In this lesson, we will learn how a quantity varies in relation to two or more other quantities.
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. We say that , where A is the area, l is the length and w is the width.
The figure below shows a rectangular solid with a fixed volume. Express its width, w, as a joint variation in terms of its length, l, and height, h.
In other words, the longer the length l or the height h, the narrower is the width w.
Example 2: A quantity varies directly as one quantity and inversely as another.
The speed, s, of a moving object varies directly as the distance travelled, d, and varies inversely as the time taken, t. Express s as a joint variation in terms of d and t.
In other words, the longer the distance or the shorter the time, the faster is the speed.
Suppose y varies jointly as x and z. What is y when x = 2 and y = 3, if y = 20 when x = 4 and y = 3?
Direct, Inverse and Joint Variation
Determine whether the data in the table is an example of direct, inverse or joint variation. Then, identify the equation that represents the relationship.
How to set up and solve combined variation problems.
Lesson on combining direct and inverse or joint and inverse variation
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