definition of mathematics

Let us learn about definition of mathematics

Mathematics is a study of relationships using different numbers & the study of the relationships between numbers, shapes, & quantities. Mathematics uses signs, symbols, & proofs & includes arithmetic, calculus, algebra, geometry, & trigonometry.

Mathematics is referred as Mathematical operations & processes involved in the solution of a problem or study of some scientific field

Mathematics is a group of related sciences, including geometry, algebra, & calculus, concerned with the study of number, quantity, shape, & space & their interrelationships by using a specialized notation

Mathematics is a science or group of related sciences that deals with the logic of quantity & shape & arrangement

The mathematics is deductive study of shape, quantity, & dependence.

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inequalities calculator

Let us learn how to use inequalities calculator

Add all numbers in left side from the in equality.

Then add all numbers in right side from the inequality.

Add the entire variable with coefficients on the left side from inequality.

Add the entire variable with coefficients on the right side from the inequality.

Subtract all number on left side from both sides of the inequality.

Add all number on the left side from both sides of the inequality

Subtract all variable with a coefficient on the right hand side of the inequality from both sides of the inequality

Add all variable with a coefficient on the right hand side of the inequality from both sides of the inequality.

Simplify by dividing on both sides or by multiplying on both side with reciprocal of inequality.

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sin 30 degrees

Let us learn about sin 30 degrees

Value of 30 Degree

• The value of sin 30 degrees = ½
• The value of cos 30 degrees =√3/2
• The value of tan 30 degree = 1/√3

zero degree angle is known as an acute angle, because the angle of 2 rays Is less than 90 degree & greater than 0 degree.

sin(135) = sqrt(2)/2
cos(135) = -sqrt(2)/2
sin(30) = 1/2
cos(30) = sqrt(3)/2

Note 135 deg is just the 45 deg angle in the upper left quadrant of the unit circle, where sines are postiive & cosines are negative

sin(135-30) = sin135cos30 - cos135sin30
................... = [sqrt(2)/2][sqrt(3)/2] - [-sqrt(2)/2][1/2]
.................. = sqrt(6)/4 + sqrt(2)/4
.................. = [sqrt(6) + sqrt(2)]/4
................... = 0.9659

sin(135) - cos(30) = sqrt(2)/2 - sqrt(3)/2
................................= [sqrt(2) - sqrt(3)]/2
................................= -0.1589

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factoring calculator online

Let us solve problem using factoring calculator online

Factor the given expression, 2x² + 4x
Solution:
= 2x² + 4x
Taking the common terms outside,
= 2x(x + 2)
The solution is 2x (x+2).
Solve 6x² + 18x - 24 = 0 for x.
Solution
Given equation is 6x²+18x-24=0 for x.
Solve the given equation we get
. (6x - 24)(x + 1)=0
Here by equating the values to zero
6x-24=0, x+1=0
Here keep constant terms on 1 side & move the variables to other side.
6x=24, x=-1
The final solution is X=3/2, x = -1.

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college level books

Let us learn about college level books

college level books are very important, helps Student to build our spirit, give information, help to pass time, make us more deep an cultural, helps us to write & think better, help us to chose people, because with college level books student will able to chose the persons that like the same books that student like... Since millions of centuries mankind write it's the way to preserve history, facts that without them all mankind was lost without identity... finally, open our mind to the world & makes us better persons.

College level books are real, true friend. Books provide lot of experience to us. They improve our knowledge. It helps us to collect countless information. It is true that books are our best friend the only thing they cannot talk them but we can read them. Student should always carry college level books while traveling. College level books help a lot to maintain a good vocabulary. Above all these college level books help solve the mystery of life sometimes, so they act as a true companion. Whenever student feels disturbed they should read college level books. College level books are the identity of college level students, a college student is known by the books he/she reads. No books are boring depends on interest of the college grade students declare them as boring or interesting.

College level books give peace to Student mind, increase attention & concentration, increases vocabulary, presence of mind, creativity & above all, college level books gives us knowledge which is considered to be the world's greatest treasure.

college level books make us feel heavenly.

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midpoint formula calculator

Let us learn about midpoint formula calculator

The midpoint formula calculator is very handy while calculating the midpoint between any 2 points & is very commonly used in geometry both practically & during learning. In math, midpoint formula questions are very common & Learner should be well aware of how to use the midpoint formula calculator. The formula to find midpoint using calculator is actually quite logical, if you try to look at it closely, you will find that it is derived from the average of the x coordinates & y coordinates

The midpoint formula calculator is used when you need the point that is exactly between 2 other points. The midpoint formula is used when you need to find a line which bisects a specific line segment. Essentially, the 'middle point' known as the "midpoint"

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square root of 0

Let us learn about square root of 0

The square root of zero would be zero always, because zero multiplied by itself or zero squared & would equal zero.
The best example Question based on what is the square root of 0 is mentioned below that,

Best Example

What is the square root of 0?
The square root of Zero (0) is nothing but √0
The value for √0 = 0

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alphabet of lines

Let us learn about alphabet of lines

The "Alphabet of Lines" defined as the different styles of lines used in drafting such as to show different features about an object which is drawn, hidden, Construction, cutting-plane, visible object, dimension, phantom, center, extention, section, & border. Or alphabet of lines is a geometrical object that is straight, infinitely long & infinitely thin.

Drafting or Computer Aided Drafting: The alphabets of lines are the different line that architects, draftsmen, engineers, et al use when constructing a drawing. The Alphabet of lines is referred as the different types of lines. The use of line types on a drawing is used to describe the various features of an object to the person reading the print. Alphabets of lines help to illustrate & describe the shape of objects which will later become real parts.
The best example, a thick solid line is known an object line and represents the outline of a part on a drawing. A dash line represents an edge which is not visible in a particular view; therefore it is called a hidden line. Other common lines used in drafting include extension lines, dimension lines, construction lines, border lines, center lines, among many others depending on the type of drawing.
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free exam papers

Let us learn how free exam papers helps students in learning math.

Students are well boasted & well encouraged to view the sample answer sheet so that they are familiar with the way they are required to show their solutions in the test.

These free exam papers, past papers have been published to assist students to familiarize themselves with the format of the test & to provide material which will enable them to develop more effective exam technique. Some features of good exam technique include the ability to manage the allocated test time evenly & the understanding that it is better to guess solution than leave it blank.

There are many website which provides free previous math exam papers for students to help them in learning math better. It enables students to understand & establish the type of questions being asked. Student will learn how to manage your time during the exam

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formal charge equation

Let us learn about formal charge equation

a formal charge “FC” is referred as the charge assigned to an atom in a molecule, assuming that electrons in a chemical bond are equally shared between atoms, regardless of relative electronegativity.
Formal charge equation:

FC = V - N - B/2

Where as “V” is the number of valence electrons of the atom in isolation. “B” is the total number of electrons shared in covalent bonds with other atoms in the molecule. “N” is referred as the number of non bonding electrons on this atom in the molecule.

C_f = E_v - (E_u + 1/2E_p)

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gaussian elimination calculator

Let us learn about gaussian elimination calculator

Gaussian elimination calculator is a method to find the inverse of any square matrix. Student simply chooses their matrix’s dimensions & then enters the elements of the matrix student want inverted in the left frame.
Gaussian elimination calculator is a variant of Gaussian Elimination. We are transforming the coefficient matrix into another matrix which is much easier to find solution, & the system represented by the new augmented matrix has the same solution set as the original system of linear equations. In Gaussian elimination calculator, the aim is to transform the coefficient matrix into a diagonal matrix, & the zeros are introduced into the matrix 1 column at a time. We work to eliminate the elements both below & above the diagonal element of a given column in 1 pass through the matrix
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biconditional statement

Let us learn about biconditional statement

If 2 simple statements “p” & “q” are connected by the connective. 'if & only if', then the resulting compound statement is said to be as the biconditional statement. Symbolically it is characterized by p<-> q.

An integer is even if & only if it is divisible by two. Then it is biconditional having the truth value T.

The biconditional statement p <->q is true when either both p & q are true or both p & q are false.

A statement is said to be as biconditional when it expresses the idea which presence of some property is a necessary & sufficient condition for the presence of some other property. Such a statement is usually phrased in the terms "P, if & only if Q." The phrase "if & only if" is often abbreviated as iff.

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perimeter of triangle

Let us learn about perimeter of triangle

The perimeter is the space or distance around a closed plane figure.

The perimeter “P” of a triangle is given by the formula

P = a + b + c
Where a, b & c are the side lengths of the triangle.
Perimeter = a + b+ c. where a, b, and c are sides of triangle.

find the perimeter of a triangle given a = 3 cm, b = 5 cm, and c = 7

P = 3 + 5 + 7 = 15 cm

Find the perimeter when a = 4 cm, b = 8 cm, and c = 12

P = 4 + 8 + 12 = 24 cm

Find the perimeter when a = 1/2 cm, b = 3/2 cm, and c = 6/2

P = 1/2 + 3/2 + 6/2 = ( 1 + 3 + 6)/2 = 10/2 = 5 cm

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linear programming problem

Linear programming problem below, state the dual problem, solve by the simplex or dual simplex method & also states the solutions to both problems.

1. Maximize x1 − 2x2 − 3x3 − x4 subject to the constraints xj ≥ 0 for all j and

x1 − x2 − 2x3 − x4 ≤ 4

2x1 + x3 − 4x4 ≤ 2

−2x1 + x2 + x4 ≤ 1.

2. Minimize 3y1 − y2 + 2y3 subject to the constraints yi ≥ 0 for all i and

2y1 − y2 + y3 ≥ −1

y1 + 2y3 ≥ 2

−7y1 + 4y2 − 6y3 ≥ 1.

3. Maximize −x1 − x2 + 2x3 subject to the constraints xj ≥ 0 for all j and

−3x1 + 3x2 + x3 ≤ 3

2x1 − x2 − 2x3 ≤ 1

−x1 + x3 ≤ 1.

4. Minimize 5y1 − 2y2 − y3 subject to the constraints yi ≥ 0 for all i and

−2y1 + 3y3 ≥ −1

2y1 − y2 + y3 ≥ 1

3y1 + 2y2 − y3 ≥ 0.

5. Minimize −2y2 + y3 subject to the constraints yi ≥ 0 for all i and

−y1 − 2y2 ≥ −3

4y1 + y2 + 7y3 ≥ −1

2y1 − 3y2 + y3 ≥ −5.

6. Maximize 3x1 + 4x2 + 5x3 subject to the constraints xj ≥ 0 for all j and

X1 + 2x2 + 2x3 ≤ 1

−3x1 + x3 ≤ −1

−2x1 − x2 ≤ −1.

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integrated algebra regents

Let us learn about integrated algebra regents

The integrated algebra regents contain the fundamental concepts of algebra like simple expressions, rational, linear equations, & radical expressions. Geometry, Algebra, & Trigonometry are included in the parts of integrated algebra regents examination. The integrated algebra regents test gives the clear idea & picture of solving different types of questions.

Calculators like Graphing calculators are required for the Integrated Algebra Regents examination. During the period the administration of the Regents exam, schools are required to make a graphing calculator available for the exclusive use of each learner. You will need to use your calculator to work with evaluate roots, trigonometric functions of angles, & perform routine calculations. Knowing how to use a graphing calculator gives you an advantage when deciding how to solve a problem. Instead than solving a problem algebraically with paper & pen, it may be easier to solve the same problem using a graph or table created by a graphing calculator. A numerical or graphical solution using a calculator can also be used to help confirm a solution obtained using standard algebraic methods.

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like terms calculator