Here are the essential concepts you must grasp in order to answer the question correctly.
Joint Variation
Joint variation occurs when a variable is directly proportional to the product of two or more other variables. In this case, if x varies jointly as y and z, it means that x = k(yz) for some constant k. Understanding this relationship is crucial for setting up the equation correctly.
Inverse Variation
Inverse variation describes a relationship where one variable increases as another decreases. Specifically, if x varies inversely as the square of w, it can be expressed as x = k'/(w^2) for some constant k'. This concept is essential for incorporating the inverse relationship into the overall equation.
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Solving for y
To solve for y in the equation derived from the joint and inverse variations, one must isolate y on one side of the equation. This typically involves algebraic manipulation, such as multiplying or dividing both sides by appropriate terms. Mastery of these techniques is necessary to find the value of y in relation to x, z, and w.
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