===

*It acquired Los Angeles-based Princess Cruises in 1974 and Sitmar Cruises in 1988, which P&O chose to merge. Even more expansion followed for its Princess Cruises subsidiary. In October 2000, the company underwent another major change: P&O's parent company was acquired by Carnival Corporation and is now known as P&O Princess.

:: <math> y sin \phi + x cos \phi - p = 0\,</math>

: Where φ is the angle of inclination of the normal and p is the length of the normal. The normal is defined to be the shortest segment between the line in question and the origin. Normal form can be derrived from general form by dividing all of the coefficients by the following:

::<math>\frac {-C\sqrt{A^2 + B^2}}{|C|(A^2 + B^2)}</math>

And Taken from P&O Cruises' website:

===Standard form===

*In April 2004 P&O Princess plc, the parent company of P&O Cruises, joined together with Carnival Corporation, bringing together two of the best known and most successful organisations in the cruise industry. Already Britain’s market leading cruise company, P&O Cruises is now part of one of the world’s largest leisure travel companies.

:: <math>Ax + By = C\,</math>

: Here, ''A'' and ''B'' are not both equal to zero and A, B, and C are integers whose greatest common factor is 1. As above, ''A'' ≥ 0. The standard form can be converted to the general form.

*P&O Princess Cruises demerged from the Peninsular and Oriental Steam Navigation Company on 23 October 2000 when it started trading as an independent company on the London and New York Stock Exchanges. Carnival Plc is now the third largest cruise company in the world by revenue

===Point-slope form===

:: <math>y = mx + b \,</math>

'''In conclusion,''' I'm totally confused!

: m is the slope of the line and b is the y-intercept.

==Ships==

===Intercept form===

you listed historic cunard ships like RMS Queen Elizabeth 1940 and old Carpathia under Carnival Corp. ships. What's that? It's wrong!

:: <math>\frac{x}{E} + \frac{y}{F} = 1</math>

QE 2 and QM 2 are okay. 10:01, July,29th 2005 DEF

: Here ''E'' and ''F'' must be nonzero. The graph of the equation has ''x''-intercept ''E'' and ''y''-intercept ''F''. The intercept form can be converted to the standard form by setting ''A'' = 1/''E'', ''B'' = 1/''F'' and ''C'' = 1.

:I'd argue that since Cunard is now a subsidiary of Carnival Corporation, that these were correctly placed. As would RMS Titanic for example. However it would have to be properly noted. [[User:JonEastham|JonEastham]] 15:27, 23 May 2006 (UTC)

===Two-point form===

:: <math>y - K = \frac{Q - K}{P - H} (x - H)</math>

: Here ''P'' ≠ ''H''. The graph passes through the points (''H'',''K'') and (''P'',''Q''), and has slope ''M'' = (''Q''&minus;''K'') / (''P''&minus;''H'').

So, how come I can't get to a P&O Cruises (Australia) or a P&O Cruises (UK) page where I would find info on the ships Pacific Sky, Pacific Star, Pacific Sun or Arcadia, Artemis, Aurora, Oceana, Oriana and soon Ventura? Where is all this located? Because when I search for P&O Cruises, I'm basically told it doesn't exist, when it does. --[[User:Eeclwa|Eeclwa]] 21:56, 26 December 2006 (UTC)

===Parametric form===

:: <math>x = Tt + U\,</math> and <math>y = Vt + W\,</math>

: Two [[simultaneous equations]] in terms of a variable parameter ''t'', with slope ''M'' = ''V'' / ''T'', x intercept (''VU''&minus;''WT'') / ''V'' and y intercept (''WT''&minus;''VU'') / ''T''.

:This can also be related to the two-point form with ''T'' = ''P''&minus;''H'', ''U'' = ''H'', ''V'' = ''Q''&minus;''K'', and ''W'' = ''K'':

:: <math>x = (P - H)t + H\,</math> and <math>y = (Q - K)t + K\,</math>

: In this case ''t'' varies from 0 at point (''H'',''K'') to 1 at point (''P'',''Q''), with values of ''t'' between 0 and 1 providing [[interpolation]] and other values of t providing [[extrapolation]].

===Special cases===

:: <math>y = F\,</math>

: This is a special case of the standard form where ''A'' = 0 and ''B'' = 1, or of the slope-intercept form where the slope ''M'' = 0. The graph is a horizontal line with ''y''-intercept equal to ''F''. There is no ''x''-intercept, unless ''F'' = 0, in which case the graph of the line is the ''x''-axis, and so every real number is an ''x''-intercept.

I agree that P&O cruises should have it's own page, Carnival may own P&O, but it owns Princess to and they have their own page (incidentally P&O took over Princess before both brands were taken over by Carnival, deepening the injustice!) P&O Cruises has a history of over 100 years that stretches back way before Carnival comes along. Just because we trade as Carnival now (ok, so the cat's out of the bag, I work for P&O, well, Cunard, but that's another rant...) we still trade as P&O in the UK, most people don't know who Carnival are!

:: <math>x = E\,</math>

: This is a special case of the standard form where ''A'' = 1 and ''B'' = 0. The graph is a vertical line with ''x''-intercept equal to ''E''. The slope is undefined. There is no ''y''-intercept, unless ''E'' = 0, in which case the graph of the line is the ''y''-axis, and so every real number is a ''y''-intercept.

<br /> I'll agree to the last two comments. Definately something that needs doing one day. [[User:Newda898|Newda898]] 21:04, 29 January 2007 (UTC)

:: <math>y = y \ </math> and <math> x = x \ </math>

: In this case all variables and constants have canceled out, leaving a trivially true statement. The original equation, therefore, would be called an ''[[identity (mathematics)|identity]]'' and one would not consider the graph (it would be the entire ''xy''-plane). An example is 2''x'' + 4''y'' = 2(''x'' + 2''y''). The two expressions on either side of the equal sign are ''always'' equal, no matter what values are used for ''x'' and ''y''.

:I started a separate article for [[P&O Cruises]]. It's a tad shortish as I didn't dare to get into the company history after all this confusion... so if anyone can wrap their heards around this better than me, go and improve the article right now! - [[User:Kjet|Kjet]] 11:17, 29 March 2007 (UTC)

Note that if algebraic manipulation leads to a statement such as '''1 = 0''', then the original equation is called ''inconsistent'', meaning it is untrue for any values of ''x'' and ''y''. An example would be 3''x'' + 2 = 3''x'' &minus; 5.

Great idea, it was the pain of taking a leap and starting it that seemed so daunting. Ah well, there's a project for the Easter holidays! [[User:Newda898|Newda898]] 18:34, 29 March 2007 (UTC)

In addition, there may be more than two variables in the equation or several [[simultaneous equation]]s. For more information see [[System of linear equations]].

== Titanic ==

== Connection with linear functions and operators ==

Yes Carnival did not own Titanic, but threw the purchase of Cunard, it has become part of its history. Please do not just revert back with talking about it. -[[User:Texaswebscout|Ben]] 02:10, 15 June 2007 (UTC)

In all of the named forms above (assuming the graph is not a vertical line), the variable ''y'' is a [[function (mathematics)|function]] of ''x'', and the graph of this function is the graph of the equation.

In the ''particular case'' that the line crosses through the origin, if the linear equation is written in the form ''y'' = ''f''(''x'') then ''f'' has the properties:

:<math> f ( x + y ) = f ( x ) + f ( y ) \,</math>

:<math> f ( a x ) = a f ( x ) \,</math>

where ''a'' is any [[scalar (mathematics)|scalar]]. A function which satisfies these properties is called a '''linear function''', or more generally a [[linear operator]].

Because of the linear property above, the solutions of linear equations of this kind can in general be described as a [[superposition]] of other solutions of the same equation. This makes linear equations particularly easy to solve and reason about.

Linear equations occur with great regularity in [[applied mathematics]]. While they arise quite naturally when modeling many phenomena, they are particularly useful since many [[non-linear]] equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state.

== See also ==

* [[Line (mathematics)]]

* [[Quadratic equation]]

* [[Cubic equation]]

* [[Quartic equation]]

* [[Quintic equation]]

== External links ==

* [http://www.algebra.com/algebra/homework/coordinate/ Linear Equation and System Solvers] &mdash; Solve Linear equations and 2x2 systems at Algebra.com; see instant graphs and work shown

* [http://eqworld.ipmnet.ru/en/solutions/ae.htm Algebraic Equations] at EqWorld: The World of Mathematical Equations.

* [http://calc101.com/webMathematica/lines.jsp points and lines] Step-by-step equations of a line using your input, on the web 24/7, for free.

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