When a quantity p varies jointly with two other variables, say r and s, it means that p can be expressed as a product of r and s, multiplied by a constant of variation, denoted as k. The mathematical relationship is represented as:
p = k imes r imes s
Here, the constant of variation k is a fixed value that indicates how p changes in relation to changes in r and s. To find the value of k, you can rearrange the equation:
k = rac{p}{r imes s}
This means that once you know the values for p, r, and s, you can calculate the constant of variation k. For example, if you have:
- p = 20
- r = 4
- s = 5
You would substitute these values into the equation:
k = rac{20}{4 imes 5} = rac{20}{20} = 1
Thus, the constant of variation k for this set of values is 1. This concept is crucial in understanding joint variation as it provides insights into how changes in multiple variables simultaneously impact a given quantity.