Adverbs and its types

Adverb is one of the eight parts of speech in English grammar. Adverb is a part of speech that modifies the meaning of a verb, adjective or another adverb in a sentence. For example: Mary instantly bought the cutlery stand after hearing about the discount. Adverbs can be classified into seven classes, namely time, frequency, place, manner, degree, affirmation and negation and reason. Let’s have a closer look at the same in this post.

Adverbs of Time:
Adverbs of time are the type of adverbs that are used to answer to the question “when”. Most commonly used adverbs of time are now, yesterday, today, once. For example: Mary bought the cutlery stand yesterday. Here, the answer is to the question: when Mary bought the cutlery stand?

Adverbs of Frequency:
Adverbs of frequency are the type of adverbs that are used to answer to the question “how often” i.e. answering about the frequency of occurrence. Popularly used adverbs of frequency are: seldom, rarely, frequently, often and more. For example: She often buys branded girls’tops  from online stores. Here, the answer is to the question: how often she buys branded girls’ tops from online stores?

Adverbs of Place:
Adverbs of place are used to answer to the question “where”. Commonly used adverbs of place are: forward, everywhere, out, in and more. For example: She has gone out of the house. Here, the answer is to the question: where has she gone?

Adverbs of Manner:
Adverbs of manner are used to answer to the question “how”. Some of the most popularly used adverbs of manner are: honestly, bravely, happily and more. For example: She happily accepted the gift from him. Here, the answer is to the question: How did she accept the gift from him?

Adverbs of Degree:
Adverbs of degree are used to answer to the question “how much”. Popularly used adverbs of degree are: fully, partly, altogether, almost etc. For example: She bought almost every baby essential from Chicco Talcum India collection.  Here, the answer is to the question: How much she bought from Chicco Talcum India collection.

Adverbs of Affirmation and Negation:
Adverbs of affirmation and negation are used either to confirm or deny a statement. Certainly, absolutely are some of the commonly used adverbs of affirmation and negation. For example: I trust my friend absolutely.

Adverbs of Reason:
As the term suggests, adverbs of reason are used to give the reason. Therefore and hence are the most commonly used adverbs of reason. For example: Chicco is one of the trusted baby brands hence, I buy products from this brand. These are the seven classes of adverbs.

Basic Understanding of Sets and Its Operations

There are various operations on sets which must be mastered to completely understand them. Some of them are intersection, union and so on. These operations have to be learnt. The sets and set operations form an integral part of mathematics. The terms Venn diagrams and set operations are closely related to each other. Venn diagrams can be used to explain various operations. The operations with sets can be fun to work with.  The union will give all the elements present in both the sets. The intersection will give the common elements. This is the basic difference between the two operations and can be easily understood.

Venn diagrams can be very helpful in this. They are graphical representation of the sets. It is always to better to explain a concept using a diagram. It improves the clarity of the concept and also makes the concept easy to understand. Venn diagrams do a great deal in achieving this. The set operations math can be understood using them.  Cardinality is another important concept that has to be learnt. It basically denotes the number of elements. It is not tough to find the number of elements but a term has been assigned for the same. So, there is nothing much to worry about it. It is quite a easy concept and can be easily learnt. There can be various types of sets like empty, unit and sometimes even special ones. Empty ones are those which have no elements in them. Unit ones are those which will be having only a single element in them.

There are several others like ones for prime numbers which is denoted by the letter ‘P’. There is also one for the natural numbers which is usually denoted by the letter ‘N’. The integer one contains both the positive and negative integers. Also there is one which contains all the real numbers in it. There can also be sets for rational numbers and complex. Rational numbers are contained in the former and the complex numbers are contained in the latter. There is similarity between all of them. The only difference being that the natures of elements vary in each of them. This is the basic difference and has to be understood. Once this is understood the concept becomes easy to understand and apply. It is not a complex subject and can be understood with a little bit of practice.

Past Tense and its Types

In English, there are three types of tenses – Present tense, Past tense and Future tense. Past tense is a type of tense that expresses something in past or states about some action that takes place in the past. For example: I got a baby bather India online yesterday. Here, the action of getting baby bather India online is done in past and therefore, the sentence is in past tense.  Past tense further can be classified into sub categories. Let’s have a look at the types of past tense along with examples.
Types of Past Tense:
•         Past Perfect Tense
•         Past Continuous Tense
•         Past Perfect Continuous Tense

Past Perfect Tense:
Past perfect tense refers to an action that is completed in the past. For example: My cousin bought branded baby foods online for her baby. Here, the action of buying branded baby foods online is completed in the past and therefore, the sentence is in past perfect tense.

Past Continuous Tense:
Past continuous tense refers to an action that was completed over a period of time in the past. For example: I was exploring a lot of baby online shops few days back and finally I got few good online baby stores. Here, the action of finding baby online shops was completed over a period of time and therefore the sentence is in past continuous tense.

Past Perfect Continuous Tense:
Past perfect continuous tense refers to an action that started in the past and continued up until another time in the past. Unlike present perfect continuous tense, in past perfect continuous tense the action doesn’t continue till the present. For example: I had been working on this problem from five days. Here, the action of working out the problem started and ended in two different times in the past and therefore, the sentence is in past perfect continuous tense.
These are the basics about past tense and its types.

Perpendicular Postulate

The number refers to the ordinal position is, thus the number is the sequence of the result set. And the ordinal numbers does not show the quantity.

When we learn about numbers and its applications, we will study the three types of numbers, there are,

Ordinal numbers
Cardinal numbers and
Nominal numbers.

Explanatory:

Cardinal numbers:

Cardinal numbers shows that “how many”in the group or list. This cardinal numbers are also called counting numbers. Because it shows the quantity. Also it does not have any decimal numbers or fractions, only used for counting.

Example: how many months in a year? Answer is 12 months.

Nominal numbers:

Nominal numbers used to only identify the things. It does not show the quantity or rank.

Example: A bike number on the race.

But here we have to go for only ordinal number and its positions, so let us see what are ordinal numbers?

Ordinal Numbers:

An Ordinal Number is a number that shows the position of something in a group or Ordinal numbers shows the Position (order) of the things in a group from - first; second, third, fourth, etc…and the ordinal numbers does not shown the quantity.

Example: in a bag contains “apple, mango, papaya, jack fruit, pineapple and chappotta” the word “pineapple” is in fifth from order.

Easy to remember: "ordinal" shows what "order" things are in.

Example Problems in Ordinal Numbers:

Example 1:

There are six children in a running race means find the ordinal positions in this?

Solution:

Ordinals locate a place in a sequence, when we describe the child who came in sixth; we are using an ordinal number

A number that tells the position of something in a race in 1st, 2nd, 3rd, 4th,  5th, 6th.

Example 2:

Indian cricket team players are ordered from Sachin, Shewag, Raina, Yuvraj, Yousuf, Dhoni, Virat,  Irfan, Harbhajan, Praveen, Zaheer,  who is 1st and who is 8th place from the list?

Answer is:       Sachin is 1st from the order of list and Irfan is 8th from the order of given list.

What is a Integer?

What is a Integer- Integers includes all whole numbers along with all negative numbers. That is all negative numbers and positive numbers along with zero are called integers. Definition of Integer says all positive and negative whole numbers are termed as integers. For example: - -3, 15, -8, 0, 78, 91 they all are integers. We can plot integers on the number line. Numbers towards right side on the number line are greater than number on its left. That is if we plot the number line with integers we see that all negative numbers lie on left side of number line and all positive lies on right hand side. They follow a trend of increasing towards right side. For example:- -3  falls on left side of 0 as -3 is smaller than zero, similarly 6 falls on right of 0 as 6 is greater than 0. Integer Definition says all the positive and negative whole numbers along with zero so the list of integers goes on.

To add, subtract, multiply and divide integers, we follow certain Integers Rules. For adding two integers, we should remember that on adding two negative integers, we get a negative integer and we get a positive integer if we add two positive integers. For example -3 + (-2) = -5 and 4 + 6 = 10. And if we are adding a positive and negative integer, we find their absolute values and then subtract the smaller number from the larger one and put the sign of the integer which has a larger absolute value. For example, if we have to add -3 and 5, then we find their absolute values which will be 3 and 5. We subtract 3 from 5 which gives 2 and then we add sign of 5 which is plus. Hence the solution will be +2.

Subtracting Integers– To subtract two integers, we need to change the sign of the integer to be subtracted that is if we have to subtract -3 from -5 then the equation becomes -5 + 3 because -3 was the integer to be subtracted. Now we can find their absolute values and can perform the action of addition. Subtracting two positive integers gives a positive integer. Subtracting two negative integers will give a negative integer. There are many Integer Word Problems that can be solved by using the integer rules of addition and subtraction.

Octal Representation of Numbers

Numbers is a vast subject but not a very tough topic in mathematics to understand. The vastness is because of the deductive skills of scholars and different representation of the same number to increase the security of the same. Octal Numbers is one such type of representation of number like the other representations like decimal, binary, etc. The word Octal or octa number system refers to the number eight and in Octal Number System the number is supported with the base 8. Octals are very similar to the decimal number other than in decimal we have 0 – 9 and in this we have 0 – 7.

It is not a very big task to convert decimal to octa number system or from this to decimal number. The Decimal to Octal Conversion can be understood through an example. But before going to an example let us get to know the steps to be followed while converting the decimal to octa number system.

The following are the steps used for the conversion: One should know the division and multiplication of numbers well so that he / she can solve the problem in ease. The decimal number should be written. The number should be divided by 8.

The quotient of the number should be written below. The remainder of the number after dividing has to be written on the right end. The number written below has to be further divided by 8. This division process has to be done until the number that is the remainder is less than the octa number system digits.

The process is completed once the above steps are followed. The answer has to be written now. The answer can be found by writing the numbers that is the remainder starting from the final remainder bottom to top. The answer should be written with subscript 8 to avoid confusion. Before going to an example for further explanation we should know the Octal Table which represents the octa number system in a table form with the corresponding decimal number for them.

This representation helps in the conversion of octa number system to decimal and the conversion of decimal to octa number system.

Let us consider the following example for understanding the conversion of decimal to octa number system.
Convert 9910 to octa number system: 99 / 8 = 12 with a remainder 3, 12 / 8 = 1 with a remainder 4, the answer for the question which is given will be: 9910 = 1438.

linear algebra sample final

Linear algebra is mainly use to find the solution of systems of linear equations in some unknowns. Linear algebra has a demonstration in analytic geometry and is generalize in operator theory. Linear algebra associates with the families of vectors called vector spaces, and with functions contain one input vector and output another vector, according to rules. Linear algebra has the application with the theory of systems of linear equations, determinants, and matrices. The sample problems are discussed below for final review.

Linear Algebra Sample Problems for Final:

The sample problems are solved in detail for final review as shown below.

Problem 1:

Evaluate the linear equation   -3(x - 4) / 6 - (x - 2) / 3 = -2 x

Sol:

The given equation has rational expressions. To eliminate the denominators by multiplying by the LCD
-3(x - 4) / 6 - (x - 2) / 3 = -2 x

The LCD is equal to 6*3 = 18. Multiply both sides by LCD.
18 * [-3 (x - 4) / 6 - (x - 2) / 3] = 18* [-2 x]

Simplify to eliminate the denominator.
-9(x - 4) - 6(x - 2) = -36x

Multiply factors and grouping the terms

-15x + 48 = -36x

Subtract 48 to both sides
-15x + 48 - 48 = -36x -48

Group like terms
-15x = -36x - 48

Add 36x to both sides
-13x + 36x = -36x - 48 +36x

Grouping the terms
23x = -48

Multiply both sides by `1/23 `
x = - `48/23`

Conclusion:
x = - `48/23` is the solution for the above given equation.

Sample Linear Algebra Practice Problems for Final:

1) Evaluate the linear equation   -3(x - 4) / 7 - (x - 2) / 2 = -2 x

2) Solve the linear equation -5(-x - 7) = 5x – 32.

3) Evaluate the linear equation   -3(-x +3) = x - 7

Answers:

1)   X = -38/15 is the solution for the above given equation.

2) The above equation has no solution.

3)  X=One is the solution for the above equation.