Binary Numbers

In the previous post we have discussed about domain math and In today's session we are going to discuss about Binary Numbers. Before discussion about the Binary Numbers first we have to know about the number system that is a basic need for presenting a number. When we talk about any number it consist some of the digits in it and these digits is decided by the number system which is used to express the number. So there are basically four types of number system as decimal , binary , octal and hexadecimal number system . When we talk about the binary number system in which binary means two , so there are only two digits for expressing a number that are zero (0) and one (1). (know more about Binary Numbers, here)
In binary number system, all the values having two digits. When we talk about any number probably it is define into the decimal number system in which number having the value from 0 to 9 and all these 10 digits are used  to make different types of number and when we want to change any decimal number into the binary number that means every single digits of the given number will be multiplied with the  exponent of two that means if there is a number xyz and we want to change it in the binary number then in x y z ,digit x has a hundred position , y has a tens position and z has a ones position and then z is multiplied with the  2 >0 and y multiplied with the 2 > 1 and x is multiplied with the 2 > 2.
 Temperature Conversion Chart is used for define the temperature in different units and also describe the relation between these units that is used for changing the temperature in one unit to another.
Cbse board that stands for central board of secondry education provides Cbse Syllabus For Class 10 students that describe all the topics that will covered in the respective session.

domain math

In mathematics, function is used to show the relationship between values. Each input values of a function gives back exactly one output value. Now we will see how to find the domain math? Suppose that we have a function and we want to find the domain of a function then first it is necessary to know about the definition of domain in function.

If we select the entire ‘x’ coordinate values of a function, all the x – coordinate values are said to be domain of a function. In the same way, the possible ‘y’ coordinate values are said to be range of a function.

Suppose we have some values (8, -15), (-10, 1), (16, -5), (-2, 6), then the domain of function is all the ‘x’ coordinate values. (know more about domain math, here)

Domain = 8, -10, 16, 6.

Range is all ‘y’ coordinate values,

Range = -15, -10, 16, 6.

let's see some steps to find domain of a function.

To finding the domain of a function we follow some steps:

Step1: To find the domain of a function first we have to assume a function which contains ‘x’ and ‘y’ coordinates.

Step2: As we know the domain of a function is all ‘x’ coordinates values.

Step3: In a function if we have values of ‘x’ and ‘y’ coordinates then we can easily find the domain and range of a function.

If we follow these steps then we can easily find the domain of a given function. This is how we can find the domain of a function. Now we will see Taylor Series Expansion. Taylor series can be defined as a series of a function about a function. It is generally used in the approximation of a function. To get more information about Taylor series then follow online tutorial of icse syllabus. In the next session we will discuss about Binary Numbers. 

Translation Math

In the previous post we have discussed about Symbolic Logic and In today's session we are going to discuss about Translation Math. In mathematics, to move a figure or a shape from one place to another we use translation. In this a figure in a plane can be move upward and downward, right, left or anywhere. It is a function that moves every point a constant distance in a particular direction. Suppose we move one point of a shape like Triangle, Square, Line, etc up to five unit in a particular direction by translation, then all the points will move by five unit in same direction. Thus only the position of the object changes but its size remains the same.

To understand better let us translate in the following graph:

The graph on the left side is translated to the graph on the right side.

The equation of the absolute value function of left hand side graph:

y = |x|.

When the function f(x) is translated ‘p’ units horizontally, then the argument of f(x) becomes x − p.

Thus as the origin is moved to (3, 4), the new equation by its translation is:

y − 4 = |x − 3|.

Let us have a rectangular on a graph with the points P(-4, 8), Q(1, 8), R(-4, 4), S(1, 4). To shift it by four unit downward we use the following steps:

As the figure is being translated by “four” unit in downward direction, there will be no changes in x- coordinate. (know more about Translation Math, here)

1. subtract by 4 in y coordinate, we get

P(-4, 8) after translation (x - 0, y – 4),

=> (-4 - 0, 8 – 5),

• (-4, 3)

2. For Q(1, 8) after translation, we get (x - 0, y - 4)

• (1 - 0, 8 - 5)
• (1, 3) translated coordinate.

3. For R(-4, 4) so, after translation (x - 0, y - 4)

=> (-4 - 0, 4 - 4)

=> (-4, 0) translated coordinate.

4. For S(1, 4), after translation,we get (x - 0, y - 4)

=> (1 - 0, 4 - 4)

=>(1, 0) translated coordinate.

So, translated figure coordinates will be points P(-4, 3), Q(1, 3), R(-4, 0), S(1, 0).

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Symbolic Logic

Hi friends, in this blog we are discussing an important topic that is 'Symbolic Logic'. Symbolic Logic is a method that is used to distinguish logical expressions using symbols and variables, relatively than in ordinary language. Symbolic logic is used in removing the uncertainty. In mathematical field, so many systems of symbolic logic are mention below:
(1.) Classical propositional logic,
(2.) First-order logic,
(3.) Modal logic.
In mathematics, all the symbolic logic are divided by different symbols, or exclude the use of certain symbols. Let's see some of the symbolic logic symbols. Here we will see the basic logic symbols.
(1.) (┑): - This given symbol is known as negation.
Explanation: Let we have a statement ┑A that is true if and only if the value of 'A' is given as false.
= ┑ (┑A) ⇔ A.
(2.) (∨): - This given symbol is known as logical disjunction.
Explanation: The statement A ∨ B is true if and only if the value of 'A' and 'B' both are true, or if both are false.
(3.) (⊕): - This symbol is known as exclusive disjunction.
Explanation: let we have a given statement A ⊕ B then the condition is true if value of 'A' and
'B' are true but not both the value true.
(4.) (T): - This symbol is known as Tautology.
Explanation: Here the meaning of this symbol is A ⇒ B is always true.
(5.) (∃): - This symbol is known as existential quantification.
Explanation: let we have a given statement ∃ x A (x), it means there is at least one x such that A (x) is true.
(6.) (∃!): - This symbol is known as uniqueness quantification.
Explanation: let we have a given statement ∃! x A (x), it means there is exactly one x such that A (x) is true. Solving Differential Equations is a part of trigonometry. It includes application of derivative. To get more information then we need to follow icse syllabus 2013. It helps so much for solving the differential equation.