Posts Tagged ‘equation’
Friday, October 30th, 2009
Overview of Hubble’s Law
Description
A detailed tutorial on Hubble’s law. Step by step tutorial including several examples of Hubble’s law including a visual example for reference.
Overview
Hubble’s law states that the velocity at which various galaxies are receding from the Earth is proportional to their distance from us. This law is often expressed by the equation v = H_0 * D, where H_0 is the constant of proportionality (or Hubble constant) between the distance D to a galaxy and its velocity v.
Tags: algebra, constant, distance, equation, galaxy, Hubble, law, observation, proportional, proportionality, velocity
Posted in Algebra | No Comments »
Thursday, October 22nd, 2009
How to Identify a Concave Function
Description
A detailed tutorial on concave functions. Step by step tutorial including several examples of concave functions and concave down curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss concave functions. A concave function is one with the endpoints facing down, forming the shape of an upside down bowl. When looking at the graph of a concave function, we say that it is concave down. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Identify a Convex Function
Description
A detailed tutorial on convex functions. Step by step tutorial including several examples of convex functions and concave up curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss convex functions. A convex function is one with the endpoints facing up, forming the shape of a bowl. When looking at the graph of a convex function, we say that it is concave up. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | 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
An Overview of Basic Graphs
Description
A detailed tutorial on seven different basic graphs. Step by step tutorial including several visual examples of seven different basic graphs for reference.
Overview
A lot of time in any math class is devoted to the subject of graphs and graphing. But forming a graph when you are only given an equation can be difficult – unless you have some basic graphs memorized. Once you have these seven graphs memorized, it is very easy to follow the patterns in the equation and and simply fix your basic graphs to fit these new requirements. The basic graphs are the most basic patterns that x can be found in on any function – this is x, x squared, and x cubed. There is also the absolute value of x, the natural log of x, and the exponential function of x. The last one is one divided by x, which while not being a basic form of x, is a very important form.
Tags: absolute value, basic, cubed, divided, equation, exponent, exponential function, function, graph, logarithm, natural log, squared, trigonometry, x, y
Posted in Trigonometry | No Comments »
Friday, October 9th, 2009
Indentifying Prime Polynomials
Description
A detailed tutorial on how to identify prime polynomials. Step by step tutorial including several examples of identifying prime polynomials for reference.
Overview
Prime polynomials are any polynomial that cannot be factored. Just like a number is prime if you can not break it down into two seperate whole numbers to multiply, a polynomial is prime if you cannot break it down into two separate binomials with whole numbers to multiply. When you run into a prime polynomial when trying to solve a quadratic equation, you cannot use the factoring method. what the factoring method does is split the polynomials into a binomial, which cannot be done to a prime polynomial. If you have a prime polynomial, you have to use the quadratic formula to solve it. At first, you can spot prime polynomials by attempting to factor it, but eventually you will be able to do it just by looking at it.
Tags: algebra, binomial, equation, factoring, formula, Math, multiply, number, polynomial, prime, quadratic, whole
Posted in Algebra | 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
Witch of Agnesi Explained
Description
A detailed tutorial of the Witch of Agnesi. Step by step tutorial including a visual example of the Witch of Agnesi for reference.
Overview
The Witch of Agnesi is actually a curve. This curve can be a circle, or it can be a regular curve. The movement of the curve flows up and down, and the curve itself changes as it moves. This curve is defined by the Cartesian equation 
.
It is called the Witch of Agnesi by a simple mistranslation into English. This curve was named in Italian – la versiera di Agnesi, which means the Curve of Agnesi. When translating the name, “la versiera” was accidentally read as “l’awersiera”, which means a woman who is contrary to God, or a demon or witch. Hence it was called the Witch of Agnesi.
Tags: Calculus, cartesian, circle, curve, equation, l'awersiera di Agnesi, la versiera di Agnesi, Maria Agnesi, Math, Witch of Agnesi, Witch of Maria Agnesi
Posted in Calculus | No Comments »
Friday, October 9th, 2009
How to Solve Literal Equations
Description
A detailed tutorial on solving literal equations. Step by step tutorial including several examples of how to solve literal equations for reference.
Overview
A literal equation is any mathematical equation that contains more than one variable. This can mean an equation that just has 2 variables, or one that has more than two – this can also include equations that only have variables, and no real numbers. This usually involves a technique called replacing. This is when you solve for one variable, and find the answer which will have other variables in it. Then replace that variable in the equation. Eventually you will be left with one variable, and you can then put the number value for it in your equation, and find the answer for all of your variables. This technique only works if you have at least one real number in your equation.
Tags: algebra, equation, literal, Math, more than one, order of operations, real number, repeat, replace, replacing, variable
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Lissajous Curve Explained
Description
A detailed tutorial of a lissajous curve. Step by step tutorial including several visual examples of lissajous curves for reference.
Overview
A Lissajous curve represents the graph of a system of parametric equations, which can be mathematically expressed as 
. This also decribes complex harmonic motion. The way that the figure appears is very sensitive to the ratio a / b, so the figure can appear in many different forms.
Tags: Bowditch, Calculus, complex, curve, equation, figure, form, graph, harmonic, Lissajous, Math, motion, paramentric, ratio, system
Posted in Calculus | No Comments »
