Binomial Coefficient

The Binomial theorem gives the coefficients of the product of n equal binomials:

(x + b)n = (x + b)(x + b)• • • (x + b).

If we expanded

(x + b)4

for example, then before adding the like terms, we would find term in

x4, x3b, x²b², xb3, and b4.

A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal’s triangle. These numbers are called binomial coefficients because they are coefficients in the Binomial theorem.


What the binomial theorem does is tell how many terms there are of each kind -- it adds those like terms. Those are the binomial coefficients.

We will see that determining those coefficients depends on the theory of combinations.

Binomial coefficient is intimately related to Bernoulli numbers, Catalán numbers, Fibonacci numbers, statistics and a host of combinatoric problems.

DISTANCE FORMULA

Distance is a numerical description of how far apart objects are.

The main purpose of the distance formula is to measure the distance between two points using the Pythagoras Theorem. Without the distance formula, it is not always possible to measure the exact distance if a measuring tool like the ruler is not available. Instead, the distance formula makes use of relative coordinate points that are given to allow us to calculate the distance.


The formula of distance can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points.

The distance formula math is a very handy tool while calculating the distance between any two locations and is commonly used in geometry both practically and during learning. Distance formula questions are very common and students should be well aware of how to use the distance formula. It is also possible to calculate the radius of a circle using the distance formula if you know the location of the midpoint and the location of a point on the circumference.

GEOMETRIC FORMULAS

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Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. A formula (plural: formulas or formulae is an entity constructed using the symbols and formation rules of a given logical language. Formulae are applied to provide a mathematical solution for real world problems.

There are many geometric formulas, and they relate height, width, length, or radius, etc, to perimeter, area, surface area, or volume, etc.

Listed below are some Geometric Formulas.

Formula to calculate area of a Parallelogram.

Area = base*height

Formula to calculate Area of a Triangle

Area = ½ of the base * height

Formula to calculate Area of a Circle.

Area= 2*pi*r²

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Area of a Rectangle formula

Area= length*width

TRIANGLES TYPES

A triangle is a polygon with three sides. There are different triangles types. There are of course triangles of different shapes and sizes. A triangle is a closed polygon with three sides. Area is a measure of the space covered by a two dimensional region. A given triangle can be more than one type at the same time.

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TYPES OF TRIANGLES:

Acute triangles are triangles in which the measures of all three angles are less than 90 degrees.

Obtuse triangle are triangles in which the measure of one angle is greater than 90 degrees.

Right triangles are triangles in which the measure of one angle equals 90 degrees.

Equilateral triangles are triangles in which all three sides are the same length.

Isosceles triangles are triangles in which two of the sides are the same length.

Scalene triangles are triangles in which none of the sides are the same length.

All the above triangles can be classified by side and by angle.

For more information about triangle and its types

LINEAR INEQUALITY

An inequality is really just any mathematical statement relating two quantities using an inequality symbol such as <, >, ≤, or ≥. For solving inequalities that contain variable expressions, you may be asked to solve the inequality for that variable. This just means that you need to find the values of the variable that make the inequality true. Remember that when you solve a linear equation there is usually one value that makes the equation true. But when you solve an inequality, there can be many values that make the statement true!

Solving Linear Inequalities is very similar to solving equations. Instead of using the Properties of Equality, you use the Properties of Inequalities. These two sets of properties are almost identical except for one very, very important rule:

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality symbol.

-->GRAPHING LINEAR INEQUALITY

Graphing inequalities is much easier than your book makes it look. Think about how you've done linear inequalities on the number line. For instance, you were asked to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing linear inequalities two-variable are very much the same.

Distance Formula Math

-->The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points. Without the distance formula, it is not always possible to measure the exact distance if a measuring tool like the ruler is not available. Instead, the formula of distance makes use of relative coordinate points that are given to allow us to calculate the distance.

Listed below is one solved example on Distance formula math.

John travels from the one coordinate point (2, 4) to another coordinate point (5, 6). Find the distance traveled by john.

Solution:

We can solve the above question by using the distance formula.