Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation occurs when one variable is a constant multiple of another. In the context of the equation z = k√x / y², z varies directly with the square root of x, meaning that as x increases, z increases proportionally, provided y remains constant.
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Inverse Variation
Inverse variation describes a relationship where one variable increases as another decreases. In this equation, z varies inversely with y², indicating that as y increases, z decreases, assuming x remains constant. This relationship highlights how changes in one variable can affect another in opposite ways.
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Constant of Variation
The constant of variation, represented by k in the equation, is a fixed value that determines the strength of the relationship between the variables. It scales the relationship between z, x, and y², indicating how much z changes in response to changes in x and y, thus providing a specific context for the variation described.
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