Posts Tagged ‘positive’
Thursday, November 12th, 2009
How to Solve Negative Exponents
Description
A detailed tutorial on how to solve negative exponents. Step by step tutorial including several examples of solving negative exponents for reference.
Overview
An exponent is a number representing how many times you multiply the base – the number the exponent is on – by itself. Which is why negative exponents are so confusing – how can you multiply something by itself a negative number of times? The easiest way to think of a negative exponent, is that if you take away the negative sign and put the base and exponent under the number 1 (like as a fraction), you are saying the same thing! A negative exponent simply needs to be moved to the denominator (or the numerator, if it is in the denominator) to make it a positive exponent. This can be tricky when there are other numbers or expressions found in the same fraction, but not impossible.
Tags: algebra, base, denominator, equation, exponents, expression, fraction, multiply, negative, numerator, positive, power
Posted in Algebra | No Comments »
Friday, October 30th, 2009
Introduction to the Euclidean Algorithm
Description
A detailed tutorial on the Euclidean algorithm. Step by step tutorial including several examples of the Euclidean algorithm for reference.
Overview
The Euclidean algorithm, sometimes referred to as Euclid’s algorithm, is the most efficient way of determining the greatest common factor of two numbers. The greatest common factor of two numbers is the largest number that divides them both evenly. The Euclidean algorithm is used in a series of steps – it follows a pattern that helps to find numbers and their factors with accuracy.
Tags: algebra, algorithm, common, divides, divisor, Euclid, Euclidean, evenly, factor, greatest, highest, negative, pattern, positive, remainder, steps
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
How to Identify Coprime Numbers
Description
A detailed tutorial on identifying coprime numbers. Step by step tutorial including several examples of how to identify coprime numbers for reference.
Overview
Two numbers are considered to be coprime, or relatively prime, if they have no common positive factor other than 1, or if their greatest common divisor is 1. Sometimes the notation for perpendicular is used to say that a number A is coprime to another number B. The term coprime was invented because the numbers are prime together, but are not prime themselves. A prime number can be coprime with any number.
Tags: arithmetic, common, coprime, divisor, factor, greatest, notation, number, one, perpendicular, positive, prime, relatively
Posted in Arithmetic | 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 »
Thursday, October 22nd, 2009
How to Identify the Initial Side
Description
A detailed tutorial on the intial side of an angle. Step by step tutorial including several examples of the initial side of an angle for reference.
Overview
The initial side of an angle is the side of an angle where the measurement begins. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of an initial side would be when you draw angles with a protractor – the line that you trace along the bottom of your protractor forms a ray which is known as the initial side.
Tags: angle, begins, ends, Geometry, initial, measurement, negative, positive, ray, side, terminal, triangle
Posted in Geometry | No Comments »
Thursday, October 22nd, 2009
How to Identify the Terminal Side
Description
A detailed tutorial on the terminal side of an angle. Step by step tutorial including several examples of the terminal side of an angle for reference.
Overview
The terminal side of an angle is the side of an angle where the measurement ends. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of a terminal side would be when you draw angles with a protractor – the line that you draw for your degree forms a ray which is known as the terminal side.
Tags: angle, begins, ends, Geometry, initial, measurement, negative, positive, ray, side, terminal, triangle
Posted in Geometry | No Comments »
Thursday, October 22nd, 2009
How to Identify the Phase Shift
Description
A detailed tutorial on the phase shift of a function. Step by step tutorial including several examples of the phase shift of a function for reference.
Overview
The phase shift is another way of saying a horizontal shift – that is, when a graph moves from left to right. If the phase shift is positive, the graph shifts to the left, and if the phase shift is negative, the graph shifts to the right. Finding a phase shift is not difficult – when a value is included with x (instead of included with something relating to x), then a horizontal shift or phase shift will be performed. Simply look at the equation of the function to find the value.
Tags: algebra, equation, function, graph, horizontal, left, negative, phase, positive, right, shift, value, x
Posted in Algebra | No Comments »
Tuesday, October 20th, 2009
How to Graph the Tangent Function
Description
A detailed tutorial on solving the graph of the tangent function. Step by step tutorial including several examples of how to solve the graph of the tangent function for reference.
Overview
The graph of the tangent function looks a great deal like the graph of x cubed – just repeated several times. The graph of tangent is drawn in a period of pi – meaning a “line” is put down every pi spaces for a guideline on where to draw the graph – and hits all of the major points of the graph, also in intervals of pi. There is no amplitude of the tangent function because it extends up to both negative infinity and positive infinity in vertical directions.
Tags: amplitude, asymptote, function, graph, infinity, intervals, negative, period, pi, positive, tangent, trigonometric, trigonometry, vertical, x, y
Posted in Trigonometry | 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 »
Friday, October 16th, 2009
How to Identify Coterminal Angles
Description
A detailed tutorial on identifying coterminal angles. Step by step tutorial including several examples of how to identify coterminal angles for reference.
Overview
Coterminal angles are opposite angles that when put together share a terminal side, or common side, and therefore create a circle. One of the angles is positive, and the other angle is negative – a negative angle is one that is formed from the opposite side and using the second scale on a protractor. The absolute value of the first angle plus the absolute value of the second angle must add up to 360 degrees in order for them to be coterminal angles.
Tags: 360, absolute value, angle, circle, coterminal, degrees, Geometry, Math, negative, opposite, positive, protractor, side, terminal
Posted in Geometry | No Comments »
