Posts Tagged ‘coordinates’
Friday, November 20th, 2009
Overview of the Preimage of a Set
Description
A detailed tutorial on the preimage of a set. Step by step tutorial including several examples of the preimage of a set for reference.
Overview
The preimage of a set is defined over a function. If there is a function over A and B, then we can say that y = f(x), provided that (x, y) belongs to f. Based on this definition, x is the preimage of y under f. To find the preimage, simply look for the value of x that matches with the proper value of y in any function of ordered pairs in A and B.
Tags: a, b, belongs, coordinates, defined, definition, discrete math, f, function, image, ordered pairs, preimage, set, theory, value, x, y
Posted in Discrete Math | No Comments »
Thursday, November 19th, 2009
How to Determine the Center of a Circle
Description
A detailed tutorial on how to determine the center of a circle. Step by step tutorial including several examples of the center of a circle for reference.
Overview
The center of the circle is very easy to find. It is one of the endpoints of the radius and the midpoint of the diameter. The video shows you how to find it based on a series of accurate drawing. However, there is a mathematical way to find the center of the circle, which is also sometimes called the origin of the circle. Just use the midpoint formula with the diameter. If you have the radius just multiply it by two, because you cannot use the distance formula without already having the coordinates of the origin.
Tags: center, circle, coordinates, diameter, distance, endpoint, formula, mathematical, midpoint, origin, point, radius
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Overview of Half-Circles
Description
A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.
Overview
A half-circle is truely half of a circle. If you take a circle and cut it in half, you will get a half circle. Because of this, the equations of the half-circle are very similar to the equations of a full circle – simply divide the equation by two. The only ones that you cannot find that way are the radius, diameter, and circumference. The radius and diameter do not change on a half-circle. There is no circumference on the half-circle, but if you need the circumference for another formula you can use the circumference of the whole circle of that half-circle.
Tags: area, basic, circle, circumference, coordinates, cut, diameter, divide, equation, Geometry, half, half-circle, pi, radius, shape, split, two, whole
Posted in Geometry | No Comments »
Tuesday, October 27th, 2009
The Range of Relations
Description
A detailed tutorial on the range of relations. Step by step tutorial including several examples of the range of relations for reference.
Overview
The range of a relation is denoted as Rng(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The range is the set of all the y endpoints – that is to say, all the endpoints that come second in the ordered pair. If you are taking the range of the inverse of a relation, then that would be all the x endpoints. When writing the range, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, element, endpoint, ordered pair, range, relations, second, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Domain of Relations
Description
A detailed tutorial on the domain of relations. Step by step tutorial including several examples of the domain of relations for reference.
Overview
The domain of a relation is denoted as Dom(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The domain is the set of all x endpoints – that is to say, all the endpoints that come first in the ordered pair. If you are taking the domain of the inverse of a relation, then that would be all the y endpoints. When writing the domain, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, domain, element, endpoint, First, ordered pair, relations, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Inverse of Relations
Description
A detailed tutorial on the inverse of relations. Step by step tutorial including several examples of the inverse of relations for reference.
Overview
Inverse is a term you should be familiar with. An inverse operation is one that undoes the original operation. But what is an inverse relation? When you take the inverse of a relation, you are switching the endpoints in every ordered pair in the original relation. For each ordered pair in the relation, instead of being written as (x, y) it will now be written as (y, x).
Tags: cartesian, coordinates, discrete math, endpoint, inverse, operation, ordered pair, relations, x, y
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
An Introduction to Relations
Description
A detailed tutorial on the introduction to relations. Step by step tutorial including several examples of the introduction to relations for reference.
Overview
A relation is defined as an ordered pair. However, that is not entirely accurate. A relation could either be an ordered pair or a set of ordered pairs. A relation can be used with either one or more normal sets, or one Cartesian product set. When used with a normal set, it is a set of ordered pairs. When used with a Cartesian product, it is the power set of that set.
Tags: cartesian, coordinates, discrete math, element, ordered pair, power, product, relation, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Cartesian Products in Set Theory
Description
A detailed tutorial of Cartesian products in set theory. Step by step tutorial including several examples of Cartesian products in set theory for reference.
Overview
A Cartesian product is an operation that can be performed in set theory. It is named not for the multiplication that occurs, but for the way the resulting set is written: it is written in ordered pairs, just like Cartesian coordinates. Two sets are said to be multiplied, such as A and B. Whichever set is written first in the operation has its first coordinate written with the second coordinate of the second set. This continues until all coordinates have been used at least once.
Tags: cartesian, coordinates, discrete math, element, multiplication, operation, ordered pair, product, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Definition of a Scalar Triple Product
Description
A detailed tutorial on scalar triple products. Step by step tutorial including several examples of scalar triple products for reference.
Overview
A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.
A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: 
This is the same as saying 
Tags: absolute, algebra, box, coordinates, figure, independent, linear, mixed, multiplication, operator, parallelpiped, positive, product, properties, right-handed, scalar, three-dimensional, triple, value, zero
Posted in Algebra | No Comments »
