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Introduction for Linear Programming:

Linear programming solver is the universal method of most favorable part of limited wherewithal such as labor, substance, engine, resources etc., to quite a few competing behavior such as goods, services, jobs, projects, etc, on the fundamentals of known criterion of optimality. The phrase limited at this point is used to describe the availability of scarce resources during planning period. The principle of optimality usually means either performance, return on investments, utility, time, distance etc.

Structure of Linear programming examples:

The LP model contains the following 3 fundamental elements.

• The decision variable that we seek to determine.
• Objective (goal) that we aim to optimize (minimize or maximize )
• Constraints that we need to satisfy.

Formulation of linear programming problem:

The procedure consists of the subsequent chief steps

Step 1: Study the given situation to find the key decision to be made.

Step 2: Identify the variables involved and designate them by symbols x_j (j=1, 2…)

Step 3: Express the feasible alternatives mathematically in terms of variables, which generally are: x_j >=0 for all j for Math Question and Answer.

Step 4: Identify the constraints in the problem and express them as linear inequalities or equation involving the decision variables

Step 5: Identify the objective of the function and express it as a linear function of the decision variables.

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Let us learn about bar graph examples:

In pictograph, we use pictures to represent data. This Process of representing numerical data take more time and it is difficult to compare two items. Here rather than symbols and pictures it is better to use bars. This type of using bars is called bar graph or bar diagram. The bar-graph represents the information by rectangular bars in which a unit square is taken to indicate the value of certain number or quantity. Here, let us know how to draw or how to construct the simple bar graph.

Simple Bar Graph-example Problem :

1. Draw the simple bar graphs for every month expenditures of a family:

items	expenditures
House rent	2000
Food	3000
Education	800
Electricity	400
Transport	600
miscellaneous	600

Solution:
Bar graphs showing the every month expenditure of a family on various items.

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Let us learn about plane trigonometry:

Trigonometry is the division that deals with study of plane and spherical triangles. Plane trigonometry consists of 2 dimensional triangles the ones that we can draw on the paper.or we can say Plane trigonometry is the sub division of trigonometry in which its principles are applied to the plane triangles.If enough sides and angles are known we can calculate the remaining sides and angles as well as area and hence we can solve the triangles. Triangles can also be solved by the law of sine and law of cosines.

Important things to remember

1) Pythagorean theorem

2) Trignometric Functions

3) law of Sines and Cosines

4) Trigonometric identities

5) Half and double angle formula

Do you need to know more about kinds of triangles .

Basic Formulas Used in Plane Trigonometry

Pythagorean theorem

As square of the hypotenuse is = sum of the squares of the other 2 sides in the Right Triangle.The hypotenuse is the longest side.if two sides of triangles are given as a and b and hypotenuse = c so according to the theorem

From the above right triangle we have ( hypotenuse)²= (leg)²+ (height)²

c²= a²+ b²

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Introduction to algebra factorising:

In algebra equations factorisation is one of the important method. Factorisation gives the x values of the given algebraic equations. Factoring the equations gives the desired value of the function. It is very easy and simple. General form of the algebraic equation can be written as, ax² + bx + c. In factorisation, we find two or more factor values. Quadratic equations are mainly used for factorising process.

Problems - Algebra Factorising

Find the factor value of the given quadratic equation x² - 2x - 35 = 0

Solution:

Given quadratic equation is x² - 2x - 35 = 0

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First, we have find the two numbers that add to be give the value of (- 2) and give the product of (- 35).

For in this case, that two numbers are - 7, 5. So we exchange - 2x as (- 7x + 5x)

Therefore, the given equation can be rearranged and written as,

x² - 2x - 35 = 0

x² - 7x + 5x - 35 = 0

Then, group the first two terms and second two terms

(x² - 7x) + (5x - 35) = 0

Take the biggest common number from the group, we get

x (x - 7) + 5 (x - 7) = 0

(x + 5) (x - 7) = 0

Separately equate the two values to zero, we get

x + 5 = 0, x - 7 = 0

x = - 5, 7

Answer:

The factors are x = - 5, 7

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Introduction to histogram definition online tutoring:

Histogram is an easy method to represent database. The histogram graphs are useful to compare the data that which one is high and low range. The histogram graphs have area of rectangles by representing frequencies. One of the most important source for students since students can easily access the materials for their related subjects; this can be achieved by online. Histogram chart is one of the quality tools. Tutoring helps to online relationship between students and staffs. Students get the information from the tutor. Here we are going to see about histogram definition online tutoring.

Histogram Definition Online Tutoring - Steps:

The following steps used to construct the histogram in definition of histogram tutoring:

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Step 1:

In histogram graph, the information ranges are dividing by equal intervals in a column. For example (0 to 5, 5 to 10, and 10 to 15)

Step 2:

We need to create x-axis and y-axis. X-axis represented by horizontal position and y-axis represented by vertical position.

Step 3:

Given data (class intervals) are plot into x-axis (horizontal position).

Step 4:

Given data (frequency) are plot into y-axis (vertical position).

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Geometry Helps for Kids

Learn three dimensions;
Here we are going to learn the three dimension objects, it has length, width and height it will be come under the category of solid geometry problems free , there are two types of solid geometry those are

• Polyhedra
• Non polyhedra

Polyhedra:
These kinds of shapes made up of the flat surfaces.
Example: triangular prism, tetrahedron
Non Polyhedra:
These kind of shapes have curved surfaces or it is the combination of mixed and flat surfaces so they are not Polyhedra
Example:
Sphere, torus
Example 6-geometry helps for kids
Which objects is used to measure the degrees?
Solution:geometry answers free
We can use the protractor to measure degree, the shape of the protractor is look like a below

from that we can measure the angle 50 degree it will be shown in the below diagram

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Euclid’s Definitions, Axioms and Postulates

Consider the three steps from solids to points (solids-surfaces-lines-points). In
each step we lose one extension, We can get online geometry tutor also called a dimension. So, a solid has threedimensions, a surface has two, a line has one and a point has none. Euclid summarized solved geometry problems these statements as definitions. He began his exposition by listing 23 definitions in
Book 1 of the ‘Elements’. A few of them are given below :

1. A point is that which has no part.
2. A line is breathless length.
3. The ends of a line are points.
4. A straight line is a line which lies evenly with the points on itself.
5. A surface is that which has length and breadth only.
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6. The edges of a surface are lines.
7. A plane surface is a surface which lies evenly with the straight lines on itself.

Permutation and combination

The permutation and combination takes place on different types of objects. The permutation of a different object is the number of different ways they can be ordered i.e. which is first, second, third, etc. If you desire to choose some objects from a larger number of objects, the way you place the chosen objects is also important. When comes to combination, on the other hand, one does not consider the order in which objects were selected or placed, just which objects were selected.

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Permutation has two types:

• Permutation with Repetition.
• Permutation without Repetition.
  

Combination has two types:

• Combination with Repetition.
• Combination without Repetition.

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