Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation describes a relationship where one variable is a constant multiple of another. In mathematical terms, if y varies directly as x, it can be expressed as y = kx, where k is a non-zero constant. This concept is essential for understanding how changes in one variable affect another in a proportional manner.
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Inverse Variation
Inverse variation occurs when one variable increases while another decreases, maintaining a constant product. If y varies inversely as the square of z, it can be represented as y = k/z². This relationship is crucial for solving problems where one variable's increase leads to the decrease of another, particularly in the context of the given problem.
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Combined Variation
Combined variation involves both direct and inverse relationships among variables. In this case, y varies directly with x and inversely with the square of z, leading to the equation y = kx/z². Understanding combined variation is vital for solving complex problems where multiple variables interact in different ways, as seen in the exercise.
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