Variation

Introduction

Mathematics deals with two kinds of quantities such as constant quantities or constants as well as variable quantities or variables. However, when the value of the quantity remains the same under the varied situations, then it is said to be constant. On the other hand, when the value of the quantity differs under varied situations, then it is said to be variable. In this study, the concept of variation is discussed. 

What is the meaning of variation in mathematics? 

Mathematical equations work with a diverse range of parameters while establishing a relationship. The variable in mathematics that is changed with the varied situations is termed as a variation. This implies that the changes that occur in the parameters of the variables are called variations. Mathematical problems are mostly associated with two and more than two variables. It has been seen that in some situations the value of a variable quantity differs because of the different quantities. For instance, it can be assumed that a car is running at a uniform speed of S km./h. and take time of T hours to travels a distance of D kilometres. Thereupon, when time (T) remains unaltered then S will be decreased or increased according to the alterations of D. However if D remains unaltered, then S will be increased or decreased according to modifications of T variable. This situation shows that the changes in the value of the variable quantity might be altered if any changes occur associated with the values of the related variables. Therefore, the changes of the variable parameters are often termed Variation. 

What are the types of variation in mathematics? 

The types of variations in mathematics are discussed below: 

• Direct Variation

In the direct variation, if a variable quantity changes proportionately this means that it either decreases or increases together then it is said to be a direct variation. For instance, if P is in a direct variation relationship with Q, then it can be symbolically represented as P α Q.

• Inverse Variation 

Inverse variation is also termed as an indirect variation in which a variable quantity changes disproportionately. This implies that while one variable will be increased the other variable will be decreased and vice versa. Hence, it possesses the opposite characteristics of direct variation. For instance, if P is in an inverse variation relationship with Q, then it can be symbolically represented as P α 1/Q.

• Joint Variation

In the joint variation, more than two variable quantities are directly related to each other. This implies that a variable quantity will be changed with the changed quantities of two and more than two variables. Therefore, if P shares a relationship of joint variation with Q and R then it can be symbolically represented as P α QR. 

• Combined Variation 

Combined variation is the combination of joint variation or direct variation and indirect variation. Hence, a combined variation can consist of three or more variables. For instance, id P is in a relationship of combined variation with Q and R then it can be symbolically represented as P α Q/R or P α R/Q. 

• Partial Variation

Whenever two variable quantities are associated with a variable or a formula that defines the sum of two and more than two variables then it is said to be as partial variation. For instance, P = KQ + C, where C and K are constants and thus is not variable. This is an equation of a straight line, which is also an example of partial variation.

Direct, Inverse, and Joint variation examples 

• Direct Variation example

The distance of a man from the lightning and the time that the man takes to hear the sound of thunder can be a form of direct variation. 

• Inverse Variation example

When numerous individuals at work take less time to finish the work and vice versa, then the situation can be a form of inverse variation. In addition, less speed and more time are required to cover an equal distance. 

• Joint Variation example

The cost of bus fare of students for different school trips changes, when the distance from the school and the number of students attending the trip varies.

Conclusion

After the discussion, it can be concluded that the concept of variation delivers different advantages to solve various mathematical applications. Variations are categorized into differentiation types including direct variation, inverse variation, and joint variation to solve the problems according to the situations. In addition, the concept has been used in mathematics to solve different real-life applications such as calculating the time that man takes to hear the sounds of thunder by assessing the speed, distance.