text:
Talk:Intermediate Algebra

Holy cow I can't believe I remembered my login and password from 2006, it's 10/17/2017. Yes feel free to merge or do whatever you want with this book; I wrote this when I was 15/16 years old. I just liked Algebra and wanted to write a guide about it. (from Mathos) (Jaden Mathos (discuss • contribs) 03:27, 18 October 2017 (UTC))

I like this outline/Table-of-Contents, but this branch should be eliminated for lacking any technical merit whatsoever. Mouselb (discuss • contribs) 03:25, 8 October 2011 (UTC)

In my school, all of this and some more advanced stuff is all Algebra I. Cactusbin (talk) 20:46, 10 February 2009 (UTC) Wait, scratch that. Why is Algebra I and Algebra II both under the "Intermediate Algebra" book, when there is already an Algebra I book? Cactusbin (talk) 20:47, 10 February 2009 (UTC)

I have all the notes necessary to complete this. I don't expect it to take too long, but unfortunately I'm bedridden currently so I'll be writing it up before I can put it on the Internet, because I have a laptop but no wireless Internet.

Redlinks
There are way too many redlinks in the table of contents. Please finish the book or remove those links. 169.204.230.246 22:02, 26 November 2007 (UTC)

Merge
Unless there's last minute objections, merge will proceed to the book Algebra. --Sigma 7 (talk) 00:43, 17 September 2010 (UTC)

Pages to merge:
 * Expressions [[Image:100%.png]]
 * Solving Equations [[Image:100%.png]] Already merged to Algebra/Solving Equations
 * Solving Word Problems [[Image:75%.png]] -> Algebra/Word Problems
 * Absolute Value Equations [[Image:100%.png]]
 * Solving Inequalities [[Image:100%.png]]-> Algebra/Inequalities
 * Compound & Absolute Value Inequalities [[File:00%.svg]]
 * Chapter Test [[Image:100%.png]]
 * Chapter Test Answers [[Image:100%.png]]
 * Linear Equations [[Image:75%.png]] -> Algebra/Linear Equations and Functions
 * The Coordinate (Cartesian) Plane -> Algebra/The Coordinate (Cartesian) Plane
 * Slope [[Image:50%.png]] -> Algebra/Slope
 * Writing Linear Equations [[File:00%.svg]]
 * Solving Systems of Equations By Graphing [[File:00%.svg]]
 * Algebraically Solving Systems of Equations [[Image:25%.png]]

 * Excellent, I had been working on this slowly at one point but got side tracked. I would be glad to have any help on this task. Thenub314 (talk) 00:53, 17 September 2010 (UTC)
 * why the fuck would you merge the articles? There is no reason! I must object.John Holmes II (talk) 14:10, 11 October 2010 (UTC)

title: Talk:Intermediate Algebra


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Muggles' Guide to Harry Potter/Characters/Nymphadora Tonks

Overview
Nymphadora Tonks, or as she prefers to be called, Tonks, is an Auror, and a member of the Order of the Phoenix. Her parents are Andromeda (Black) Tonks, who was Sirius' favorite cousin, and Ted Tonks, who was a wizard, though Muggle-born. Narcissa Malfoy and Bellatrix Lestrange are Tonks' aunts from her mother's side, though none of them would admit that. She attended Hogwarts around 1984-1991 as a Hufflepuff.

Order of the Phoenix
Nymphadora Tonks joins the cast of characters at the beginning of the fifth book, when she arrives at Number Four, Privet Drive to help escort Harry to the headquarters of the Order of the Phoenix. From Harry's conversation with her, we learn that Tonks is a Metamorphmagus, and that she went to Hogwarts, but was not made a Prefect, mostly because she was unable to control herself. Most of the time, her hair is shocking pink; it appears that this is her favorite hair color, because she seems to revert to it quite easily. We learn that she is an Auror working for the Ministry of Magic, which is a great help to the Order. With the Order being largely underground at this time, Tonks still has to work at her regular Auror duties; we see her occasionally, doing guard duty for the Order.

At dinner at Headquarters, Tonks amuses Ginny and Hermione by changing the shape of her nose. Apparently, this is a common game, because they keep asking for their favorites.

Tonks accompanies the group to the train station to board the Hogwarts Express. For the duration of the trip, she disguises herself as an old lady.

Several times over Christmas break, Tonks visits Headquarters. She accompanies the Weasley family as they visit Arthur Weasley in hospital. At the end of Christmas Break, she travels to Hogwarts with the Weasleys, Harry, and Hermione in the Knight Bus. Stan Shunpike says that "that bossy lady 'oo is witchu" has paid a premium to get them to Hogwarts quicker, so their stop will be the next but one.

Tonks takes part in the battle in the Department of Mysteries in the end of the book where she fires a Stunning Spell at Lucius Malfoy and then begins to duel Bellatrix Lestrange. Bellatrix, however, quickly knocks Tonks out.

Half-Blood Prince
In this book, we first see Tonks briefly when Harry is taken to The Burrow by Dumbledore. She is sitting in the kitchen, apparently talking something serious over with Molly Weasley. Harry is immediately struck by how depressed she looks. Tonks does not stay, but departs almost immediately once Harry has arrived, and Harry observes that Mrs. Weasley looks troubled.

Discussing Tonks' listless appearance with Hermione, Ginny, and Ron the next morning, Harry discovers that Mrs. Weasley had apparently been hoping that Bill would express an interest in Tonks, instead of Fleur Delacour, to whom he is now engaged. Ron suggests that with Tonks looking as sad as she does, there was little chance of Mrs. Weasley's hopes being fulfilled.

On the Hogwarts Express, Harry is caught by Draco Malfoy attempting to eavesdrop. Draco immobilizes him, and after breaking his nose, leaves him on the train as it returns towards London. Tonks, getting onto the train before it has completely left, frees him and returns him to the platform. She then takes him up to the school, where she sends a message for assistance entering the school grounds. As Hagrid is not present, the messenger reaches Severus Snape, who comes to the gate to let them in. Snape comments that Tonks' Patronus has changed; the one Harry saw was something large and hairy, Snape cuttingly remarks that he had liked the old one better, and it had seemed stronger.

On the way to The Three Broomsticks, Harry sees Mundungus Fletcher talking to the Hog's Head Inn barman. Mundungus drops a suitcase, spilling its contents, including a silver goblet bearing the Black family crest. Harry, enraged, seizes Mundungus' throat, claiming he has looted Sirius Black's house. Mundungus blasts Harry away and Disapparates. Tonks appears and says it is useless to hunt for him, but Harry intends to report Mundungus to Dumbledore.

It is mentioned at Christmas time at The Burrow that Tonks had been invited, but had instead chosen to spend Christmas alone. This demonstrates that she has become depressed and withdrawn. Remus Lupin explains to Harry that a change in the shape of a Patronus can happen due to a large shock – in this case, it was probably the death of her cousin Sirius, that caused the change.

On one occasion when Harry is attempting to enter the Room of Requirement, he is surprised by Tonks, looking more burdened still, who claims to be looking for Dumbledore, but seems rather aimless when she wanders away after their meeting.

Tonks is one of the members of the Order of the Phoenix who is present at Hogwarts, fighting Death Eaters at the school in the climactic battle in this book.

In the end of the book, we learn that the real reason for Tonks' depression is because she has fallen in love with Lupin, who has been trying to convince her that they cannot be together because he is a werewolf. However, in the last chapter, we see Tonks and Lupin holding hands, and Tonks has obviously regained her ability to change her appearance, as her hair is once again bright pink.

Deathly Hallows
Tonks proudly shows Harry her wedding ring when a group of Order members go to get Harry. Tonks then also says she's sorry Harry couldn't be there and that it was a small event, leaving us to believe that Lupin didn't want it that public but would have liked Harry to be there. When the Order members and their "Harrys" leave the House and Ron is the "Harry" that goes with Tonks, she tells Ron to hop on and hold tight. We then see Ron hops on, then sends an apologetic glance towards Lupin before holding on to her waist.

Tonks arrives quite late at The Burrow; apparently she had been intercepted by Bellatrix Lestrange and had quite a battle to get away from her.

Lupin later reveals to Harry, Ron, and Hermione that Tonks is pregnant. Lupin seems to be angry with himself, fearing that his son might be a werewolf; he feels that is a burden too great to saddle anyone with, and he had not wanted to pass on the horrible and painful trait to someone else. Additionally, he does not want Tonks and the child to face the same prejudice he faces, even though Tonks, being a half-blood, is already facing that sort of prejudice as the Wizarding world falls under Voldemort's control.

Tonks has the baby, and Lupin travels to Shell Cottage, where Harry, Ron, and Hermione are staying, to tell them the good news. Lupin asks Harry to be godfather, saying that he and Tonks had discussed it.

When the Order members come to Hogwarts through the Room of Requirement, Lupin shows everyone a baby picture and it proves that the baby has inherited his mother's Metamorphmagus traits. Tonks had been left at home with Teddy, her son, for the final battle but is worried about Lupin and shows up to look for him. She hears he was last seen battling Dolohov on the grounds, and runs off to find him.

Later as Harry walks back into the Great Hall with Severus Snape's memories, he spots Lupin and Tonks lying on the ground together, both dead.

Strengths
The fact that Tonks is a Metamorphmagus has made her extremely valuable, both as an Auror and as a member of the Order of the Phoenix. Tonks is a very strong, friendly, funny, and outgoing person.

Weaknesses
As soon as we are introduced to Tonks, we learn that she is extremely clumsy – she enters the story by breaking a dish in the Dursley's kitchen. Throughout the books, she is always breaking things, knocking objects over, and falling down. Because of this, she says she almost failed the "Stealth" portion of her training to become an Auror. However, this got better over the course of book six.

Relationships with Other Characters
Tonks has a romantic interest in Remus Lupin and they are seen holding hands at the end of the sixth book. By the beginning of the seventh book they are married, and have a child on the way. They die together at the battle of Hogwarts, leaving their child to be raised by Tonks' mother, Andromeda.

Analysis
One of the things that makes this series of books so powerful is that through the seven-year arc of the series, characters mature and change. This is particularly true of Harry, Ron, and Hermione, of course, as they are in a stage of their lives where there is normally great change; that is discussed in greater detail in their articles. However, a particular strength of this series is that this character growth is not restricted to the main characters, but happens to all characters in the story to some degree. As a case in point, let us take Tonks. She is quite young, having just completed her Auror training; she would be about seven years older than Harry, making her about 22 to Harry's 15 when they meet at the beginning of Harry Potter and the Order of the Phoenix. She is disapproving of the sterile neatness of the Dursley's house, and feels much more at home in Harry's room which has been inhabited by the equivalent of a caged beast for four days. She indicates that she has never gotten the hang of cleaning, herself. She apparently routinely makes a show at dinner, changing her nose shape between bites. She is very much the young, carefree witch at this stage in her life.

During the course of Harry Potter and the Order of the Phoenix, Tonks keeps up her carefree ways, right up to the battle at the Ministry. There, possibly for the first time in her life, she is engaged in a battle against superior odds with a very real possibility that she will die. This is, for anyone, a maturing experience.

It is quite possible that upon regaining consciousness and discovering that her cousin Sirius had literally gone beyond the Veil, Tonks had done some rather serious reconsideration of her life. It was likely in the course of this that she discovered that what she had previously shared with Remus, which we don't see, but can infer, was rather more serious than she had thought. When we see Tonks in September after the battle, she seems much more mature: her hair color is subdued, and she herself is much more reserved. She also seems quite depressed, having difficulty changing her appearance, always seeming on the verge of tears, and even appears thinner than usual. Ron, Harry, and Hermione assume she is upset over Sirius' death, and Harry even suggests that Tonks may have been in love with him, which is why she's so crestfallen. It is only at the end of the book that we find that it is Lupin, rather than Sirius, who is the object of her affections. One must assume that she had attempted to move her relationship with Remus on to the next stage and been rebuffed; and there almost certainly was something going on before that, as six weeks (from the battle at the Ministry, to when Harry arrives at The Burrow) is a very short time to re-assess your life, fall in love, start considering marriage, and show the effects of being refused. It is a safe assumption that there had been some snogging going on behind the scenes for the duration of Harry Potter and the Order of the Phoenix. We can only speculate that the author chose to not show us these scenes of Lupin and Tonks together because of Lupin's delicacy concerning these matters.

We can easily see that Tonks is taking a much more serious view of life throughout Harry Potter and the Half-Blood Prince; from the time we first see her in July, right to the end of the book, she seems less care-free. It is perhaps a criticism of aging in general that maturity seems to rule out being care-free, but that is the case; as one matures, one starts taking an interest, and being concerned by, things outside oneself, which does lead one to act with increased sobriety. We do know that Tonks wants to make a life-long commitment to Lupin by the end of the book, which is something that she clearly would not have imagined possible at the beginning of Harry Potter and the Order of the Phoenix. It is this growth and change in her that brings Tonks alive for us, that makes us care about her, and that makes us glad that Lupin seems to be willing to entertain the idea of settling down with her.

One editor has recently asked if there is a stated date for Tonks' wedding. Internal evidence suggests the third week of July, but does not refine it further: Harry is to be moved to a safe house on "Saturday next", we are told in the meeting at Malfoy Manor in Harry Potter and the Deathly Hallows, a meeting where Voldemort makes fun of Tonks' wedding the previous week. We also know that the Seven Potters, when Harry actually leaves Privet Drive, occurs shortly before his birthday on the 31st. But the date is refined no more than that in the story, and we aren't even actually certain what day of the week Harry's birthday falls on.


text:
Basic Algebra/Working with Numbers/Formulas

Lesson

In this lesson we will be learning formulas. A formula is a standard procedure for solving a class of mathematical problems

There are many different kinds of formulas and like it or not most of us high school kids need to know some of them.

To give you an example of a formula we will show you the formula for finding area.

To find the area of a rectangle you multiply the length times the width. If the rectangle on the right is five inches wide and six inches long you would multiply five times six and get thirty, that would be the area of this rectangle. That is the formula for the area of a rectangle: Length * Width.

Of course there are other harder formulas you will have to work with but now you know the basics of what a formula is.

A formula is an established form of words or symbols for use in a ceremony or procedure.

Example Problems
Example A:

Solve for 'y':

(a = 7)

a +5 + y = 20

Answer:

a + 5 + y = 20               (Put the 7 in place of the 'a')

7 + 5 + y = 20               (Add the integers, add 7+5=12)

12 + y = 20

12-12 + y = 20 - 12          (to get the 12 to the other side, add -12 to each side.)

y = 8                        (20-12=8, so this leaves y=8)

Check:

a + 5 + y = 20               (to check it, put the 7 in place of the a, and the 8 in place of the y.)

7 + 5 + 8 = 20               (7+5+8=20, it's correct!)

Example B:

Solve for 'x':

(a = 7)

5 + 2 + x + a = 24

Answer:

5 + 2 + x + 7 = 24

14 + x = 24

14-14 + x = 24-14

x = 10

Check:

5 + 2 + x + a = 24

5 + 2 + 10 + 7 = 24

Practice Games
put links here to games that reinforce these skills

Practice Problems
(Note: put answer in parentheses after each problem you write)


text:
Basic Algebra/Solving Equations/Solving Multi-Step Equations

Lesson
A multi-step equation is an equation that needs two or more steps to do. Our goal is to let the variable to be on its own on one side of the equal sign. You have to get rid of the numbers other than the variable on the side before the equal sign. If you do anything to a side you have to do the same thing on the other side. Solving multi-step equation is just like solving a one-step equation with more steps.

Example Problems
Solve 4 x - 5 = 15

First we must get rid of the five by addition on both sides.

4 x - 5    = 15 4 x - 5 + 5 = 15 + 5 4 x        = 20

Then divide four on both sides.

4 x    = 20 4 x ÷ 4 = 20 ÷ 4 x    = 5

We found our answer, x = 5

Solve 3 x + 6 = 27

First we must get rid of the 6 by subtraction on both sides.

3 x + 6    = 27 3 x + 6 - 6 = 27 - 6 3 x        = 21

Then we have to divide by three on both sides. 3 x    = 21 3 x ÷ 3 = 21 ÷ 3 x    = 7

The Answer is, x = 7

Practice Games
put links here to games that reinforce these skills

Practice Problems
 {3x-8=7 x={ 5_1 }
 * type="{}"}


text:
Basic Algebra/Solving Equations/Solving Equations with Variables on Both Sides of the Equation

Vocabulary

 * Variable: A letter ($$a$$-$$z$$) that takes the place of a number.

 * Equation: An example would be like $$8y - 3 = 1 + 10y$$ (The answer is $$y=-2$$ )

Lesson
NOTE: WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER SIDE! NO EXCEPTIONS!

1) do the distributive property.

2) Combine like terms on both sides.

3) add/subtract numbers next to a variable on both sides.

4) divide by the number next to the variable on both sides.

5) The answer should look like: $$x=20$$ or $$20=x$$.

(Note: the variables and numbers may vary in your answer.)

Example Problems
A simple problem:

Practice Games
Put links here to games that reinforce these skills

Purplemath.com: http://www.purplemath.com/modules/index.htm

Practice Problems
Note: Use  as the fraction line and put spaces between wholes and fractions!  {$$3x - 2 = x + 16$$ Answer:{ 9_8 }
 * type="{}"}

{$$2y = 15 - y$$ Answer:{ 5_8 }
 * type="{}"}

{$$\frac{z - 5}{-3} = 9 + 3.4z$$ Answer: { -55/28|-1 27/28_8 }
 * type="{}"}


text:
Basic Algebra/Polynomials/Exponents

Vocabulary
Base: The number directly preceding an exponent

EX: a2 -> a is the base

Exponent: The number (written in superscript) used to express how many times a base is multiplied by itself

EX: a4 = a * a * a * a -> 4 is the exponent

EX: 43 = 4 * 4 * 4 = 64 -> 3 is the exponent

Lesson
Exponents are a simple way to represent repeated multiplication. For example a x a = a2. There are a few simple rules for exponents that help reduce very large problems to simple little ones. The rules are as follows:

1) The exponent of any number is always a one (1): a = a1

2) When we multiply the same base we add our exponenents: a3 x a2 = a3 + 2 = a5

3) When we divide the same base we subtract our exponents: a6 / a4 = a6 - 4 = a2

4) When we raise a power to a power we multiply our exponents: (a2)3 = a2 * 3 = a6

5) When we raise a PRODUCT to a power we raise both parts of the product to the power: (ab)3 = a3b3 [NOTE: This ONLY works with multiplication and NOT addition: (a + b)3 ≠ a3 + b3]

6) When we raise a QUOTIENT to a power we raise both parts of the quotient to the power: (a/b)2 = a2 / b2 [NOTE: This ONLY works with division and NOT subtraction: (a - b)2 ≠ a2 - b2]

Practice Problems
Use  for exponentiation and remember Order of Operations  { x3 × x6 = { x^9 (i) _15 }
 * type="{}"}

{ ax × a3 = { a^(x + 3) (i)|a^(x+3) (i) _15 }
 * type="{}"}

{ x4 / x2 = { x^2 (i) _15 }
 * type="{}"}

{ (a4b)3 = { a^12 * b^3 (i)|a^12*b^3 (i)|a^12b^3 (i) _15 }
 * type="{}"}

{ (a2b3c)3 = { a^6 * b^9 * c^3 (i)|a^6*b^9*c^3 (i)|a^6b^9c^3 (i) _15 }
 * type="{}"}

title: Basic Algebra/Polynomials/Exponents


text:
Basic Algebra/Polynomials/Zero and Negative Exponents

Lesson
There are two very important things you need to know when working with Zero Power or Negative Exponents.

First, any number to the Zero Power always equals one. For example (-50)0 = 1

There is one number that CANNOT be raised to the Zero Power, 00 does not exist!

When dealing with Negative Exponents there is a simple trick. Whatever part of a fraction the negative exponent is in, switch it and the exponent becomes positive.

a-2 = 1/a2

1/a-3 = a3

If we have something a little more complicated, we only move things with Negative Exponents. These processes only work with multiplication. If there is addition/subtraction involved, then we are in something a little more complicated than Algebra 1...

(a-2c3)/b-1 = (bc3)/a2

Something like this wouldn't follow the aforementioned rules

(a-2 + b5)/(c6)

This problem would require a little more work: splitting up the fraction and working with both parts individually and having an answer with two fractions instead of one nice one. It's possible but it doesn't flow like the other examples or the practice problems.

Example Problems
(-2)2 = 4. -22 = -4.

Practice Problems
Use  for exponentiation  { (5645848213489487561864756189465548914564751567)0 = { 1_19 }
 * type="{}"}

{ (a-3b4c-1)-2 = { a^6 * c^2 / b^8 (i)|a^6*c^2 / b^8 (i)|a^6c^2 / b^8 (i)|a^6*c^2/b^8 (i)|a^6c^2/b^8 (i)|a^6 * b^(-8) * c^2 (i)|a^6*b^(-8)*c^2 (i)|a^6b^(-8)c^2 (i)|a^6 * b^-8 * c^2 (i)|a^6*b^-8*c^2 (i)|a^6b^-8c^2 (i) _19 }
 * type="{}"}

{ a-8b-2c-1 = { 1 / (a^8 * b^2 * c) (i)|1 / a^8 * b^2 * c (i)|1 / (a^8*b^2*c) (i)|1 / a^8*b^2*c (i)|1 / (a^8b^2c) (i)|1 / a^8b^2c (i)|1/(a^8 * b^2 * c) (i)|1/(a^8*b^2*c) (i)|1/a^8*b^2*c (i)|1/(a^8b^2c) (i)|1/a^8b^2c (i)|1 / a^8 / b^2 / c (i)|1/a^8/b^2/c (i) _19 }
 * type="{}"}

{ a2b-3c4 = { a^2 * c^4 / b^3 (i)|a^2*c^4 / b^3 (i)|a^2c^4 / b^3 (i)|a^2*c^4/b^3 (i)|a^2c^4/b^3 (i) _19 }
 * type="{}"}


text:
Basic Algebra/Polynomials/Adding and Subtracting Polynomials

Vocabulary
Polynomial: Mathematical sentence with "many terms" (literal English translation of polynomial). Terms are separated by either a plus (+) or a minus (-) sign. There will always be one more term than there are plus (+) or minus (-) signs. Also, the number of terms will (generally speaking) be one higher than the lead exponent.

EX: A Quadratic function has a lead exponent of 2, but generally has three terms (ax2 + bx + c; lead exponent = 2, # of + (or -) signs = 2, # of terms = 3)

Like Terms: Terms in a polynomial that have the same power of the variable

EX: 3x2 and 2x2 are like terms, but 3x2 and 4x3 are not!

PROPERTIES TO REMEMBER:

If we see a variable standing alone (it has no coefficient, no number next to it) then we assume that there is an invisible one (1) standing there:

x2 = 1x2

We are extremely lazy in math and do not like to write numbers that we feel are unnecessary. This is one of the cases in which we do not write what is actually there but we always remember it is. Another case is with fractions and whole numbers. The DEMONIMATOR of every whole number is a one (1) but we do not write this one (1) because we do not feel the need. We always remember it is there though.

4 = 4/1 [READ: 4 over 1]

Lesson
There are many, many types of polynomials in the world of mathematics and are classified by the power (or exponent) of their leading term.

Some Common Functions

1) f(x) = ax + b (more commonly seen as y = mx + b).  The leading term has an exponent of one (1) and is called a LINEAR FUNCTION because it creates a line when graphed.  Because there are two terms, this function is called a binomial, or two-termed, function.

2) f(x) = ax2 + bx + c  The leading term has an exponent of two (2) and is called a QUADRATIC FUNCTION because the first x is squared and squares are QUADrilaterals.  This function generally has three terms and is therefore called a trinomial.  A QUADRATIC FUNCTION has amazing properties that span years of mathematical studies.  Since this is the first polynomial to have more than two terms, it is the first polynomial able to be factored.  However, there are special cases in which ax2 + bx + c cannot be factored.

3) f(x) = ax3 + bx2 + cx + d  The leading term has an exponent of three (3) and is called a CUBIC FUNCTION because the first x is cubed (raised to the third power).  This function generally has four terms and will always be able to factor out at least one term of the form (x - h) [where h is any number].

There are an infinite number of polynomials and each one has amazing features unique to that function. However, there are a few universal traits to all functions. Every function with an even lead exponent (ax2, ax4, etc. . .) have a chance of not being factorable. Every function with an odd lead exponent (ax, ax3, etc. . .) will be able to factor AT LEAST ONE term of the form (x - h) [where h is any number].

_______________________________________________________________________________________________________________________________

As with regular numbers, we can add and subtract polynomials. However, instead of only worrying about which numbers have an x and which numbers do not, we also have to keep in mind that the exponents have to be the same in order for us to add and subtract terms.

EX: Add (4x3 + 3x + 1) + (-3x3 + 2x2 + 4)

Step 1: We have to match up our terms: (4x3 + -3x3) + (2x2) + (3x) + (1 + 4)

Step 2: We combine the coefficients of the like terms: x3 + 2x2 + 3x + 5 <- We've solved the problem

(4x3 + 3x + 1) + (-3x3 + 2x2 + 4) = x3 + 2x2 + 3x + 5

Subtracting polynomials is the same thing, except we add an extra step. When we subtract polynomials we use the distributive property first and multiply the second polynomial by a negative one (-1). This changes all the signs of the second polynomial to the OPPOSITE of what they are. [NOTE: When we add a negative number we actually subtract!!!]

EX: Subtract (3x4 + 2x2 + 2) - (x4 + 6x2 + 12x - 1)

Step 1: We distribute the negative one (-1) across the second polynomial and our new polynomial reads:

(-x4 - 6x2 - 12x + 1) <- Notice how the signs are all opposite of what we were given.

Step 2: We match up our terms: (3x4 + -x4) + (2x2 + -6x2) + (-12x) + (2 + 1)

Step 3: We combine our coefficients of the like terms: 2x4 - 4x2 - 12x + 3

(3x4 + 2x2 + 2) - (x4 + 6x2 + 12x - 1) = 2x4 - 4x2 - 12x + 3

Now we've successfully subtracted two polynomials.

Practice Problems
Use  for exponentiation  { (2x2 + 3x + 4) + (5x + x2 + 3) = { 3x^2 + 8x + 7 (i)|3x^2+8x+7 (i) _26 }
 * type="{}"}

{ (-3x5 + 12x3 + 15x - 2) + (4x5 - 8x3 + 2x2 - 7x) = { x^5 + 4x^3 + 2x^2 + 8x - 2 (i)|x^5+4x^3+2x^2+8x-2 (i) _26 }
 * type="{}"}

{ (9x - 5) - (8x + 6) = { x - 11 (i)|x-11 (i) _26 }
 * type="{}"}

{ (3x3 + 2x) - (-x2 - 1) = { 3x^3 + x^2 + 2x + 1 (i)|3x^3+x^2+2x+1 (i) _26 }
 * type="{}"}


text:
Basic Algebra/Polynomials/Multiplying Monomials

Practice Problems
Use  for exponentiation  {Easy}

{ (4g3h)(-2g5)={ -120g^2*h (i)|-120g^2h (i) _9 }
 * type="{}" coef="1"}

{ (4g3h)(-2g5)={ -8g^8*h (i)|-8g^8h (i) _9 }
 * type="{}" coef="1"}

{ Medium}

{ Hard}


text:
Multibody Mechanics/Euler Parameters

Euler parameters (also known as Euler-Rodrigues parameters or unit quaternions) are an alternative to Euler angles as a means to describe the relative orientation of reference frames in three dimensions.

The significant difference between Euler parameters and Euler angles is that where there are only three Euler angles, there are four Euler parameters. The Euler parameters are not independent, and a valid set of parameters must satisfy the constraint that the sum of their squares is constant.

The Euler parameters are defined by an axis and angle, i.e. the relative orientation of frames is described by a rotation about a common axis. If the axis defined by the vector $$\vec{u}$$ decomposed as $$u_1,u_2,u_2$$ in both frames (the axis is common), and the rotation by an angle $$\phi$$ (right-handed about the vector) to arrive at orientation of the second frame, then the Euler parameters are

$$e_0=\cos\left(\frac{\phi}{2}\right)|\vec{u}|$$

$$e_i=\sin\left(\frac{\phi}{2}\right)u_i, i=1...3$$

Note that it is common for one to consider Euler parameters in normalized form where the vector $$\vec{u}$$ is a unit vector $$\hat{u}$$, in which case the Euler parameters will, by definition, satisfy the constraint that their squares sum to one.

title: Multibody Mechanics/Euler Parameters


text:
Basic Algebra/Factoring/Factors of Integers

Vocabulary

 * Factor: A factor of an integer n is any number that divides n without remainder.
 * Prime Number: A positive integer n is called prime if its only factors are 1 and n (and -1 and -n).
 * Composite Number: An integer n is called composite if it is not prime. This means that n is composite if it has a factor that is not 1 and not n.

Lesson
Sometimes numbers can be written as the product of other numbers. When we write a number n as a product (n = a x b) then say that a and b are factors of n. The equation n = a x b is called a factorization of n.

For example, 6 is a factor of 12 because 12 = 2 x 6. Also, 3 is a factor of 6 because 6 = 2 x 3. If we put these factorizations together we get 12 = 2 x 6 = 2 x (2x 3) = (2x2)x3 = 4 x 3 and so 3 and 4 are factors of 12.

But, for example, 4 is not a factor of 13 because 4 cannot multiply any other whole number and come out with an even 13.

If we have a number n we can always factor it as n = 1 x n. So 1 and n are always factors of n.

If we have a factorization n = a x b then n = (-a) x (-b). This means that if a is a factor of n then -a is also a factor of n. A positive integer can always be factored into positive integers.

We call a positive integer p a prime if it can only be factored into positive numbers as p = 1 x p or p = p x 1. The number 1 is a special number which we do not call prime.

There are many prime numbers: 2,3,5,7,11,13,17 and more.

When a positive integer is not prime we call it composite. Since we can write 12 = 2 x 6, we know that 12 is not prime. That means we call 12 composite.

There are many composite numbers: 4,6,8,12,14,15,16,18 and more.

Every positive number can be factored into a product of positive primes in only one way. For example, 30 = 2 x 15 = 2 x 3 x 5 where 2, 3 and 5 are prime. A factorization of a number into a product of primes is called a prime factorization. There is only one prime factorization of a number.

If we write a factorization of 30 that then it must either contain a composite number of be 2x3x5. The factorizations of 30 are listed below:
 * 30 = 1 x 30,
 * 30 = 6 x 5,
 * 30 = 2 x 15,
 * 30 = 10 x 3, and
 * 30 = 2 x 3 x 5. This is the prime factorization of 30.

What, then, is the prime factorization of 100?

100 = 1 x 100, 100 = 2 x 50 100 = 4 x 25 100 = 2 x 2 x 5 x 5

Example Problems

 * 1) Is 4 a factor of 20? Answer: Yes. The number 4 is a factor of 20 because 20 = 4 x 5.
 * 2) Is 6 a factor of 20? Answer: No. The number 6 is not a factor of 20 because 6 does not divide 20 without remainder; 20 = (6 x 3) + 2.
 * 3) Find all factorizations of 20. Which factorization of 20 is the prime factorization. Answer:
 * 4) * 20 = 1x20,
 * 5) * 20 = 2x10,
 * 6) * 20 = 4x5, and
 * 7) * 20 = 2x2x5 are the factorizations of 20. This last factorization is the prime factorization of 20.

Practice Games
One way to think of factor games is as all the different ways you can package groups of given numbers. For instance 12 items can be packaged as a string of 12, like a giant skinny chocolate bar, or as 2 groups of six like a carton of eggs, or as 4 sets of 3 like two six packs of soft drinks. Experience with factors and numbers can make other people respect your ideas when you use your number sense to find more attractive or efficient ways to create or display something.

There are many online games you can play involving factorization. One of my favorites is the factor game. In order to win this game you must pick numbers with small prime factors while leaving numbers with special large composite factors for the end game.

A factor game you can play without a computer is to pick a range of prime numbers. You can give one player a time limit to construct a composite number with these primes. If there are just two players you can allow player number 2 to factor the number and then compare the factorizations. If player 1 made a mistake constructing the number then player 2 gets a point, if player 2 does not factor the number correctly then player 1 gets a point. This game can be extended for multiple players by allowing the players factoring the numbers to race for the factorization, and then checking the answers in the order which they are turned in. Something that makes this game interesting is that multiplications with larger prime numbers become harder to perform correctly and harder to decompose. You can easily handicap this game by giving some players more times to pick their number then other players. For instance how big a number can you build with the primes 2, 3, 5, 7, 11, and 13 in 30 seconds? It takes less time to double numbers than multiply them by 11, but these numbers are also easier to factor.

Practice Problems
Easy

Medium

Hard


text:
Basic Algebra/Factoring/Squares of Binomials

Vocabulary
Binomial - An algebraic expression with exactly two terms.

Square - Multiply a number by itself.

FOIL - The product of two binomials is the sum of the products dio of the First terms, the Outer terms, the Inner terms, and the Last terms.

Quantity -Total amount or number.

Please note that the ‘FOIL’ method as well as the shortcut shown below is ONLY for binomial(s).

Technical Equation
(a+b)2 = a2 + 2ab + b2

(a-b)2 = a2 - 2ab + b2

NOTE : These equations will work if you substitute the first term for a and the second term for b. You may find these equations easier to understand after the concept is learned using the three steps described below.

Lesson
Lesson 4 has shown you how to multiply binomials. In Lesson 5 we are going to learn how to square binomials. Squaring a binomial can be done using two different methods. The first method uses FOIL (refer to lesson 4). The second method is a shorter alternative to FOIL. The way we use the shortcut is to follow three simple steps.

Step 1: 	Square the first term of the binomial.

Step 2: 	Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

Step 3: 	Square the last term of the binomial.

Example Problems
Here is an example to follow.

Using the binomial x2+12x+36 we will square it creating the problem (x+6)2

Step 1 	Square the first term of the binomial.

(x)2=x2

Step 2 	Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

[(x)*(6)]*2 = (6x)*(2) = 12x

Step 3 	Square the last term of the binomial.

(6)2 = 36

Finally we put the three term we have acquired together and get the answer

(x+6)2 = x2 + 12x + 36

Let’s try another problem that may be a bit more difficult.

Let’s square the binomial (x2-4x) giving us (x2-4x)2

Step 1 	Square the first term of the binomial.

(x2)2 = x4

Step 2 	Multiply the first term and last term of the binomial together and then double that quantity (in other words multiply by 2).

*Notice we keep the negative sign with the second term

[(x2)(-4x)]*2 = (-4x3)*(2) = -8x3

Step 3 	Square the last term of the binomial.

(-4x)2 = (-4)2(x)2 = 16x2

Our final answer will be the answers from the three steps combined

(x2-4x)2 = x4 -8x3 + 16x2

Problem 3 (2x-6y)2 = 4x2 - 24xy + 36y2

Online Lesson
You can use this link to view this lesson illustrated by a teacher.

http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431067.html

Practice Problems
Use  for exponentiation.  { (s+4)2 = { s^2 + 8s + 16 (i)|s^2+8s+16 (i) _23 }
 * type="{}"}

{ (x+y)2 = { x^2 + 2xy + y^2 (i)|x^2+2xy+y^2 (i) _23 }
 * type="{}"}

{ (2x2 + 3y2)2 = { 4x^4 + 12x^2*y^2 + 9y^4 (i)|4x^4 + 12x^2y^2 + 9y^4 (i)|4x^4+12x^2*y^2+9y^4 (i)|4x^4+12x^2y^2+9y^4 (i) _23 }
 * type="{}"}


text:
Talk:PSP Programming

Dead Book
This wiki-book is not being up-kept. While it serves a basic purpose, you will find more information at PSP_Development. This is not a shameless plug, as a member of the PSP development community who wants to see the community exist, I am just leaving this here. --PauSix (discuss • contribs)

Copyright infringement
the following tutorials were dumped without permission: They say they were written by Brad Dwyer.
 * PSP Programming/Advanced Video
 * PSP Programming/Hello World

Confirmation
From:	"Brad Dwyer"  To:	"'Zach Morgan'"  Subject:	RE: possible copyright infringement at wikibooks Date:	Fri, 14 Jul 2006 22:40:46 -0500

No, I didn't give permission.

Cheers, Brad

-Original Message- From: Zach Morgan [mailto:grunt5000%)@yahoo.r?com] Sent: Friday, July 14, 2006 3:27 PM To: Yeldarb(@Barbdwyer,r.com Subject: possible copyright infringement at wikibooks

Hi.

I think that one or more of your PSP programming tutorials were pasted into wikibooks some time ago: see http://en.wikibooks.org/wiki/PSP_Programming/Hello_World there may be more in the psp programming wikibook.

Did you give permission for this? If not, your tutorials'll be removed from wikibooks. If so, some credits at http://en.wikibooks.org/w/index.php?title=Talk:PSP_Programming&action=edit might prevent prevent confusion in the future.

Thanks, Zach (..Snarius)

Scrap the intro?
There's a little problem with this wikibook, one that dissuades others from editing it. Any additional work will easily be overshadowed by the introduction, which has remained virtually unaltered since midway 2005, by Mgstough, who hasn't been seen since. Not that it's bad writing or anything. It just says very little to introduce the PSP or any other PSP programmer other than Mgstough. Any thoughts? --Snarius 22:24, 17 April 2007 (UTC)

title: Talk:PSP Programming


text:
Talk:Algorithm Implementation/Sorting/Bubble sort

I found a number of mistakes in the VBA example (atleast when it is run in VB6): Anyway, I fixed it up, the following example runs fine in VB6 enterprise: Sub bubble(bblarray As Integer)
 * 1) Array is a reserved word, and cannot be usede as a variable.
 * 2) This causes a subscript out of rage error when it goes Array(J + 1)
 * 3) The N argument is not needed, UBound can return the number of arrauy elements.

'N is the number of integers in the array' '0 to N-1' Dim I, J, P, Temp As Integer For I = UBound(bblarray) To 0 Step -1 P = 0 For J = 0 To I - 1 If bblarray(J) > bblarray(J + 1) Then Temp = bblarray(J) bblarray(J) = bblarray(J + 1) bblarray(J + 1) = Temp Else P = P + 1 End If        If P = I Then GoTo premend Next J Next I

'premend = premature ending = all integers are allready sorted' premend:

End Sub I dunno if it is compatible with VBA though... anyone know? MichaelBillington 02:36, 16 July 2006 (UTC)

Thanks for correcting that was my bubblesort/mistake and I wrote it for VBA (just badly changed the variables when posting here) so it works in VBA. Cheers YB 0:10 16 November 2006

Bubblesort Java implementation
Hi there,

I found an error in the Java Implementation. The problem is that numberOfTimesLooped is incremented on the inner loop instead of the outer...

Here is the corrected version (which also has some questionable performance enhancements which were required for my purpose), please somebody else insert it because I just stumbled upon this page and don't have a clue what the rules for commiting stuff here are...

public static void bubbleSort (int[] data) { boolean isSorted; int numberOfTimesLooped = 0; do { isSorted = true; int a = data[0]; int b;		for (int i = 1; i < data.length - numberOfTimesLooped; i++) { b = data[i]; if (b < a) { data[i] = a;				data[i - 1] = b;				isSorted = false; }			else a = b;		} numberOfTimesLooped++; } while (!isSorted); }

- Jannik Jochem, 2007-07-20

New algorithm for Bubblesort
I've found a slightly better implementation of bubblesort, that in the average case will have a slightly better round time. The theory behind it is the same as having a flag that checks whether or not it made any swaps, and if it has, it exits immediately. However, this will keep track of the last place where it made the swap, and cut off the list after that, when it goes through. The benefit of this implementation is that if a portion of the latter-part of your list is already sorted, it'll cut that off. My implementation of it in C# will show you what I mean.

public static void BubbleSort(LinkedList list) {  LinkedListNode tail = list.Last; while(tail != list.First) {     LinkedListNode swapped = list.First; LinkedListNode current = list.First; while(current != tail && swapped != tail) {        if(current.Value.CompareTo(current.Next.Value) > 0) {           swapped = current.Next; list.Remove(swapped); list.AddBefore(current, swapped); }        else current = current.Next; }     tail = swapped; } }

C
Instead of using two for loops, one can choose  for the same job. The algorithm for it would be: Once can note that, the variable  that was used to run a loop is no longer required. At the same time,  is used as a switch. acagastya   ✍ Dicere Aliquid  🐾 18:15, 2 February 2016 (UTC)

Ada Bubble Sort
The listed implementation for Ada isn't bubble sort.

What is currently happening: If the last integer in the array is less than the currently indexed at J, swap them. This means that if we have a 10 integer array, the 10th gets swapped multiple times per iteration. This doesn't happen with bubble sort.

Bubble sort says if the *next* element after J is less, then swap. In other words, the Ada implementation isn't comparing adjacent elements as it should, but always the last element with the currently indexed element.

I am not experienced enough with Ada to correct this myself.

2605:A601:AD74:2D00:B508:A447:E481:3CAE (discuss) 11:29, 16 October 2020 (UTC)


text:
William Shakespeare's Works/Poems/The Phoenix and the Turtle

Let the bird of loudest lay, On the sole Arabian tree, Herald sad and trumpet be, To whose sound chaste wings obey.

But thou shrieking harbinger, Foul precurrer of the fiend, Augur of the fever's end, To this troop come thou not near!

From this session interdict Every fowl of tyrant wing, Save the eagle, feather'd king: Keep the obsequy so strict.

Let the priest in surplice white, That defunctive music can,
 Be the death-divining swan,
 Lest the requiem lack his right.

And thou treble-dated crow,
 That thy sable gender makest
 With the breath thou givest and takest,
 'Mongst our mourners shalt thou go.

Here the anthem doth commence:
 Love and constancy is dead;
 Phoenix and the Turtle fled
 In a mutual flame from hence.

So they loved, as love in twain
 Had the essence but in one;
 Two distincts, division none:
 Number there in love was slain.

Hearts remote, yet not asunder;
 Distance, and no space was seen
 'Twixt the Turtle and his queen:
 But in them it were a wonder.

So between them love did shine,
 That the Turtle saw his right
 Flaming in the phoenix' sight;
 Either was the other's mine.

Property was thus appalled,
 That the self was not the same;
 Single nature's double name
 Neither two nor one was called.

Reason, in itself confounded,
 Saw division grow together,
 To themselves yet either neither,
 Simple were so well compounded,

That it cried, How true a twain
 Seemeth this concordant one!
 Love hath reason, reason none,
 If what parts can so remain.

Whereupon it made this threne
 To the phoenix and the dove,
 Co-supremes and stars of love,
 As chorus to their tragic scene.

THRENOS.

Beauty, truth, and rarity,
 Grace in all simplicity,
 Here enclosed in cinders lie.

Death is now the phoenix' nest
 And the Turle's loyal breast
 To eternity doth rest,

Leaving no posterity:
 'Twas not their infirmity,
 It was married chastity.

Truth may seem, but cannot be:
 Beauty brag, but 'tis not she;
 Truth and beauty buried be.

To this urn let those repair
 That are either true or fair
 For these dead birds sigh a prayer.


text:
Intermediate Algebra/Expressions and Formulas

Expressions
Throughout your mathematical journey through Arithmetic, Pre-Algebra, and Geometry, you have been introduced to (and analyzing) equations, and perhaps even expressions, but may have ignored these aspects of math. Equations, of course, involve an equal sign ($$=$$) while an expression is merely the calculations involved.

When you simplify an expression, you are answering simple arithmetic problems until you result in the simplest answer, most likely a single number, but sometimes a fraction. When you evaluate an expression, you are utilizing variables to find a single number. Of course, you are familiar with all this from the Arithmetics classes you previously took and the Arithmetic review, correct? If your memory needs some refreshing and some practicing the Order Of Operations (Please Excuse My Dear Aunt Sally), here are some practice problems.

Practice Problems
 {Simplify the following expressions.}

{ $$2 \!\cdot\! 4=$${ 8_4 }
 * type="{}"}

{ $$6 + 3^2 - 14 \div\! (3 - 2^2)=$${ 29_4 }
 * type="{}"}

{ $$(-4)^2 \!\cdot\! 3 + (42 - 12)=$${ 78_4 }
 * type="{}"}

{Evaluate the following expressions.}

{a = 2 b = 3 c = (-3) $$a + bc^2 - c(b + ac)^2=$${ 56_4 }
 * type="{}"}

{a = 4 b = (-2) c = 3 $$b - (ac)^2 + (3 - b)=$${ -141_4 }
 * type="{}"}

Formulas
Now that we understand how to simplify and evaluate expressions, we can analyze formulas. Formulas are expressions made primarily of variables that are plugged in to evaluate the expression. Formulas are used for science and mathematics often, especially Geometry.

Practice Problems
 {Evaluate the following formulas.}

{$$F = \frac{9}{5}C + 32$$ is the formula to convert Fahrenheit to Celsius or vice versa. What would the temperature be in Fahrenheit if it was 25 Degrees Celsius? { 77 °F (i)|77°F (i)|77 'F (i)|77'F (i)|77 F (i)|77F (i)|77_12 }
 * type="{}"}

{$$C = 2\pi\!r$$, where $$2r = d$$ is the formula to find the Circumference of a circle with a given radius. Find the Circumference if the diameter was 4 inches long. Assume that $$\pi$$ = 3.14 { 12.56 inches (i)|12.56inches (i)|12.56 inch (i)|12.56inch (i)|12.56 in (i)|12.56in (i)|12.56 "|12.56"|12.56_12 }
 * type="{}"}

{$$I = PRT \,$$ when I represents interest earned, P represents the principal (starting money), R represents interest rate, and T represents the time, usually express in years. This formula is often used for banking and account. After 2 years, how much interest would have been built up if you placed $5000 into an account that has an interest rate of 9.5% per year? { $950|950_12 }
 * type="{}"}

Lesson Review
Unlike equations, expressions contain no equal sign. In equations, there are two separate expressions that are equal to each other, and you are trying to make both sides of the equal sign... equal. Well, with expressions, you are either simplifying or evaluating them. To simplify an expression, you do as many of the Order of Operations as you can to get to the simplest answer. Meanwhile, to evaluate, you plug in numbers for variables and simplify from there. Formulas are special kinds of expressions and/or equations that are used for science and mathematics.

Lesson Quiz
 {Evaluate the expression if $$a = 2$$, $$b = (-3)$$, and $$c = (-2)$$. $$ab^2 \cdot\! (ac)^2 + c(b - a)=$${ 298_7 }
 * type="{}"}

{I put $300 into a savings account that has an Interest Rate of 4.5% per year, and I've had this account for exactly a year now. How much do I have in total (Principal with Interest Earned added on)? { $313.50|$313.5|313.5_7 }
 * type="{}"}

{To find the area of a trapezoid, we use this formula: $$A = \frac{1}{2}h(b_1 + b_2)$$, where $$h$$ represents the perpendicular height of the trapezoid, $$b_1$$ represents one of the bases, and $$b_2$$ represents the other base. What would the area of a trapezoid be with $$h = 4$$, $$b_1 = 3$$, and $$b_2 = 13$$? { 32_7 }
 * type="{}"}

{Does $$a^{(b^c)} = (a^b)^c$$? -yes +no
 * type=""}


text:
Radiation Oncology/Head & Neck/Larynx/Glottis

Glottic Larynx

Overview

 * Anatomy - true vocal cords, anterior and posterior commissures down to 5 mm below free margin of vocal cords
 * Most common laryngeal cancer in USA. Majority occur in anterior 2/3 of vocal cords
 * Symptoms - persistent hoarseness, later dyspnea, chronic cough, hemoptysis, stridor
 * Staging
 * T1 - limited to vocal cords, with normal mobility
 * T1a - limited to one vocal cord
 * T1b - involves both vocal cords
 * T2 - extends to supraglottis or subglottis, and/or with impaired vocal cord mobility
 * T3 - vocal cord fixation or invades paraglottic space or minor thyroid cartilage erosion
 * T4 - invades through other tissues (thyroid cartilage, thyroid, trachea, pharynx, etc)
 * T4a - invades through thyroid cartilage or tissues beyond the larynx
 * T4b - invades prevertebral space, carotid, mediastinum
 * Lymphatics - true vocal cords don't have any; lymphatic spread via tumor extension to supraglottis or subglottis
 * LN+ <2% in T1, 5% in T2, 15-20% in T3, 20-30% in T4
 * Treatment:
 * No randomized trials comparing surgery to RT to laser resection
 * For T1-T2: local control, laryngeal preservation, and survival comparable after laser resection, RT, and partial laryngectomy. Voice quality comparable with laser resection and RT in smaller lesions, worse in larger lesions after partial laryngectomy. Therefore recommendation for T1 and T2 with normal cord mobility treated with RT or laser resection for superior voice preservation. Bulky T2 and impaired cord mobility treated with RT or partial laryngectomy
 * Neck dissection in T1-T2 is controversial
 * RT fields:
 * T1 and early T2 - two small opposing lateral fields centering on vocal cords, parallel to trachea. From upper thyroid notch to lower border of the cricoid (at C6). Anterior border 1 cm anterior to the skin surface at the level of vocal cords. Posterior border to include anterior portion of posterior pharyngeal wall. 5 x 5 cm2 field usually good.

Outcomes

 * Florence; 2005 (1970-1999) PMID 16095847 -- "Radical radiotherapy for early glottic cancer: Results in a series of 1087 patients from two Italian radiation oncology centers. I. The case of T1N0 disease." (Cellai E, Int J Radiat Oncol Biol Phys. 2005 Dec 1;63(5):1378-86.)
 * Retrospective. 831 T1 glottic patients in 2 institutions. RT: two lateral parallel opposed or slightly angled photon beams with or without wedges or a direct anterior electron field.
 * Outcome: 5-year OS (10-year OS): 77% (57%); local control 84% (83%), salvage 95% (93%)
 * Predictors of local control: gender, tumor extent, anterior commissure involvement, beam type, dose >65 Gy
 * 20-year second tumor probability: 23% (second tumor deaths > laryngeal tumor deaths)
 * Conclusion: Use doses >65 Gy and field size 36-49 cm2

 * Florence; 2005 (1970-1999) PMID 16115737 -- "Radical radiotherapy for early glottic cancer: Results in a series of 1087 patients from two Italian radiation oncology centers. II. The case of T2N0 disease." (Frata P, Int J Radiat Oncol Biol Phys. 2005 Dec 1;63(5):1387-94.)
 * Retrospective. 256 T2 glottic patients in 2 institutions. RT: two lateral parallel opposed or slightly angled photon beams with or without wedges or a direct anterior electron field.
 * Outcome: 5-year OS (10-year OS): 59% (37%); local control 73% (70%), salvage 86% (85%)
 * Predictors of local control: bulky tumor, impaired cord mobility
 * 20-year second tumor probability: 23% (laryngeal tumor deaths > second tumor deaths)
 * Conclusion: Consider RT a standard treatment for T2. Late damage infrequent

 * Aviano; 2003 PMID 12910521 -- "Radiotherapy for patients with early-stage glottic carcinoma: univariate and multivariate analyses in a group of consecutive, unselected patients." (Franchin G, Cancer. 2003 Aug 15;98(4):765-72.)
 * Retrospective. 410 patients with T1-T2 SCC treated 1986-2001
 * 10-year OS (5-year): 64% (83%); median time to recurrence 7 months
 * Predictors of local control: persistent dysphonia, year of RT
 * 22% rate of 2nd primary malignancy -> major cause of death; only 2 died of laryngeal CA

 * U Florida; 2001 PMID 11600604 -- "T1-T2N0 squamous cell carcinoma of the glottic larynx treated with radiation therapy." (Mendenhall WM, J Clin Oncol. 2001 Oct 15;19(20):4029-36.)
 * Retrospective. 519 patients with T1-T2
 * 5-year local control: T1 93-94%, T2 72-80%; low complications
 * Predictors of local control: overall treatment time, T-stage, grade

Carcinoma in situ
RT for treatment of carcinoma in situ of the glottic larynx:
 * U.Florida; 2002 (1967-1998) PMID 11933181 -- "Radiotherapy for carcinoma in situ of the true vocal cords." (Garcia-Serra A, Head Neck. 2002 Apr;24(4):390-4.)
 * 30 pts; 2/3rd of referred pts had recurrence after at least one stripping procedure.
 * 5-yr LC, LC with preservation, ultimate LC (including salvage surgery): 88%, 88%, 100%
 * 10% treated pts had local failure with Invasive squamous cell carcinoma (14 mo, 34 mo and 48 months later)
 * Conclusion: "RT to approximately 60 Gy at 2.25 Gy per fraction using small (5 x 5 cm) fields produces excellent results with CIS of the TVC."

 * U.Florida; 1993 (1964-1990) PMID 8407413 -- "Carcinoma in situ of the glottic larynx: the role of radiotherapy." (Fein DA, Int J Radiat Oncol Biol Phys. 1993 Sep 30;27(2):379-84.)
 * 19 pts; minimum of 2 yrs f/u. Previous procedures: biopsy only in 4, 11 patient with 1 stripping procedure, 4 pts with 2-5 strippings. RT doses 5625 cGy - 6300 cGy (median: 5625 cGy).
 * 5-yr LC, ultimate LC, and LC w/ voice preservation: 93%, 100%, 93%.
 * Literature review: local control rates after primary treatment with RT, laser resection, and vocal cord stripping were 84%, 68%, and 66%.
 * Conclusion: "Primary treatment with radiotherapy should be strongly considered for patients with carcinoma in situ of the true-vocal cord who have a recurrence after vocal cord stripping or who cannot have close follow-up after treatment."

Randomized

 * Osaka (Japan)(1993-2001) -- RT 2 Gy/fx (60-66 Gy) vs. RT 2.25 Gy/fx (56.25-63 Gy)
 * Randomized. 180 patients with glottic T1N0. Arm 1) RT 60/30 (small tumors) or 66/33 (large tumors) @ 2 Gy/fx over ~46 days vs. Arm 2) RT 56.25/25 (small tumors) or 63/28 (large tumors) @ 2.25 Gy/fx over ~39 days. Parallel opposed fields with individualized wedge-filtered technique, majority 5x5 cm
 * 5-years; 2006 PMID 16169681 -- "Radiotherapy for early glottic carcinoma (T1N0M0): results of prospective randomized study of radiation fraction size and overall treatment time." (Yamazaki H, Int J Radiat Oncol Biol Phys. 2006 Jan 1;64(1):77-82. Epub 2005 Sep 19.)
 * Outcome: 5-year LC 2 Gy/fx 77% vs. 2.25 Gy/fx 92% (SS); CSS 97% vs. 100% (NS)
 * Late Toxicity: no severe late toxicity, no difference in early/minor late toxicity
 * Conclusion: Use of 2.25 Gy/fx with shorter overall treatment time showed superior local control compared to conventional 2 Gy/fx, without worse toxicity

 * RTOG 95-12 / EORTC 22992 -- 70/35 vs. 79.2/66 @ 1.2 Gy BID
 * Randomized. 250 patients. T2a-bN0 vocal cord. Modified AJCC staging: T2a - tumor extends to supraglottic and/or subglottic structures without impaired mobility; T2b - tumor causes impaired mobility. Randomized SFX 70 Gy (2 Gy/fx) vs HFX 79.2 Gy (1.2 Gy BID). Boost after 50 Gy (std fx) or 60 Gy (BID). Primary fields: (minimum) 6x6 cm field, centered over mid-thyroid cartilage. Upper border 0.5-1 cm above thyroid notch, posterior border 1 cm behind thyroid cartilage, inferior border at the bottom of the cricoid cartilage, and 1 cm fall off anteriorly. Larger field sizes may be needed to obtain 2 cm margins around the primary. No elective nodal irradiation. Boost includes tumor plus 1 cm margin. Boost may reduce posteriorly off the arytenoids if the posterior 1/3 of the cord is not involved by tumor. Bolus (2-5mm) may be used over the anterior larynx for anterior tumors.
 * 2006 ASTRO Abstract "A Randomized Trial of Hyperfractionation vs. Standard Fractionation In T2 Squamous Cell Carcinoma of the Vocal Cord" (Trotti A, IJRBOP Volume 66, Issue 3, Supplement 1, 1 November 2006, Page S15)
 * 5-year outcome: LC HFX 79% vs. SFX 70% (NS); DFS 51% vs. 37% (NS); OS 73% vs. 62% (NS)
 * Toxicity: HFX modestly higher acute skin, mucosal, and laryngeal toxicity; high grade late effects uncommon
 * Conclusion: Local control modestly higher, but with only 58 failures, don't have sufficient power
 * Comment: SFX relatively low

Retrospective

 * New Zealand; 2006 (1986-1998) PMID 16635034 -- "TN/TN glottic carcinoma: a comparison of two fractionation schedules." (Short S, Australas Radiol. 2006 Apr;50(2):152-7.)
 * Retrospective. 145 patients with T1-T2 glottis. RT 6MeV beams, standard fractionation (SFX) 60-66 Gy in 30-33 fx (2 Gy/fx) over 6-6.5 weeks (1986-1992) vs. accelerated/hypofractionated regimen (AHFX) 52.5-55 Gy in 20 fx (2.75 Gy/fx) over 4 weeks. Median F/U 4.9 years
 * 5-year OS: 78%, toxicity comparable
 * T1N0: loco-regional control AHFX 95% vs. SFX 75% (SS), 5-year laryngectomy-free survival AHFX 95% vs. SFX 75% (SS)
 * T2N0: loco-regional control AHFX 81% vs. SFX 80% (NS), 5-year laryngectomy-free survival AHFX 92% vs. SFX 80% (NS)
 * Conclusion: Accelerated hypofractionation better for T1, same for T2. Comparable toxicity.

 * MD Anderson; 2003 PMID 12527044 -- "Results of radiotherapy for T2N0 glottic carcinoma: does the "2" stand for twice-daily treatment?" (Garden AS, Int J Radiat Oncol Biol Phys. 2003 Feb 1;55(2):322-8.)
 * Retrospective. 230 patients with T2, treated 1997-1998. Median f/u 82 months
 * RT: 180 patients treated with parallel-opposed fields. 89 patients treated with 2 Gy/fx to 32-75 Gy, 57 patients treated with 2-2.2 Gy to 66-70 Gy, and 81 patients treated with BID fxs to 74-80 Gy
 * 5-year local control: 72% (91% after salvage); BID fxs 79% vs. QD fxs 67% (p=0.06)
 * Predictors of local control: subglottic extension, daily dose <=2 Gy/fx
 * Conclusion: BID to 77 Gy better than QD to 70 in 2 Gy/fx in T2N0

 * Poland; 1999 PMID 9989520 -- "Clinical radiobiology of glottic T1 squamous cell carcinoma." (Skladowski K, Int J Radiat Oncol Biol Phys. 1999 Jan 1;43(1):101-6.)
 * Retrospective. 235 patients with T1N0 treated by RT alone. RT conventional 5-day schedule, dose 51-70 Gy, dose/fx 1.5-3.0 Gy/fx, on-treatment time 24-79 days. Median f/u 4 years
 * Outcome: 5-year LC 84%
 * Predictors of control: worse if dose <61 Gy, increase in treatment time 45 to 55 days decreased TCP by 13%. Potential doubling time: 5.5 days. Hemoglobin: drop in 1g/dl resulted in TCP decrease by 6%
 * Conclusion: The significant correlation between the total dose, overall treatment time, hemoglobin concentration, and tumor control probability has been found for T1 glottic cancer

 * Amsterdam; 1998 (1965-92) PMID 9788401 -- "The impact of treatment time and smoking on local control and complications in T1 glottic cancer." (van der Voet JC, Int J Radiat Oncol Biol Phys. 1998 Sep 1;42(2):247-55.)
 * Retrospective, 383 pts with T1N0 treated with 6 different fractionations. 65 Gy (20 x 3.25 Gy), 62 Gy (20 x 3.1 Gy), 61.6 Gy (22 x 2.8 Gy), 60 Gy (25 x 2.4 Gy), 66 Gy (33 x 2 Gy) and 60 Gy (30 x 2 Gy), all at 5 fx/week.
 * 5-yr LRC 89%. Larynx preservation 90% at 10 yrs. Local control decreased with increasing treatment time: 5-year LC 95% for 22-29 days (i.e. 20 fractions) vs 79% for >= 40 days (i.e 28 fractions or more). Larynx preservation by treatment: 20 x 3.25 Gy: 97%; 20 x 3.1 Gy: 96%; 22 x 2.8 Gy: 92%; 25 x 2.4 Gy: 89%; 33 x 2 Gy: 78%; and 30 x 2 Gy: 80%.
 * Complications: all grades, 15%, did not vary by treatment factors but did vary by smoking, neck diameter, and tumor extension.
 * Conclusion: overall treatment time is a significant factor for local control

 * UCSF; 1997 (1956-1995) PMID 9300746 -- "Influence of fraction size, total dose, and overall time on local control of T1-T2 glottic carcinoma." (Le QT, Int J Radiat Oncol Biol Phys. 1997 Aug 1;39(1):115-26.)
 * Retrospective. 398 patients with T1-T2 glottic cancer, daily RT. Tumor dose 46.6 - 77.6 Gy (median 63 Gy). Median F/U 9.7 years
 * Outcome: 5-year LC T1 85%, T2 70%.
 * T1 subset: No impact of size/schedule. Anterior commisure involvement 80% vs. none 88%. If treated in 1981-1995, 91%
 * T2 subset: Treatment time <=43 days 100% vs. >43 days 84%; Fraction size <1.8 Gy 44% vs. >=2.25 Gy 100%; Total dose <=65 Gy 60% vs. >65 Gy 78%; normal cord mobility 79% vs. impaired cord mobility 45%; subglottic extension 58% vs. no subglottic extension 77%
 * Toxicity: severe 1.8%
 * Conclusion: Risk factors evaluated for T1 and T2 glottic cancers

 * Robert Wood Johnson; 1988 PMID 3343152 -- "The effect of fraction size on control of early glottic cancer." (Schwaibold F, Int J Radiat Oncol Biol Phys. 1988 Mar;14(3):451-4.)
 * Retrospective. 58 pts with Stage I tumors. Of 28 pts treated with 180 cGy fractions (median dose 66.6 Gy, range 63-70.2 Gy), 25% LR in 3 yrs, vs no failures in pts treated with fraction size of 200 cGy or more (median dose 66 Gy).
 * Conclusion: suggests fraction size of 200 cGy or higher is a significant factor in the control of glottic cancer

Field Size

 * Osaka (Japan)(1982-1992) -- RT 5x5 cm vs. RT 6x6 cm
 * Randomized. 273 patients with T1N0 glottic cancer, treated with RT 4 MV bilateral portals. Arm 1) field size 5x5 cm vs. Arm 2) field size 6x6 cm. Dose 60/30
 * 5-years; 1996 PMID 8721266 -- "Radiation therapy for early glottic carcinoma (T1N0M0). The final results of prospective randomized study concerning radiation field." (Chatani M, Strahlenther Onkol. 1996 Mar;172(3):169-72.)
 * Outcome: 5-year RFS 5x5 88% vs 6x6 88% (NS)
 * Toxicity: acute toxicity same (NS); late toxicity 5x5 17% vs. 6x6 23% (SS)
 * Conclusion: Small field (5x5 cm) is recommended

Specific Situations
Anterior commissure extension
 * 2004 Lausanne PMID 14762660 -- Decreased local control following radiation therapy alone in early-stage glottic carcinoma with anterior commissure extension. (Zouhair A, Strahlenther Onkol. 2004 Feb;180(2):84-90.)
 * Retrospective. 122 patients with T1-T2N0 treated 1983-2000; median f/u 85 months
 * RT: 3D-CRT in 40%, median dose 70 Gy in 2Gy/fx over 46 days
 * 5-year OS: 80%, DFS 70%; median time to recurrence 13 months. Only 6 died of laryngeal CA
 * Poor predictors of local control: anterior commissure extension, arytenoid protection, male gender

Subglottic extension
 * 1997 Louisiana State PMID 9192435 -- Glottic cancer with subglottic extension. (Ampil FL, Radiat Med. 1997 Mar-Apr;15(2):103-7.)
 * Retrospective. 27 patients over 13 years. Surgery + RT (60%), RT alone (40%)
 * Locoregional failure: 18% in surgery + RT, 40% in RT alone (NS)
 * 2-year OS: 53% surgery + RT, 42% RT alone (NS)
 * Recommend: surgery + RT

Quality-of-life
 * PMID 15936548 -- A screening questionnaire for voice problems after treatment of early glottic cancer. (van Gogh CD, Int J Radiat Oncol Biol Phys. 2005)
 * Conclusion: "The questionnaire proved to be a reliable, valid, and feasible method to detect voice impairment in daily life. The questionnaire is easy to fill in, and interpretation is straightforward. It is useful for both radiation oncologists and otorhinolaryngologists in their follow-up of patients treated for early glottic cancer."

Set-Up
 * T1 larynx is typically a clinical verification set up, unless OBI available
 * Isocenter should line up 1cm below and 1cm posterior to the thyroid notch on visual field inspection

Review
 * 2004 PMID 15112257 -- Management of T1-T2 glottic carcinomas. (Mendenhall WM, Cancer. 2004 May 1;100(9):1786-92.)

Keywords: radiation, radiotherapy


text:
Radiation Oncology/Head & Neck/Larynx/Subglottis

Subglottic Larynx

Overview

 * Anatomy - 5mm below the free margin of true vocal cords to inferior margin of cricoid cartilage
 * Primary lesions are rare (<3%); usually extension from glottis. 50-70% are SCC
 * Symptoms - usually asymptomatic, but can present with horseness, dyspnea, stridor
 * Disease often advanced at presentation; thorcacic cavity involved in T3-T4(~50%)
 * Staging
 * T1 - subglottis only
 * T2 - extension to vocal cords, with normal or impaired mobility (no fixation)
 * T3 - vocal cord fixation
 * T4 - invades through cricoid or thyroid cartilage, or other tissues
 * T4a - invades cricoid or thyroid cartilage or tissues beyond the larynx
 * T4b - invades prevertebral space, carotid, or mediastinum
 * Lymphatics - channel unite to form one anterior and two posterolateral pedicles. Anterior drains through cricothyroid membrane into mid- and lower jugular nodes, or via prelaryngeal node into pretracheal and supraclavicular LNS. Posterior drains through cricotracheal membrane into paratracheal nodes
 * LN+ in 20-50%
 * Treatment - no consensus due to small numbers, but Toronto reports good experience with primary RT
 * Stage I-II: RT (include lower neck and mediastinum)
 * Stage III-IV: surgery (include larynx, thyroid, parastomal LNs), post-op RT if LN+ (include lower neck and mediastinum)
 * RT fields - lateral opposed fields inferiorly 2cm below primary tumor, superiorly encompassing upper jugular nodes. Also an anterior low neck and upper mediastinum T-field

Radiation

 * 2006 Ocshner Clinic PMID 16360814 -- Squamous cell carcinoma of the subglottis. (Garas J, Am J Otolaryngol. 2006 Jan-Feb;27(1):1-4.)
 * Retrospective. 15 patients over 25 years. 20% T1-2, 80% T3-4
 * 3-year OS: 25%
 * Recommend:
 * Stage I-II: RT (include lower neck and mediastinum)
 * Stage III-IV: surgery (include larynx, thyroid, parastomal LNs), post-op RT if LN+ (include lower neck and mediastinum)

 * Toronto
 * 2002 PMID 11955735 -- Results of radiotherapy for primary subglottic squamous cell carcinoma. (Paisley S, Int J Radiat Oncol Biol Phys. 2002 Apr 1;52(5):1245-50.
 * Retrospective. 43/55 (9 palliative, 3 laryngectomy) patients treated (1971-1996) with radical RT and surgical salvage. 54% T1-2, 46% T3-4, clinical N0. Median follow-up 4.2 years
 * RT: 50-52 Gy in 20 fxs (2.5 Gy/fx) over 4 weeks. Fields: Lateral oblique fields directed caudally (angled-down wedge pair technique), typically included the primary site alone, although in most cases, the first echelon nodes were encompassed in this volume. The median field size was 96 cm2 (8 cm wide by 12 cm long) and usually extended superiorly to above the hyoid, inferiorly to encompass known disease with a margin, posteriorly to the mid-vertebral body and anteriorly out beyond the skin. No severe late radiation morbidity. Authors note the dose would now be considered low (compared with current higher fractionated therapy for larynx)
 * Local RT control 56% (82% including surgical salvage)
 * 5-year OS: 50%
 * Note: As per Garas above, much better RT results than others
 * 1987 PMID 3117073 -- Carcinoma of the subglottis. Results of initial radical radiation. (Warde P, Arch Otolaryngol Head Neck Surg. 1987 Nov;113(11):1228-9.)
 * Retrospective. 23 patients (1971-1982), 40% T1-T2, 60% T3-T4
 * Local RT control 70% (74% including surgical salvage)

 * 2000 Florence PMID 11195034 -- Primary carcinoma of the subglottic larynx. (Santoro R, Eur Arch Otorhinolaryngol. 2000 Dec;257(10):548-51.)
 * Retrospective. 49 patients (1969-1993), 35% T1-T2, 65% T3-T4
 * 5-year OS: surgery 47%, RT alone 0%, surgery + RT 83%

 * 1999 London PMID 10229604 -- Submucosal squamous cell carcinoma of the subglottis. (Porter GC, Otolaryngol Head Neck Surg. 1999 May;120(5):745-6.)

 * 1998 Washington U PMID 9591557 -- Primary subglottic cancer. (Dahm JD, Laryngoscope. 1998 May;108(5):741-6.)
 * Retrospective. 39 patients with primary subglottic cancer, 1955-1988
 * 5-year OS: 58%
 * 5-year DFS: 46% (RT alone 22%, surgery alone 42%, surgery + RT 100%)

 * 1993 Sussex PMID 8347536 -- Primary radiotherapy for subglottic carcinoma. (Haylock BJ, Clin Oncol (R Coll Radiol). 1993;5(3):143-6.)
 * Retrospective. 23 patients treated 1976-1990 by one therapist. Mean follow-up 5.6 years
 * RT: Small parallel opposed wedged fields to the neck. No mediastinal radiotherapy used.
 * 2-year OS: 69%, failure due to persistent disease (22%) or recurrence (10%)
 * Questionnaire to ENTs: surgeons have a pessimistic perception of the value of radiotherapy in this condition

 * 1982 MSKCC PMID 7125077 -- Carcinoma of the subglottic larynx. (Shaha AR, Am J Surg. 1982 Oct;144(4):456-8.)
 * Retrospective. 16 patients over 25 years. 25% T1-T2, 75% T3-T4
 * 5-year OS: 70%
 * Treatment: primary surgery (wide-field laryngectomy, thyroidectomy, node dissection), followed by RT in advanced cases

Review
 * 2000 PMID 10839493 -- The pathology and management of subglottic cancer. (Ferlito A, Eur Arch Otorhinolaryngol. 2000;257(3):168-73.)


text:
User:Rarr~enwikibooks

I'm a reader of and very occasional contributor to Wikibooks.

title: User:Rarr~enwikibooks


text: Russian/Vocabulary/Months

title: Russian/Vocabulary/Months


text:
Macroeconomics/Definitions of Unemployment

Unemployment has several definitions, one being those members of the population that are actively looking for work and have not found it in a certain period. The International Labour Organization (ILO) defines unemployed people as those who are: not working one hour or more; and actively seeking work; and currently available for work. The main problem with this definition is that people who become disappointed and are no longer actively looking for a job are not counted as unemployed even though they might still want to work. The way unemployment is measured also has several versions. Some are using official payroll numbers of hirings and firings, others use the number of people who apply for unemployment benefits. Other methods include sampling through phone calls, etc that inquire if any able members of the household are unemployed and looking for work. The informal sector of the economy also create problems since these are done mainly by estimates.

= Measure of Unemployment = Unemployment is usually expressed as a percentage of the labor force who are currently unemployed. This is known as the unemployment rate. The unemployment rate plays a big role in how economists measure the performance of an economy and is usually used as an indicator of economic activity. Contrary to popular beliefs, the target of the unemployment rate is not going to be zero as if the economy's unemployment rate falls below a certain level- known as the NAIRU (Non Accelerating Inflation Rate of Unemployment) - firms would be competing for labor resources, creating inflammatory pressure.


text:
Diplomacy/Middle Game Strategies

Definition of the Middlegame in Diplomacy
As in chess, the middlegame in Diplomacy is difficult to define. Some define it as the elimination of the first power, others as the elimination of the second. A less strict, but fuller definition of middlegame in Diplomacy is the point at which a power completes its first set of objectives and moves on to its second.

Middle Game Strategies
The middle game usually starts around 1903-1905 and ends 1910-1914. During this time, the large power blocks formed at the beginning of the game will either disintegrate, or continue on to a second set of objectives. Common examples of this are France and Germany dismantling England, then France turning to attack Italy and the Mediterranean, while Germany drives toward Russia. An alliance between Russia and Italy starts with the two splitting Austria, then moving on Turkey.

The middlegame is an important time to determine where your country is going to find the eighteen centers required for victory. This is especially important for the corner powers, England and Turkey, and to a lesser extent, France. If getting WAR, MOS, or MUN looks unlikely, England will sometimes try to capture TUN from Italy in the middlegame to make 18.

Entertaining stabs occur in the middlegame, as first-turn stabs are usually unnoticed except by the two parties involved. Endgame stabs, where one long-time ally will capture centers from another in order to win the game outright, are also uncommon. A middlegame stab occurs when one ally grabs centers from another, often in a bid to capture a solo victory. The result is usually a race between the stabber and the rest of the board to try and establish a stalemate before the stabber can take the 18th center.

title: Diplomacy/Middle Game Strategies