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Answer:
Direct variation occurs when one variable is a constant multiple of another variable. For example, the volume of a cylinder varies directly with its height if the radius remains constant.
Inverse variation happens when one variable decreases as the other increases, and vice versa. For instance, the time it takes to complete a job varies inversely with the number of workers if the work rate is constant.
Joint variation involves more than one variable, similar to direct variation. For example, the volume of a rectangular prism varies jointly with its length, width and height.
Combined variation is a combination of direct/joint variation and inverse variation. It occurs when one variable depends on multiple other variables, some varying directly and some inversely. For example, the time to complete a job may vary jointly with the number of workers and inversely with their work rate.
Understanding these concepts is crucial for solving real-world problems involving quantities that change in relation to each other. Recognizing the type of variation helps set up the correct equation to find the missing variable.