Algebra Terms

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Algebra Terms:In universal algebra logic, algebra terms is a freely generated algebraic structure. For case, a signature consisting of a single binary relation, term algebra over a set X of variables is exactly the free magma generated by X.Next we will see meaning of linear scale,a linear scale, also called a bar scale, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing.

Algebraic Equation Solver

-->Algebraic Equation Solver:We can learn about algebraic equation solver with the help of an example: Example: 1 Solve this equation: 3x+y=3, 5x-2y=16
equation solver Solution:
The given equation is,
3x+y=3 (1)
5x-2y=16 (2)
From (1) we get 3x+y=3
Y=3-3x (3)
Substituting y=3-3x in the equation (2), we get
5x-2(3-3x) =16
5x-6+6x=16
5x+6x=16+6
11x=22
X=22/11
X=2.
Substituting x=2 in the equation (3), we get
Y=3-3(2)
=3-6
Y=-3
Answer : X=2,y=-3

X=2,y=-3 is the solution of the given equations.Every time there is a problem students feel that it is the hardest math problem.

Radian to Degree

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Let us understand the meaning of radian and degree, The radian is the standard unit of angular measure, used in many areas of mathematics. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.whereas degree is a pair of density scales,

-->radian to degree a widely used term,it is also used while studying a 90 degree angle.

Triangles Types

-->Triangles Types:When we speak about a Triangle we mean a three sided figure with interior or exterior angles to it,now we will understand the triangles types, Based on the angles or sides of the triangle, the triangles are divided in to many types. 1.right triangle
2.Acute triangle
3.Obtuse triangle
4.isosceles triangle
5.Equilateral triangle

6.scalane triangle,now let us see what we mean by data representation,a numerical data is a set of mathematical values which is used for measuring and counting and it can be represented by graphs(Pie-chart, bar graph).

Quadratic Form

Quadratic Form:In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\! is a quadratic form in the variables x and y.Quadratic forms occupy central place in various branches of mathematics: number theory, linear algebra, group theory (orthogonal group), differential geometry.In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is

ax^2+bx+c=0,\,

where x represents a variable, and a, b, and c, constants, with a ≠ 0.Quadratic functions, in mathematics, is a polynomial function of the form

f(x)=ax^2+bx+c,\quad a \ne 0.

The graph of a quadratic function is a parabola whose major axis is parallel to the y-axis.

Binomial Theorem

Binomial Theorem:Let me explain Binomial Theorem.The binomial theorem explains the power of the binomial.Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial.We will discuss Problems on Binomial Theorem in the future blogs.

Linear Programming

Linear Programming:Let us understand about Linear Programming.Linear Programming 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.Now let us see what we mean by linear programming constraints.The linear inequalities or equations on the variables of a linear programming problem are called constraints. The conditions x >- 0, y >- 0 are called non-negative restrictions.Lastly let us see one example problem of linear programming.Let us solve linear programming.Example problem:

Solve:

Minimize: 4a + 5b + 6c

Here we can see the method of solving linear programming.

a + b >= 11

a - b <= 5 c - a - b = 0 7a >= 35 - 12b

a >= 0 b >= 0 c >= 0

Solution:

Step1: We use the equation c-a-b=0 to put c=a+b (>= 0 as a >= 0 and b >= 0) and so the linear

Programming is reduced to minimize.

=4a + 5b + 6(a + b)

=4a + 5b + 6a +6b

= 10a + 11b

Subject to

a + b >= 11

a - b <= 5 7a + 12b >= 35

a >= 0 b >= 0

The minimum occurs at the intersection of a - b = 5 and a + b = 11

This is the first step in solving linear programming.

Step2: The second step in solving linear programming involves the following step

By using Elimination method we can get the value of a = 8 and b = 3

To find the C value (substitute a and b value in c= a + b ) c = 11

The value of the objective function 10a + 11b = 80 + 33 = 113.

Thus these are the steps involved in solving linear programming.