## A Quantity P Varies Jointly With R And S. Which Expression Represents The Constant Of Variation, K?

Question

1. A quantity P varies jointly with R and S. This means that when either the value of R or S increases, the value of P will also increase. When one of these variables decreases in value, then so too does P. This type of relationship is expressed by the equation P=KRS; where K represents a constant of variation. The constant K helps to explain how much an increase or decrease in either R or S affects the resultant change in values for P.

The expression which represents the constant of variation, K, is calculated by dividing both sides by RS on both sides resulting in: P/RS = K. This expression can then be rearranged to solve for K: K = (P/RS).

2. Have you ever wondered what it would be like if a quantity P varied in tandem with R and S? Well, it is possible and it happens all the time! In these situations, we need to find the constant of variation, K.

But what exactly is the constant of variation, K? Well, K is the ratio between the change in the quantity P and the product of the changes in R and S. In other words, K is the number which represents the relationship between P, R and S.

Let’s take a look at an example. Suppose that there is a quantity P which changes by 3 units when R increases from 5 to 10 and S decreases from 8 to 5. In this case, we can calculate the constant of variation, K, by using the following formula:

K = Change in P/Change in (R × S)

= (3/ (5 × 3))

= 0.2

Therefore, the constant of variation, K, in this case is 0.2.

Now that we know what the constant of variation, K, is, let’s look at another example. Suppose that there is a quantity P which changes by 6 units when R increases from 8 to 10 and S decreases from 10 to 5. In this case, the constant of variation, K, would be the following:

K = Change in P/Change in (R × S)

= (6/ (2 × 5))

= 0.6

Therefore, the constant of variation, K, in this case is 0.6.

As you can see, the constant of variation, K, is a very important concept when it comes to understanding how a quantity P varies with R and S. Knowing the value of K will help you better understand the relationship between P, R and S and make predictions about how it will change in the future.