Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Variation
Inverse variation describes a relationship where one variable increases as the other decreases. In this context, the speed of the pulley varies inversely with its diameter, meaning that as the diameter increases, the speed decreases. This relationship can be expressed mathematically as S = k/D, where S is speed, D is diameter, and k is a constant.
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Proportional Relationships
Proportional relationships involve two quantities that maintain a constant ratio. In the case of the pulleys, the speed and diameter are inversely proportional, allowing us to set up a proportion based on the known values of one pulley to find the unknown value of another. This concept is essential for solving problems involving direct or inverse relationships.
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Setting Up Equations
Setting up equations is a fundamental skill in algebra that involves translating a word problem into a mathematical expression. For this pulley problem, we can use the known speed and diameter to create an equation that relates the two pulleys. This allows us to solve for the unknown speed of the second pulley using the established relationship.
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