The value of y is inversely proportional to the product of 4 and x squared. If y = 12 when x = 2, then find the value of y when x = 6.
Answer:
The value of y is inversely proportional to the product of 4 and x squared. Using the given values and the equation, we can find the value of y when x is 6.
Explanation:
The value of y is inversely proportional to the product of 4 and x squared. Inverse proportion is a relationship where as one value increases, the other value decreases in a predictable manner. We can set up the equation as y = k/(4x^2), where k is the constant of variation.
Given y = 12 when x = 2, we can substitute these values into the equation and solve for k. 12 = k/(4*(2^2)). Solving this, we get k = 192.
To find the value of y when x = 6, we can substitute the values into the equation. y = 192/(4*(6^2)). Solving this, we get y = 8.
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