Posts Tagged ‘zero’
Thursday, October 15th, 2009
Introduction to Singular Matrices
Description
A detailed tutorial on singular matrices. Step by step tutorial including several examples of singular matrices and how to identify singular matrices for reference.
Overview
A singular matrix is a square matrix that is not invertible. In order to not be invertible, the determinant must be zero. No other values will make a matrix singular. Single matrices are very rare – almost all square matrices are invertible. A quick way to find out if a matrix is invertible or singular is to attempt to invert the matrix.
Tags: algebra, degenerate, determinant, invert, invertible, Math, matrices, matrix, rare, singular, square, zero
Posted in Algebra | No Comments »
Tuesday, October 13th, 2009
Overview of Superelevation
Description
A detailed tutorial on superelevation. Step by step tutorial including a visual example of superelevation of a road for reference.
Overview
The superelevation of a road or of a railway is the difference in elevation between the two edges. A non-zero superelevation – meaning that the edges of the road or railway are at different heights – allows for a bank turn, letting vehicles traverse the turns at higher speeds than would otherwise be possible. Superelevation is sometimes referred to as the cant of a road or railway. An important calculation in superelevation is the maximum speed of a vehicle on a curved road. It is determined by the formula 
.
Tags: algebra, banked turn, camber, cant, cross slope, curved, edges, elevation, height, Math, railway, road, speed, superelevation, track, train, vehicle, zero
Posted in Algebra | No Comments »
Tuesday, October 13th, 2009
Empty Set in Set Theory
Description
A detailed tutorial on the empty set. Step by step tutorial including several examples and a description of the properties of the empty set for reference.
Overview
The empty set is a unique set in set theory that means a set composed of nothing. In an empty set, there are no elements at all. The empty set has one very unique property – it is the subset of all sets. The set of all natural numbers up to infinity? It’s a subset. The set of prime numbers less than 20? It’s a subset of that, too. It is also a subset of itself – although that is not particurarly unique. The empty set is not used in equations, but can be used to define them.
Tags: difference, discrete math, element, empty set, intersection, Math, none, set, set theory, subset, union, unique, zero
Posted in Discrete Math | No Comments »
Friday, October 9th, 2009
Overview of the Zero-Factor Property
Description
A detailed tutorial on solving problems using the zero-factor property. Step by step tutorial including several examples of the zero-factor property for reference.
Overview
The zero-factor property is very closely linked to solving quadratic equations by factoring. The zero-factor property takes place very close to the end of the problem. Once you have finished factoring, you are usually left with two binomials that are being multiplied. The zero-factor property involves setting each of these binomials equal to zero separately. This allowes you to solve for two different values of x. This works on anything that has more than one term with the same variable being multiplied together. The reason it works is that if you multiply anything by zero, the answer is zero. So all you need to do is set the separate parts equal to zero, and it is just as good as solving for the whole thing at one time.
Tags: algebra, binomials, equation, factor, factoring, Math, multiplication, Polynomials, property, quadratic, variable, zero, zero-factor
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Introduction to Zero and Undefined Slopes
Description
Detailed tutorial on undefined and zero slopes. Step by step tutorial including several examples of zero and undefined slopes for reference.
Overview
Zero and undefined slopes are both slopes that do have a definite value to them. They represent very uinigue graphs and lines. A zero slope is a slope of zero over anything – meaning it has a run, but no rise. It is a zero slope because zero divided by anything is simply zero. Zero slopes form horizontal lines. An undefined slope is a slope of anything over zero – meaning it has a rise, but no run. It is an undefined slope because nothing can be divided by zero. Undefined slopes form vertical lines.
Tags: arithmetic, graph, horizontal, line, Math, rise, run, slope, undefined, value, vertical, zero
Posted in Arithmetic | No Comments »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Alternating Series Test
Description
A detailed tutorial on testing for convergence using the alternating series test. Step by step tutorial including several examples of testing for convergence using the alternating series test for reference.
Overview
The alternating series test, like all convergence and divergence tests, is fairly easy. The hardest part is figuring out if you should use the AST, or a different test. An easy way to tell is, is the equation negative? What would happen if you pulled a negative one out? Or maybe, there is already a negative one outside of the equation. If you see any fraction, function, or any equation at all with a -1 to an odd power at the front (or at the front of the numerator, in a fraction) then you should use the alternating series test for it. If the series is decreasing over time, and the limit is approaching zero, then the series is convergent. The alternating series test is normally used in conjunction with another test for convergence.
Tags: -1, alternating, AST, Calculus, converge, convergence, decreasing, diverge, divergence, fraction, function, limit, Math, negative, one, series, test, zero
Posted in Calculus | No Comments »
Tuesday, October 6th, 2009
Definition of a Finite Set
Description
A detailed tutorial on the definition of a finite set. Step by step tutorial including several examples of finite sets for reference.
Overview
There are many different types of sets, but one of the most common ones to run into a finite sets. A finite set is a set that has a finite number of elements – meaning a set with a definite number of elements, such as five, or ten. The number of elements in the set must be a natural number, and it is called the cardinality of a set. An empty set is considered to be finite, with a cardiality of zero, even though zero is not considered to be a natural number.
Tags: algebra, cardinality, element, elements, empty set, finite, infinite, Math, natural number, set, sets, zero
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
How to Find Oblique Asymptotes
Description
A detailed tutorial on how to find oblique asymptotes. Step by step tutorial including several examples of how to find oblique asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing oblique asymptotes. In order to find the oblique asymptotes of a function, you must first determine if the asymptote slants. If the numerator of a rational function has exactly one degree greater than the denominator, then the function slants and therefore has an oblique asymptote. When you divide the numerator and the denominator, the term or polynomial you get is the oblique asymptote.
Tags: algebra, asymptote, asymptotes, closer, curves, degree, denominator, distance, farther, function, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, numerator, oblique, origin, polynomial, positive, slant, straight, vertical, zero
Posted in Algebra | No Comments »
Friday, October 2nd, 2009
Overview of Polynomial Long Division
Description
A detailed tutorial on polynomial long division. Step by step tutorial including several examples of polynomial long division for reference.
Overview
Polynomial long division is a mix of regular long division and rules of polynomials – it looks confusing at first, but isn’t too difficult to follow. Polynomial long division is actually a type of algorithm. It is only used when dividing a polynomial by another polynomial of either the same or a lower degree. The “degree” of a polynomial is the highest power in the polynomial, and the terms in the polynomial should be ordered from highest degree to lowest degree. When using polynomial long division, you must write out all coefficients and terms, even “invisible” ones – ones that have a coefficient of zero and so are typically not written in the polynomial. Polynomial long division is solved the same way as regular long division
Tags: algebra, algorithm, coefficient, degree, division, long division, Math, polynomial, polynomial long division, synthetic division, term, value, zero
Posted in Algebra | No Comments »
Thursday, October 1st, 2009
Identity Properties of Multiplication and Addition
Description
A detailed tutorial of the identity properties of multiplication and addition. Step by step tutorial including several examples of the identity properties of multiplication and addition for reference.
Overview
There are two definitions of the identity property. The first deals with multiplication. It states that anything multiplied by one is itself. The second property deals with addition. It states that any number with zero added to it equals itself. As you can see, they are very similar to each other. Sometimes the zero property of multiplication is confused with the identity property for multiplication, although it is something different.
Tags: add, addition, arithmetic, equals, identity properties, identity property, itself, Math, multiplication, multiply, one, zero
Posted in Arithmetic | No Comments »
