Formula | Homework Help

Posts Tagged ‘formula’

Interior Angles

Friday, November 20th, 2009

Interior Angles of Polygons

Description

A detailed tutorial on interior angles of polygons. Step by step tutorial including several examples of interior angles of polygons for reference.

Overview

There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on interior angles. Interior angles are the angles that are found along the inside of the polygon. Interior angles may seem more difficult to find than exterior angles, because they don’t always add up to the same measurement of degrees. However, there is a formula that can be used to find the total measure of the interior angles. This formula is (n – 2) * 180 = D, where n is the number of sides on the polygon, and D is the total measure of the degrees.

Tags: 180, angle, concave, convex, degrees, formula, Geometry, Inside, interior, irregular, measure, negative, polygon, positive, regular
Posted in Geometry | No Comments »

Exterior Angles

Friday, November 20th, 2009

Exterior Angles of Polygons

Description

A detailed tutorial on exterior angles of polygons. Step by step tutorial including several examples of exterior angles of polygons for reference.

Overview

There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on exterior angles. Exterior angles are the angles that are found when you draw a line of an angle on the outside of the polygon to form another angle. On a regular polygon, all the exterior angles should have the same measure. No matter what kind of polygon you have, the exterior angles will always add up to 360 degrees. Concave polygons are harder to find the measure of, because the exterior angles are negative, but they should still add up to 360 degrees. In order to find the measure of each individual exterior angle, simply use the formula 360 / n = D, where n is the number of sides, and D is the degree of each of the angles seperately. However, this formula only works for regular polygons, not irregular polygons.

Tags: 360, angle, concave, convex, degrees, exterior, formula, Geometry, irregular, measure, negative, Outside, polygon, positive, regular
Posted in Geometry | No Comments »

Center of a Circle

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 »

Orthogonal Complements

Friday, November 6th, 2009

Overview of Orthogonal Complements

Description

A detailed tutorial on orthogonal complements. Step by step tutorial including several examples of orthogonal complements for reference.

Overview

The orthogonal complement of a subspace of an inner product space is the set of all vectors in the inner product space that are orthogonal to every vector in the subspace. This can be expressed mathematically in the formula $W^\bot=\left\{x\in V : \langle x, y \rangle = 0 \mbox{ for all } y\in W \right\}.\,$ , where W is the subspace and V is the inner product space. The orthogonal complement is sometimes also called the perpendicular complement, shortened to the informal form perp.

Tags: algebra, complement, formula, inner, orthogonal, perp, perpendicular, product, set, space, subspace, v, vector, W
Posted in Algebra | No Comments »

Mass-Energy Equivalence

Thursday, November 5th, 2009

Overview of Mass-Energy Equivalence

Description

A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.

Overview

Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is $E = mc^2 \,\!$ , where E is energy, m is the mass, and c is the speed of light in a vacuum.

Tags: Albert, body, c, content, differential equations, E, Einstein, energy, equivalence, equivalent, formula, idea, light, m, mass, measure, speed, vacuum
Posted in Differential Equations | No Comments »

The Freshman Dream

Tuesday, November 3rd, 2009

How to Avoid the Freshman Dream

Description

A detailed tutorial on avoiding the freshman dream. Step by step tutorial including several examples of the freshman dream for reference.

Overview

The freshman dream is a mistake commonly made in algebra that was named for the probability that only freshman would make this mistake. In reality, this mistake can be made by anyone, regardless of your academic standing. The freshman dream is employed when you are given a squared binomial. If your equation looks like (x + n)^2, people using the freshman dream will write this as x^2 + n^2. However, this is wrong! Your equation should look like (x + n)(x + n) in the first step, and from there it is obvious to see that you would need to use FOIL to solve for it.

Tags: algebra, avoid, binomial, dream, equation, FOIL, formula, freshman, mistake, multiply, quadratic, square
Posted in Algebra | No Comments »

Unit Vector

Friday, October 23rd, 2009

Definition of a Unit Vector

Description

A detailed tutorial on the unit vector. Step by step tutorial including several examples of the unit vector and how to solve it for reference.

Overview

In linear algebra, a unit vector is a vector that only has a length or magnitude of one. They are often used to indicate direction. There is a process used to create a unit vector, called normalizing a vector. When doing this, you must divide a vector of arbitrary length by its length. To normalize a vector with three points, you would use this formula:

$<span style="font-size: x-small;">\mathbf{\hat{a}} = \frac{\mathbf{a}}{\left\|\mathbf{a}\right\|} = \frac{a_1}{\left\|\mathbf{a}\right\|}\mathbf{e_1} + \frac{a_2}{\left\|\mathbf{a}\right\|}\mathbf{e_2} + \frac{a_3}{\left\|\mathbf{a}\right\|}\mathbf{e_3}</span>$

Tags: algebra, arbitrary, direction, formula, length, magnitude, normalizing, one, point, unit, vector
Posted in Algebra | No Comments »

Vector Subtraction

Friday, October 23rd, 2009

How to Solve Vectors Using Vector Subtraction

Description

A detailed tutorial on how to solve vectors using vector subtraction. Step by step tutorial including several examples of vector subtraction for reference.

Overview

Vector subtraction involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector subtraction is:

$\mathbf{a}-\mathbf{b}=(a_1-b_1)\mathbf{e_1}+(a_2-b_2)\mathbf{e_2}+(a_3-b_3)\mathbf{e_3}.$

In general, vector subtraction is defined geomtrically instead of algebraically, so it is not used quite as often as vector addition is.

Tags: addition, algebra, algebraically, direction, equal, formula, geometrically, Geometry, magnitude, subtraction, vector
Posted in Algebra | No Comments »

Vector Addition

Friday, October 23rd, 2009

How to Solve Vectors Using Vector Addition

Description

A detailed tutorial on how to solve vectors using vector addition. Step by step tutorial including several examples of vector addition for reference.

Overview

Vector addition involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector addition is:

$\mathbf{a}+\mathbf{b}=(a_1+b_1)\mathbf{e_1}+(a_2+b_2)\mathbf{e_2}+(a_3+b_3)\mathbf{e_3}.$

Vector addition is also occassionally referred to as the parallelogram rule, because on a picture diagram of vector addition the shape of a parallelogram is formed.

Tags: addition, algebra, direction, equal, formula, graph, magnitude, parallelogram, picture, rule, vector
Posted in Algebra | No Comments »

Present Value

Tuesday, October 13th, 2009

Introduction to Present Value

Description

A detailed tutorial on solving for the present value. Step by step tutorial including several examples of solving for the present value for reference.

Overview

Present value is the value on a given date of a future payment or series of future payments. It is typically discounted to reflect the time value of money, and sometimes other factors. Because of this, the main calculation for present value is simply the calculation for the time value of money. The time value of money can be found by using the compund interest formula, which can be mathematically expressed as $C_t = C(1 + i)^{-t}\, = \frac{C}{(1+i)^t} \,$ . This is equal to the present value.

Tags: algebra, calculation, compound, formula, interest, investment, Math, money, present, risk, time, value
Posted in Algebra | No Comments »