Friday, September 24

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.

If you are interested to learn English Tenses, you can click on given link.

Thursday, September 23

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.

Tuesday, September 21

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.

Monday, September 20

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.

Friday, September 17

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.


Thursday, September 16

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.


Wednesday, September 15

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.

Tuesday, September 14

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.

Monday, September 13

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.

Thursday, September 9

angle of elevation and depression

Let us learn about angle of elevation and depression

In order to find solution for problems involving angles of elevation & depression, it is important to

* Always use basic right triangle trigonometry

* solve equations which involve 1 fractional term is also necessary to know.

* Try to find an angle that is given a right triangle ratio of sides.

* The statement that corresponding angles formed by parallel lines have the same measure.

A distinctive problem of angles of elevation & depression involves organizing information regarding distances & angles within a right triangle. In some other cases, learner will be asked to determine the measurement of an angle; in others, the problem might be to find an unfamiliar distance.

In our next blog we shall learn about animals and their young ones I hope the above explanation was useful.Keep reading and leave your comments.


Wednesday, September 8

mental ability questions with answers

Let us learn about mental ability questions with answers

If student take interest to find solution of math given problems, they can improve their mental ability.

1. Write five prime numbers between 50 and 75.

Solution: 53, 59, 61, 67, 71

2. Every prime number is odd except

Solution: 2

3. What should be added to 40.09 to make it 51 dollars?

Solution: 10.91 dollars

Math is the ability to perform arithmetic calculations without the help or aid of external computing tools. Math test require more & more background knowledge & ability in math basic skills.

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

Tuesday, September 7

equation of a line from two points

Let us learn about equation of a line from two points

If Students are given 2 points, how can they find the equation of the line passing through the 2 points? If student know the slope & a point (x1, y1) student have that

rise y - y1
m = =
run x - x1

Now multiplying by

x - x1

equation of a line from two points Point Slope Formula for the Equation of a Line

y - y1 = m (x - x1)

Find the equation of line from the point (1,2) with slope 4.

Solution:

We use the formula:

y - 2 = 4(x - 1) = 4x - 4 Therefore y = 4x - 4 + 2 = 4x - 2.

In our next blog we shall learn about how to calculate ratios I hope the above explanation was useful.Keep reading and leave your comments.

Monday, September 6

inverse log

Let us learn about inverse log

If 2 functions g(x) & f(x) are defined so that (f ο g) (x) = x and (g ο f) (x) = x we say

that g(x) & f(x) are inverse functions of each other.

Functions f(x) & g(x) are inverses of each other in case the operations of g(x) reverse all the operations of f(x) in the reverse order & the operations of f(x) reverse all the operations of g(x) in the reverse order

The Best Example: Determine the inverse log function of f(x) = log(x + 5).

Solution: f(x) = log(x + 5)

We know that, f(f-1(x)) = x.

So, f(f-1(x + 5)) = log(f-1(x) + 5) = x

i.e., 10x = f-1(x) + 5 ( log10y = x => 10x = y )

f-1(x) = 10x - 5

This is the required inverse log function.

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


Friday, September 3

square root of 45

Let us find out square root of 45

Square root property of 45: Square root of45 (√45)

General property of square root

Method 1: square root of 45 (√45)

Solution:√45 = √5 x √9

= √5 x √3x3

= √5 x √3^2

= 3√5

√45 = √(9 x 5) = 3√5


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


Thursday, September 2

increasing and decreasing functions

Let us learn about increasing and decreasing functions

A function is called increasing when it increases as the variable increases & decreases as the variable decreases. A function is called decreasing when it decreases as the variable increases & increases as the variable decreases.

The graph of a function specifies plainly whether it is increasing or decreasing.

The derivative of a function can be used to determine whether the function is decreasing or increasing on any intervals in its domain. Incase f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) <>decreasing on I. Because the derivative is 0 or does not exist only at critical points of the function, it must be negative or positive at all other points where the function exists.

Theorem on Decreasing or Increasing of Functions:

Let letter “f” be continuous on [a, b] & differentiable on the open interval (a, b).

(a) “f” is decreasing on [a, b] if f '(x) <> ε(a, b)

(b) “f” is increasing on [a, b] if f '(x) > 0 for each x ε(a, b)

Theorem on Decreasing or Increasing of Functions can be proved by using Mean Value Theorem.

Theorem on Decreasing or Increasing of Functions can be used in various problems to check whether a function is increasing or decreasing.

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


Wednesday, September 1

definite integral calculator

Let us learn about definite integral calculator

definite integral calculator is mainly for finding the indefinite integral of the given expression by getting an input value.

Find the definite integral of the function f=x6 within the limit (0,1).

Solution:

Function f=x6 has a limit (0,1)

Now the definite integral can be calculated as,

=1/7-0

= 1/7

Definite integral calculator is same as the integral calculus calculator but it is mostly for finding the integral which is covered by a specific intervals. That is definite integral calculator has upper limit value & lower limit value.

For this definite integral calculator 1st the given expression should be integrated as integral calculator & then the limits should be applied. The final output can be derived by substituting the lower limit - upper limit

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