Posts Tagged ‘variable’
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Thursday, November 19th, 2009
Overview of the Cost Function
Description
A detailed tutorial on the cost function. Step by step tutorial including several examples of the cost function for reference.
Overview
The cost function is a name for a function that is being used in optimization. It is a very important part of an optimization problem. The cost function can be any graph, because all it refers to is the function – the function could be different every time, and it could still be called the cost function. What we learn from this is that the cost function is not unique.
Tags: algebra, constraints, cost, domain, energy, function, functional, graph, linear, maximize, minimize, objective, optimization, solution, unique, variable
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Overview of the Break-Even Point
Description
A detailed tutorial on the break-even point. Step by step tutorial including several examples of the break-even point for reference.
Overview
The break-even point is used very often in business math and accounting, and first appears in basic algebra classes. The break-even point is where the cost of something equals the revenue. In other words, the break-even point is where there is no profit lost or gained on a transaction. Most businesses aim to get above the break-even point, although they will at least aim for it so they do not fall below it.
Tags: accounting, algebra, break, break-even, business, cost, equals, even, fixed, function, gained, lost, point, price, profit, revenue, variable
Posted in Algebra | No Comments »
Friday, November 13th, 2009
How to Check Your Work
Description
A detailed tutorial on how to check your work. Step by step tutorial including several examples of how to check your work for reference.
Overview
Checking your work is the process of inserting the value you solved for back into the original problem, to confirm that you came up with the correct solution. This process is quite commonly used with word problems, which nearly always have you solving for an unknown variable that would be a very important part of the original equation.
Tags: arithmetic, check, equation, guesstimation, original, problem, process, solution, unknown, value, variable, word, work
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Use Algebra Tiles
Description
A detailed tutorial on how to use algebra tiles. Step by step tutorial including several examples of how to use algebra tiles for reference.
Overview
Algebra tiles are a visual expression of polynomials and polynomial equations. Each tile is meant to represent a different polynomial. A large square tile represents the squared variable, a smaller square tile represents a single number, with no variable, and a rectangle represents the single variable. The tiles are red and green. Green represents positive monomials, and red represents negative monomials. Tiles can be combined to create equations, or the same tiles can be combined to express the coefficient. Addition and subtraction can be performed by adding and removing tiles.
Tags: addition, algebra, coefficient, cubed, green, large, negative, polynomial, positive, rectangle, red, small, square, squared, subtraction, tiles, variable
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
How to Find the Degrees of Polynomials
Description
A detailed tutorial on degrees of polynomials. Step by step tutorial including several examples of degrees of polynomials for reference.
Overview
The degree of a polynomial is the highest power found in it. For example, in your normal quadratic equation, the degree is two, because the highest power – the highest number found in an exponent – is a two. In other polynomials, the degree may be something different. No matter what order the variables and their powers are placed in, the degree is always the highest one. For example. the degree of x^2 + x + 7 is exactly the same as x + 7 + x^2.
Tags: algebra, coefficient, degree, equation, exponent, highest, polynomial, power, quadratic, variable
Posted in Algebra | No Comments »
Friday, November 6th, 2009
Identity Matrix Explained
Description
A detailed tutorial on the identity matrix. Step by step tutorial including several examples of the identity matrix and how to solve it for reference.
Overview
An indentity matrix is a matrix that is said to be of size n. It is considered to be the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted as the variable I. The identity matrix has some extremely important properties of its own, especially multiplication properties. It is a unique type of matrix that is found rarely, but is used very often in several different branches of math.
Tags: -1, 0, algebra, diagonal, i, identity, linear, main, matrices, matrix, multiplication, one, properties, square, uniquem, variable, zero
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Cancellation Properties of Natural Numbers
Description
A detailed tutorial on cancellation properties of natural numbers. Step by step tutorial including several examples of cancellation properties for reference.
Overview
Cancellation properties of natural numbers state that when two terms are equal to each other, if the same number is being multiplied or added on both terms, you may cancel them out and the terms will still be equal to each other. Knowledge of the cancellation properties is extremely important for simplification of equations and when trying to find the value of a variable. Mathematically stated, the cancellation properties are that if x + z = y + z or xz = yz, then x = y.
Tags: add, arithmetic, cancel, cancellation, equal, multiply, natural, number, out, properties, property, simplification, simplify, term, value, variable
Posted in Arithmetic | No Comments »
Friday, October 30th, 2009
How to Solve Work Rate Problems
Description
A detailed tutorial on solving work rate problems. Step by step tutorial including several examples of work rate problems for reference.
Overview
A work rate problem is a word problems that asks you to calculate the amount of time it will take to do something with two different rates of work. They first show up in basic algebra courses but work rate problems get more complicated and will continue on even in calculus. It is easier to solve work rate problems if you use a chart. First, you need to find the task rate – the rate at which each person is doing something. You do this by dividing the number of tasks (which should be one) by how many hours it takes them to finish it. Then you choose a variable for time. Your task will take that variable divided by the number of hours. You should come up with 2 (or more) results for task. Add these results together and have them equal the number of people there are total working on the task. Then solve for your time variable. Sometimes it will be difficult to solve for the time variable without using an algebra trick of multiplication to change the numbers a bit.
Tags: add, algebra, calculate, Calculus, chart, divide, hours, problem, proportion, rate, task, time, variable, word, work
Posted in Algebra | No Comments »
Tuesday, October 20th, 2009
How to Write Proofs by Exhaustion
Description
A detailed tutorial on writing proofs by exhaustion. Step by step tutorial including several examples of how to write proofs by exhaustion for reference.
Overview
A proof by exhaustion is one of the easier types of proofs to write. All this proof involves is testing cases – every case possible for what you are trying to prove. This can be made easier by using variables instead of numbers, or by testing for an even number and odd number, positive and negative number, etc. That way you do not have to test many numbers in order to prove. If even one of the cases does not work out, then whatever you are testing for has been disproven.
Tags: cases, discrete math, disproven, even, exhaustion, Math, method, negative, odd, positive, possibilities, proof, proofs, proven, variable, write
Posted in Discrete Math | No Comments »
