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It's the Law Too — the Laws of Logarithms
Feb 6, 2012 . Do you know why you can change log(x)+log(y) to a different form, but not log(x+ y)? . Multiply the Logarithm; Raising Numbers to Any Power; Divide Numbers, Subtract Their Logarithms . equation, and vice versa, just by interchanging the x and y in this way. . b ^ log_b(x) = x, where ^ means 'raised to the .

R Library: Advanced functions
y2 <- sapply(mat1.df, function(x, y) sum(x) + y, y = 5) y2 X1 X2 X3 X4 15 15 15 15 . #subtract column means from each column #centering each column around .

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5:05 pm
February 15, 2005


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Tcl Built-In Commands - expr manual page
+ -: Add and subtract. . x?y:z: If-then-else, as in C. If x evaluates to non-zero, then the result is the value of y. . operators have ``lazy evaluation'', just as in C, which means that operands are not evaluated if they are not needed to . Arg may be either integer or floating-point, and the result is returned in the same form.

Algebra Quandry
1) x = y 2) x^2 = xy (multiply both sides by x) 3) x^2 - y^2 = xy - y^2 (subtract y^2 from each side) . Now, here is my philosophical quandary: I had taken algebra to be a means of . The operation of multiplication is a shorthand form of addition.

How to Add and Subtract Algebraic Fractions |
In arithmetic, adding and subtracting fractions is a relatively straightforward . You can see this by multiplying the first expression x/(x - y) by (x + y)/(x+ y) to get x(x . A mixed fraction is written in the form of a whole number plus a fraction: 5 3/ 4.

Random Variable Combinations
Often, it is necessary to combine random variables (i.e., to add or subtract . Suppose you have two variables: X with a mean of ?x and Y with a mean of ?y. Then .

Euclid's Elements, Common Notions
If equals are subtracted from equals, then the remainders are equal. . In modern mathematics, axioms such as these would form the basis of an abstract algebra. . And let greater than just have the opposite order, that is, x > y means y < x.

Linear equations
By 'elementary operation' we mean (1) adding, subtracting, multiplying, or dividing by a . we can show the relationship between x and y in the form of a graph.

PHP Operators
x - y, Subtraction, Difference of x and y, 5 - 2, 3. x * y, Multiplication . It means that the left operand gets set to the value of the expression on the right. That is, the .

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February 15, 2005


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Matrix Addition, Matrix Subtraction - Precalculus | WyzAnt Tutoring
Addition of Matrices is commutative, meaning that given two matrices A and B: The best way to . Example 3: Solve for x,y,z given that matrix A = matrix B. Step 1 .

CHAPTER 4 Direct Proof
theorem has form “Suppose P. Then Q,” but this means the same thing as “If P, then . we define addition, multiplication, subtraction and division, though we will use . “5 < 7,” and “x < y implies ?x > ?y,” do not need to be justified. In addition .

multiplication and division problems into addition and subtraction ones. Let's take a closer . (x and y above), their sum must be the exponent of the product (log( 1234)(5678) = x + y above). . These are by no means proofs, nor are these manipulations confined to base 10 logarithms. In the . then find ap in simplest form.


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1:09 am
February 16, 2005


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Inequality Proofs
As usual, x<y means y>x, x ? y means x>y or x = y, and x ? y means y ? x. . Plainly, the same proof works if addition is replaced with subtraction. . The “· ? · ? ·” form of the inequality and the presence of the sin x in the middle remind me of .

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8:50 am
February 16, 2005



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Tutorial for Systems of Linear Equations & Matrices
A First, a linear equation in two unknowns x and y is an equation of the form . To solve a system of linear equations means to find a solution (or solutions) (x, y) that . subtracting) the equations does not result in either x or y being eliminated.

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10:32 am
February 16, 2005



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expr - Linux Command - Unix Command
+ -: Add and subtract. . operators have ``lazy evaluation'', just as in C, which means that operands are not evaluated if they are not needed to determine the outcome . Arg may be either integer or floating-point, and the result is returned in the same form. . If y is 0, an error is returned. hypot(x, y): Computes the length of the .

Algebra Help - Straight Lines
The two variables are usually (but of course don't have to be) x and y. . Any real number term may be added (or subtracted, of course); Nothing else is permitted! This means that any equation containing things like x2, y2, 1/x, xy, square roots, or any . This is not a coincidence, but is due to the standard form in which the .

Graphing Linear Equations - Algebra | WyzAnt Tutoring
This is because x is the independent variable, which means that it is the variable being changed. . We will explore this as we start to graph equations in terms of x and y. . These equations do not form a point, but rather a horizontal or vertical line. . Then we subtract 2x from both sides to get the x and y on the same side .

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February 16, 2005


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A-level Mathematics/OCR/FP1/Matrices - Wikibooks, open books for ...
A matrix is an array of numbers (elements) presented in a standard form such . and we can also say column matrix to mean a matrix with only one column, and . Subtracting matrices is also as you would expect and is the exact opposite of . To find the matrix corresponding to the reflection in the x-axis, the point (x,y) will .

Converting to slope-intercept form | Linear functions | Khan Academy
U04_L1_T4_we1 : Converting to slope-intercept form. . Exploring linear relationships · Plotting (x,y) relationships · Plot ordered pairs · Application . left- hand side, and the best way to do that is to subtract; 4x from both sides of this equation. . So that means that if I change x by positive 1 that y goes; down by negative 2.

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2:34 pm
February 17, 2005


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Honors Compilers
OP X Y Z 8-bits 8-bits 8-bits 8-bits. Some instructions combine YZ. OP X YZ . is 33; The notation $Z/Z means that an operand can be either a register or immediate . SUB/SUBU (Subtract, subtract unsigned); NEG/NEGU $X,Y,$Z/Z . Same set except register is zeroed if condition is false rather than nop (all other forms too) .

When we write the <> we mean that the vector has initial point at the origin and terminal point at (-3,1). This notation is called the component form of the vector. The length of the vector <x,y> is called the norm or magnitude. We can find it by the formula: . Properties of Vector Addition and Subtraction. We have the following .

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4:29 pm
February 17, 2005


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The general form of a simple linear function is this equation (Y = a + bX). . In this example, regardless of what value you put in for X, Y will always equal 3. . To find the variance of Y, you subtract each Y score from the mean of Y (Y - My), .

MathSteps: Grade 7: Linear Equations: What Is It?
In a linear equation in x and y, x is called x is the independent variable and y . To find how fast x is changing, subtract the x value of the second point from the x . The equation of a line can be written in a form that gives away the slope and . This means that a positive change in y is associated with a positive change in x.

Linear Regression
Units of Measurement and Functional Form . (y,x) are observable (we can sample observations on them) . Can combine with zero mean assumption to get zero conditional . ?¯x. Population analogues. Slope = Cov(x,y). Var(x). = Corr(x, y). SD(y). SD(x). Intercept . Can standardize y and x's (i.e., subtract sample avg.

Perpendicular Regression Of A Line
When we perform a regression fit of a straight line to a set of (x,y) data points we . significance, because the notion of "perpendicular" has an absolute meaning. . Then we can subtract X from each of the x values, and Y from each of the y . namely xy and x^2 - y^2, are both hyperbolic conic forms, and they constitute the .

Review of Vectors
In three dimensions a vector is a triple of numbers ?x, y, z?. Quantities like the . what we mean by the x component of the velocity since the x axis now points in a different . A vector cannot be added to or subtracted from a scalar. A vector . We will usually use the ?x, y, z? form rather than the?jˆk form in this book, because .

Primitive recursive function - Wikipedia, the free encyclopedia
2.1 Addition; 2.2 Subtraction; 2.3 Operations on integers and rational numbers . This means that there is a single computable function f(e,n) such that: For every . The operator ?yy<z R(x, y) is a bounded form of the so-called minimization- or .

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6:04 pm
February 17, 2005


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Linear Algebra: Vectors
The subscripted a, x and y quantities that appear in this set of relations may be formally arranged . Putting A next to x means “matrix product of A times x”, which is a generalization of the . Clearly (A.3) is a more compact, “short hand” form of ( A.1). . For vector subtraction, replace + by ? in the foregoing expressions. A–6 .

Calculus, Applications and Theory
6.8 Mean Value Theorem . . about using calculators or any other form of technology. . subtraction are defined in the usual way by x?y ? x+(?y) and x/y ? x .

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6:56 pm
February 17, 2005



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. replace y and each x variable with a standardized version – i.e. subtract mean and . OLS can be used for relationships that are not strictly linear in x and y by using . of x, y or both; Can use quadratic forms of x; Can use interactions of x variables . the standard error will be smallest when the c's equal the means of the x's .

GRASS GIS manual: r.mapcalc
Some characters have special meaning to the command shell. . multiplication Arithmetic 10 + addition Arithmetic 9 - subtraction Arithmetic 9 << left shift Bitwise . This is done by specifying the raster map layer name in the form: . mode value of those listed * not(x) 1 if x is zero, 0 otherwise pow(x,y) x to the power y * rand(a .

Reference for all built-in template language functions — calibre User ...
add(x, y); divide(x, y); multiply(x, y); subtract(x, y). Boolean . cmp(x, y, lt, eq, gt); strcmp(x, y, lt, eq, gt) . The separator has the same meaning as in the count function. . swap_around_comma(val) – given a value of the form “B, A”, return “ A B”.

Algebraic Fractions |
We can add, subtract, multiply and divide fractions in algebra in the same way that we do in simple . (2) Fractions using variable in the denominator are in the form, . $\frac{5}{xy}$, x $\neq$ 0 and y $\neq$ 0 . Where x and y are variables. . Simplification of fraction means to make the fraction as simple as possible.

Can adders subtract?
which also accounts for that intrusive 1 that we got at the beginning of our result. In fact, the 1 acts as a useful signal: if it's not there, then it means that X - Y is .

Principles in analysis
When there are a set of samples, it is common to compare the means (averages). . X, X - x-bar, (X - x-bar)^2, Y, X - Y, (X - Y)^2 . This form is calculated as: .

Multiplying and Dividing with Exponents
right (in superscript form) of a variable or number. . example, 65 means 6 · 6 · 6 · 6 · 6 and x3 means x · x · x. The base is the number . You can only subtract the . It is important to note in the example above that x·y and y·x are the same thing.

Operators - Adobe ActionScript® 3 (AS3) API Reference
x. Symbolic operators are characters that specify how to combine, compare, or modify . subtraction assignment, Assigns expression1 the value of expression1 .

Linear or Nonlinear Differential Equation?
Assume that y' means dy/dx. . It seems to me that squaring both sides and subtracting 2x2 from both sides renders a . an(x)y(n) + an-1(x)y(n-1) + ... a0(x)y= g(x) . differential operator) in the form f(y) and then see if f is linear in that sense, i.e., .

Binomial theorem - Wikipedia, the free encyclopedia
The coefficient a in the term of xbyc is known as the binomial coefficient \tbinom nb . These coefficients for varying n and b can be arranged to form Pascal's triangle. . For a binomial involving subtraction, the theorem can be applied as long as the . quotient and taking limits means that the higher order terms – (\ Delta x)^2 .

8.3 Addition and Subtraction of Radicals
Of course we need to define what it means for two radicals to be like . Of course, in order to tell if two radicals are like, they first need to be in simplest form. . 383. 3. 27. 4. 3. 82. 24. 3. 81. 4. 242 y xy y xy y xy y xy yxy yy x yyx yx y y x yx. = .

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1:13 pm
December 16, 2005


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Worried Dad,

Graphing Quadratic Functions
The term quadratic comes from the word quadrate meaning square or rectangular. . The second form is called the vertex-form or the a-h-k form, y = a(x - h)2 + k. . line of symmetry, it will always be y = c, where c is always the x-value of the vertex (x, y). . Also, it tells us to subtract 3 from x and then square that to get p(x).

Binomials |
A Binomial is a polynomial containing two terms, bi meaning two. In terms of . 3xyz has three variables namely x, y and z but it is a single term or a monomial.

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December 16, 2005


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Chapter 4. Point operations
. 0 end end function threshold_get_value(x,y,level) value = get_value(x,y) return . This is equivalent to shifting the contents of the histogram left (subtraction) or . The levels tool found in many image processing packages is in it's simplest form . The view is a plot of the function f(x) of the transform applied, this means that .

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An Xmgrace Tutorial
Choose the columns for the x- and y- coordinates using the drop down menus. . which means you use both X and Y from the source set but also the Y .

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