composite number chart

Let us learn about composite number chart

A composite number has factors in addition to 1 and itself. All numbers which end in 5 are divisible by 5. Hence all numbers which end with 5 & are greater than 5 are composite numbers.

A number is known as "composite" if it can be divided evenly into 2 or more parts. In other words, it is a positive integer which is divisible by numbers other than 1 & itself. The smallest composite number is four. The 1st few composite numbers are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21...... A composite number is "an integer that is exactly divisible by at least 1 positive integer other than both itself and 1. All numbers are divisible by both one & itself. That is, a number which has more than 2 divisors other than 1 & the number itself is known a composite number.

In our next blog we shall learn about cost of sales formula I hope the above explanation was useful.Keep reading and leave your comments.

quantitative variables

Let us learn about quantitative variables

Measure the variable by a number is known as quantitative variable. The numeric values are known as variable. Quantitative variables are always ordered values, interval sequence & ratio scales.

Distributions of quantitative variables are represented by dot plots, histogram, box plots & scatter plots. Quantitative variables are always discrete & continuous variables.

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integration by partial fractions

Let us learn about integration by partial fractions

If the integrand is in the form of an algebraic fraction & the integral cannot be evaluated by simple methods, the fraction requires to be expressed in partial fractions before integration takes place.

We decompose fractions into partial fractions like this due it makes certain integrals much easier to do, & it is applied in the Laplace transform, which we meet later.

Evaluate ∫ (x² + 1) / (x² -5x + 6) dx.

The integration by partial fractions is not a proper rational function on dividing

(x² + 1) by (x² - 5x + 6), we get

(x² + 1) / (x² - 5x + 6) =1 + (5x - 5) / (x² -5x + 6) =1 + (5x -5) / (x - 2) (x - 3)

Now, let (5x - 5) / ( x - 2)(x - 3) = A / ( x -2) + B / ( x -3)

=> (5x - 5) / (x - 2) (x -3) = A(x -3) + B(x -2) / (x -2) (x -3)

Placing x =2 on both sides of (i), we get A = -5

Placing x =3 on both sides of (i), we get B =10

( x² + 1) / (x² - 5x +6) =1 - 5 / (x -2) + 10 / (x -3)

=> ∫ (x² + 1) / (x² -5x + 6)dx = ∫ dx - 5 ∫ dx / (x - 2) + 10 ∫ dx / (x -3)

= x -5 log | x -2 | + 10 log | x -3 | + C

In our next blog we shall learn about extraction of aluminium I hope the above explanation was useful.Keep reading and leave your comments.

equation of ellipse

Let us learn about equation of ellipse

Equation of ellipse in standard form

[ x²/a² ] + [ y²/b² ] = 1

Let x'ox & yoy' be the co-ordinate axes.

Let F(c, o) and f'(- c, o) be 2 given fixed points .

Let us consider the locus of a point which moves in such a way that the sum of its distances from F & F' remains constant say equal to 2a where a > c.

Let P(x, y) be any point on the locus.

Then
PF + PF' = 2a

=> √[(x - c)² + y²] + √[(x + c)² + y²] = 2a
√[(x + c)² + y²] = 2a - √[(x-c)² + y²]

On squaring both sides,

we get
[(x + c)² + y²] = 4a² + (x - c)² + y² - 4a√[(x - c)² + y²]
[(x + c) ² - (x - c) ²] - 4a² = - 4a √[(x - c)² + y²]
4 x c – 4a² = - 4a √[(x - c)² + y²]
√[(x - c)² + y²] = a – (c/a) x

Again squaring on both sides ,

we get
(x - c)² + y² = a² + [c²x²/a²] - 2cx
x² - [c²x²/a²] + y² = a² - c²
x² [1 – (c²/a²)] + y² = a² - c²
[x²(a² - c²)] / a² +y² = a² - c²

Dividing by (a² - c²)

we get
(x²/a²) + (y²/(a²- c²)) = 1
(x²/a²) + (y²/b²) = 1 , where b² = a² - c²

Thus (x²/a²) + (y²/b²) = 1 is the required equation of an ellipse in standard form

In our next blog we shall learn about relative molecular mass I hope the above explanation was useful.Keep reading and leave your comments.

square root rules

Let us learn about square root rules

• The product of 2 values in the square root is always having various values in it, & then it can be rewrite in the form as like, the 2 radical values are written inside a single radical.

• The number always lies outside radical symbol, if the number lies outside the radical is squared before it taken into the radical.

• The radical existing in fraction value then it can be written in individual roots, as like a separate radical in denominator & a separate radical in numerator.

• When ever a perfect square comes out from the square root, then the root of that perfect square is negligible.

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boolean calculator

Let us learn about boolean calculator

Student can enter a formular like "a & b & (not c)" & it shows you a table where you can see on which Boolean combination of a, b & c the term is true. Boolean logic algebra is the algebra of 2 values. These values are generally taken to be 0 & 1, as we shall do here, although F & T, false & true, etc. Boolean logic algebra is also a common uses of Boolean logic calculator. More basically Boolean algebra is algebra of values from any Boolean algebra as a model of the laws of Boolean algebra. In Boolean calculator first enter the expression then enter the values of x and y. now press the calculate button then the solution will be produced.

In our next blog we shall learn about maintenance test questions I hope the above explanation was useful.Keep reading and leave your comments.

quadrants on a graph

Let us learn about quadrants on a graph

The quadrants on a graph are referred as any of the 4 equal areas made by dividing a plane by an x & y axis

The x- & y- axes divide the coordinate plane into 4 regions. These regions are said to be as the quadrants.

Quadrant is the word helps us define the parts. If you draw straight & perpendicular lines, divide the page into 4 parts, each part is called a quadrant graph. The Quadrants of Performance concept begins with a basic graph that plots 2 major thresholds

In our next blog we shall learn about quantum mechanical model of the atom I hope the above explanation was useful.Keep reading and leave your comments.