In an inverse variation, the product of the two variables is constant. This means if we have two pairs of points \((x_1, y_1)\) and \((x_2, y_2)\) that satisfy \(xy = k\), where \(k\) is a constant, we can find the missing value.
Given the points \((2.4, 3)\) and \((5, y)\):
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First, we can find the constant \(k\) using the first point: \[ k = x_1 \cdot y_1 = 2.4 \cdot 3 = 7.2 \]
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Next, we can use this value of \(k\) to find \(y\) using the second point: \[ k = x_2 \cdot y_2 \implies 7.2 = 5 \cdot y \]
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Now, solve for \(y\): \[ y = \frac{7.2}{5} = 1.44 \]
Thus, the missing value \(y\) is \(1.44\).
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