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Joint Variation refers to the scenario where the value of 1 variable depends on 2 or more and other variables that are held constant. For example, if C varies jointly as A and B, then C = ABX for which constant “X”.
Learn how to solve joint variation problems in algebra. This article includes definitions and various examples about joint variation and combined variation that will help you gauge your understanding of the topic.
What Is Joint Variation And Combined Variation? Joint variation is a variation where a quantity varies directly as the product of two or more other quantities. For example, the area of a rectangle varies whenever its length or its width varies.
Joint variation occurs when a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz. If x varies directly with y and inversely with z, we have \displaystyle x=\frac {ky} {z} x = zky.
If more than two variables are related directly or one variable changes with the change product of two or more variables it is called as joint variation. If X is in joint variation with Y and Z, it can be symbolically written as X α YZ.
Joint Variation, where at least two variables are related directly. For example, the area of a triangle is jointly related to both its height and base. Combined Variation, which involves a combination of direct or joint variation, and indirect variation.
Joint Variation refers to the scenario where the value of 1 variable depends on 2 or more and other variables that are held constant. For example, if C varies jointly as A and B, then C = ABX for which constant “X”.
This section defines what proportion, direct variation, inverse variation, and joint variation are and explains how to solve such equations. Proportion. A proportion is an equation stating that two rational expressions are equal. Simple proportions can be solved by applying the cross products rule. If , then ab = bc.
The last type of variation is called joint variation. This type of variation involves three variables, usually x, y and z. For example, in geometry, the volume of a cylinder varies jointly with the square of the radius and the height.
Joint variation is similar to direct variation. It involves two or more variables, such as y=k(xz). Combined variation combines direct and inverse variation, y=kx/z.