Units of time

Let us learn about Units of time

• Milliseconds, Minutes, Nanoseconds, Picoseconds
• Seconds, Weeks, Attoseconds, Centiseconds, Centuries
• Deciseconds, Days, Microsecond, Hours
• Leap year, Year, Yoctoseconds
• Millennia, Femtoseconds

Time is very precious especially to students. Time has been referred as the continuum in which events occur in succession from the past to the present and on to the future

In our next blog we shall learn about density altitude calculator I hope the above explanation was useful.Keep reading and leave your comments.

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easy general knowledge questions

Let us try to find answers for easy general knowledge questions

1) what is 55-17?

2) What number is 75% of 4?

3) A triangle with 2 equal sides is what kind of triangle?

4) Is this true, all Real Numbers belong to Complex Numbers?

5) The product of 2 fractions is 5. If 1 of them is the mixed number 61/5, what is the other number?

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

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.

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

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.

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