rational expressions applications

In the previous post we have discussed about Fibonacci Numbers and In today's session we are going to discuss about rational expressions applications. Rational expressions applications defines the uses of rational expressions in different area of mathematics. A rational expression is expressed as the ratio of polynomial equations as:
p > 2 + q / p – q > 2. These kind of expressions are known as relational expression. There are several formulas that having the rational expression and for solving it multiply both the side of equation with the LCD that is used for eliminate the denominators of the expression.
We can define it by a simple example as if there is an equation that express a line (-2 , 4) and have the slope 3 / 2 that is written by a rational expression (y – 4) / ( x + 2) = 3 / 2.
Now we cam solve it as (y – 4) / (x + 2) = 3 / 2
Multiply both the side of expression with the LCD (x + 2) as;
(x + 2) (y – 4) / (x + 2) = (x + 2) 3 / 2.
In this step solve all the calculations as y – 4 = 3 x / (2 + 3);
Now it will be more simplified as y = 3 x / (2 + 3 + 4)
Y = 3 x/ (2 + 7) , this expression gives a line equation for particular coordinates. (know more about Rational function, here)
There are numerous expression in mathematics as relation between rate, time and distance is also define by d / t = r where d is the distance, t is time taken to cover that distance and r describe the rate of speed.
Valence Electron Configuration is studied in atomic physics and quantum chemistry that define the configuration of electrons.
Central board of secondary education provide cbse syllabus for class 1 that mention all the topics come into the respective session.

Fibonacci Numbers

In the previous post we have discussed about Ratios and Proportions and In today's session we are going to discuss about Fibonacci Numbers. 

Fibonacci Numbers are describe as the sequencing of numbers that follow the linear recurrence rule. We can also explained it by a simple expression as if Xn is a function then according to the linear recurrence rule (Xn)  where value of n is from 1 to infinity.

This will be expressed as  Xn = x n-1 + x n -2 + x n-3 ….

In the above expression if the value of n is 1 or 2 then X1 = X2 = 1 and in case of X0 is is equal to one.

When we present the Fibonacci numbers for the values of n = 1 , 2 and so on then it will show as 1,1 ,2 ,3 ,5 , 8 ,13 , 21 ,34 …. So on.

We can define some of the problems that are defined by the Fibonacci numbers series as there is a problem stated as one male and one female those are born on first January and if all the months having the equal number of days then find the number of pairs that are produce after the birth of first pair in next two months and when a pair have the age of two months then it produce another pair and this pair also generate the another pair after two months and no pair dies.

So we have to find the number of pairs after the period of one year?

So these kind of problems are solved by Fibonacci numbers.

For solving the problems like Subtracting Fractions With Unlike Denominators, need to make the denominators of both the fractions same and for this we have to calculate the LCM that is stated as least common multiple and then we calculate the answer of the given problem. (know more about Fibonacci Numbers, here)

Cbse Board Papers are organized by the central board of secondary education (CBSE board) in month of march of every year for the students.

Ratios and Proportions

A ratio that is used to show the relation between two or more values. For example: if there are 12 pencils and 17 pens then we can write the ratio as: 12:17; In other word for every 12 pencils there are 17 pens. If any equation written in the form of P / Q = R / S, here both the ratios are equal are said to be proportion. For example (5 / 9) = (20 / 32). Let's see how find the Ratios and Proportions? Steps for ratio and proportions are shown below:
Step1: First we have two values for which we have to find the relation.
Step2: Then we find the relation in both the values.
Step3: Let we have two proportion sets, these two ratios are equal to each other. In one ratio, the quantities of two proportions do not fulfill, so we use cross multiplication and solve the equation and fulfill the quantities. There are different ways to find the ratios and proportions.
If 60 books for 32 students that can be represented in the ratio as 60:32. Now set the second ratio for another larger group of students, assume that the numbers of books move in the numerator and the numbers of students move in the denominator. Here we don’t know the total number of students. (know more about Ratios and Proportions, here)
Here assume the number of students be ‘U’. The total number of students is 42, and then the ratios of students are U / 42. Now we set these ratios according to the definition of ratio and proportion. So the ratio is:
=> (60 / 32)= U / 42,
Now find these ratios with the help of cross multiplication:
When we cross multiply these ratios we get:
⇒(60) (42) = (32) (U), Now solve these values for ‘U’.
⇒2520 = 32 U, here we find the value of ‘U’.
⇒32 U = 2520
⇒U = 2520 / 32
⇒U = 78.75;
After solving we get the value of U = 78.75;
There are 78.75 books for 42 students.

Surface Area of a Cylinder Formula is given as:
Surface area of cylinder = 2 * pi * r² + 2 * pi * r * h. We get new information about all grades syllabus in cbse syllabus 2013 and In the next session we will discuss about Fibonacci Numbers. 

  

Greatest Integer Function

In the previous post we have discussed about How to Deal with Ordered Pair Problems and In today's session we are going to discuss about Greatest Integer Function. 

Greatest Integer Function gives the highest integer number that is lies among the several numbers. We can also simplify the statement as ,it will give the highest number and all other number are lesser or equal to the given number. Sometimes we call the floor function of integer numbers. It will be expressed by a big bracket as[ ].

We can explain it is the process of finding number that have less than and equal value among the given number for a given integer value. So according to the definition of greatest integer function that is stated for the integer number will provide the number equal to the given number. When we find the greatest integer and when we find for any non integer number then in that case it will give only the integer part of that number and remove the decimal part. (know more about Greatest Integer Function, here)

We define it by some examples as, Find the greatest integer function of 7?

Solution: [7] = 7.

Explanation: As the given number is an integer number, hence the closest integer number to the left of the given number is the same number.

Find the greatest integer function of 4.7?

Solution: [4.7] = 4

Explanation: As the closest integer number to the left of the given number on the number line is 4.

 Find the greatest integer function of -3.4?

Solution: [-3.4] = -4,

Explanation: As the closest integer number to the left of the -3.4 is -4

According to Van Der Waals Equation, it states for composition of fluid that made by the particles that have a non zero volume and also for a pair wise inter particle force that is an attractive force .

Cbse Sample Papers 2013 provided by the central board of secondary education to the students for help them in preparation of examination.

How to Deal with Ordered Pair Problems

Ordered pair in mathematics can be considerd as a set of mathematical objects. Ordered pair is a part of graph concept that helps in plotting the points at certain pixel position. In mathematics, when we discuss about the ordered pair of graph then we can say that a pair of two values that are written inside a parenthesis. Generally, ordered pairs are written in a particular order like (x , y). Here x and y are considered as an objects of ordered pairs where x can be consider as a first entry and b as second entry of order pair. (want to Learn more about Ordered Pair, click here),

The value of ordered pair can be represented as pixel position on a graph where the value of x variable can be plotted on x-axis and value of y can be plotted on y-axis of the graph.

To understand the concept of ordered pairs or to solve the ordered pair problem we need to understand the property of order pair that are describe below:

Suppose we have two ordered pairs that is (x1,y1 ) and ( x2, y2 ).

By following the ordered pair definition we can say that the ordered pair (x1,y1) and (x2, y2).are equal to each other when the value of x1 = x2 and y1 = y2. on the other side of ordered pair  the collection of all  first entry of ordered pairs are considered in s[] and collection of second entries are considered in y[].

Then multiplications of entries of multiple ordered pairs are known as Cartesian product. Generally the concept of ordered pair deals with the real number that can easily be plotted on the graph and various calculation can be performed very easily and in simpler manner. In study of graph, sometime we have to face the question How to Make a Bar Graph. In board examination, cbse syllabus provide the complete syllabus to protect the student from any Inconvenience. 

Ratio

Sometimes ,comparison is needed among different things and for that purpose we have several kind of methods. In which ratio is one that is define the relationship among the given things. Ratio stated as the relationship between two or more than two values. As if in a bucket there are six mangoes and three oranges than the ratio is describe as 6 : 3 that is simplify as 2 : 1. It will be expressed as in the bucket ratio of mangoes and oranges, 2 is to 1.

If there are two numbers that are p and q then it is expressed as p : q then p is called as antecedent and q is stated as consequent. So a ratio depict as the relative size between two or more values. (Know more about Ratio in broad manner, here,)

Ratio have the same concept as fraction and we can show the ratio in the fraction form as p : q have the fraction form as p / q.

There is one other type of ratio that is known as the percentage ratio. It is achieved by dividing the number with the total value and multiplied it with 100 ,it gives percentage and we can put these percentage in the form of ratio . Ratio is represented as x % : Y% or x : y because x % is expressed as x / 100 and y % is y / 100 then their ratio is x / 100 : y / 100 and as we stated above ratio can be describe by the fraction as x / 100 / y / 100 that is equal to x / y that is also depict as x : y.

How to Make a Histogram helps the students to understand the different ways of making histogram and define it into simple way.

CBSE math Syllabus that is provided by the cbse board gives all the information to the students that is related with the theme of subject that help them to understand what kinds of topics will come into the respective class and In the next session we will discuss about How to Deal with Ordered Pair Problems

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