Posts Tagged ‘formula’
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, September 25th, 2009
Using Simpson’s Rule to Solve Error Bounds
Description
A detailed tutorial on using Simpson’s rule and solving error bounds. Step by step tutorial including examples of solving error bounds using Simpson’s rule for reference.
Overview
Simpson’s rule is a rule in calculus that is used to solve error bounds. It is the more complicated form of both the trapezoidal rule and the midpoint rule, both of which are also used to calculate error bounds. Although this rule is harder to use than either one of those, it is more accurate. The Simpson’s rule does not use anything except for numbers to calculate the space under a graph, and is expressed by this formula:
![\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]](http://s.wordpress.com/latex.php?latex=%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%20%5C%2C%20dx%20%5Capprox%20%5Cfrac%7Bb-a%7D%7B6%7D%5Cleft%5Bf%28a%29%20%2B%204f%5Cleft%28%5Cfrac%7Ba%2Bb%7D%7B2%7D%5Cright%29%2Bf%28b%29%5Cright%5D&bg=ffffff&fg=000000&s=0 "\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]")
Tags: accurate, area, calculate, Calculus, error bounds, formula, function, graph, Math, midpoint, Simpson's rule, trapezoidal
Posted in Calculus | No Comments »
Friday, September 25th, 2009
Using the Midpoint Rule to Solve Error Bounds
Description
A detailed tutorial on using the midpoint rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the midpoint rule for reference.
Overview
The midpoint rule, also known as the rectangle method, is the easiest way of solving error bounds. The region under the graph of a function is sectioned off into rectangles of equal width. You then must find the areas of these rectangles. Then all the areas are added together to find the approximation of the integral. The formula for this is:
The least complicated form of the midpoint rule is expressed as:
Tags: addition, approximation, area, Calculus, definite integral, error bounds, formula, function, graph, Math, mid-ordinate rule, midpoint rule, rectangle, rectangle method, sum, width
Posted in Calculus | No Comments »
Friday, September 25th, 2009
Using the Trapezoidal Rule to Solve Error Bounds
Description
A detailed tutorial on using the trapezoidal rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the trapezoidal rule for reference.
Overview
The trapezoidal rule is a rule in calculus that is used to solve error bounds and evaluate the definite integral 
The way that the trapezoidal rule works is that you take the region under a graph, approximate it as a trapezoid, and calculate the area. As a mathematical formula, this is the trapezoidal rule:
The least complicated form of the trapezoidal rule is expressed as:
Tags: Calculus, definite integral, error bound, formula, function, graph, Math, trapezium rule, trapezoid, trapezoid rule, trapezoidal rule
Posted in Calculus | No Comments »
Friday, September 18th, 2009
The Tangent Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Tangent.
Overview
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent sides. The formula for tangent is:
Tags: cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
Friday, September 18th, 2009
The Sine Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Sine.
Overview
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The formula for sine is:
Tags: angle, cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
Tuesday, September 15th, 2009
Finding the Slope of a Line
Description
A detailed tutorial on how to find the slope of a line. Step by step tutorial including several examples of how to find the slope of a line for reference.
Overview
Finding slope isn’t all that difficult. The slope of a line is the numerical expression of the slant of a line on a graph. The slope is represented by the letter m and is written in the format of rise over run – in other words, from point to point, how many spaces up the line goes and how many spaces over. Negative numbers are used if the slope runs either down or to the left instead of up and to the right. If the graph is already provided, the slope can be found by counting. But the correct way to find slope is to use a formula.
m = (change in y) / (change in x)
In order to use this formula, you need to have two points on the line. The change in x is the first x-coordinate minus the second x-coordinate, and the change in y is the first y-coordinate minus the second y-coordinate. The equations in the numerator and denominator are solved seperately and will form one fraction, which will be the slope.
Tags: algebra, change in x, change in y, formula, fraction, graph, graphing, line, m, Math, rise over run, slope, x-coordinate, y-coordinate
Posted in Algebra | 1 Comment »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Cone
Description
This video gives a clear example on how to solve for the surface area of a cone. The formula is explained and a sample problem is solved in the video.
Overview
The surface area is the area of each side, or face, of the shape added together. Cones are a very tricky shape to calculate the surface area of, because there is something called a “slant height” that needs to be used. The formula for the surface area of a cone is:
SA = B + pi * r * l
B is the area of a base. The base of a cone is always a circle. r is the radius of the circle – the base. l is the slant height. Sometimes you are given the slant height, but not always. If the slant height is not given to you then you can use this formula to find it:
l = sqrt(r^2 + h^2)
h represents the regular height of the cone, as opposed to the slant height. This is actually the pythagorean theorem – you can form a right triangle with it if you draw a picture.
Tags: area, circle, cone, formula, Geometry, Math, surface, surface area
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Pyramid
Description
This video gives a specific example for how to find the surface area of a pyramid, and also provides one of the basic formulas. The problem is completely worked through in the video to raise students understanding of the subject matter.
Overview
The surface area is the area of each side, or face, of the shape added together. For a pyramid, this typically means the rectangle or square that is the base, and the four triangles that make up the sides of the pyramid. There are more complicated versions of a pyramid, ones that have different shapes on the bottom and a different number of triangles, but the most common shape to see is a simple pyramid. First, solve for the areas of the triangles. The area formula for a triangle is A = (1/2) * b * h. If the shape on the bottom is a square, all the triangles have the same area and you will only need to multiply your answer by 4. If the shape is a rectangle or a more complicated shape, it is entirely possible that the triangles have different areas, and you may want to solve for area more than once. Then you need to find the area of the base. Depending on what your base is there will be a different area formula. Once you have all the areas, add them together to get the surface area of your pyramid.
Tags: area, formula, Geometry, Math, pyramid, rectangle, surface, surface area, triangle
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Cylinder
Description
This video explains how to find the volume of a cylinder. It shows the different parts of a cylinder and says what parts need to be used to find the surface area and why. Examples are provided in the video.
Overview
The surface area is the area of each side, or face, of the shape added together. A cylinder as three faces – the base, which has two faces of equal area, and the middle section of the cylinder, which is actually a rectangle that has been wrapped into a round shape. However, because not all the dimensions of the rectangle are typically given in a manner easy to understand, there is a formula that can be used to solve for the surface area of a cylinder.
SA = 2 * (pi * r^2) + (2 * pi * r) * h
The first part of the formula represents the area of the two circles that form the base. The second part of the formula represents the circumference of the base (which is equal to the width of the rectangle) and the height of the cylinder (which represents the length of the rectangle).
Tags: area, circle, cylinder, formula, Geometry, Math, rectangle, surface, surface area
Posted in Geometry | No Comments »
