To find the relationship between \( X \), \( Y \), and \( Z \), we can express \( X \) as a function of \( Y \) and \( Z \). Given the values \( Y = 2 \), \( Z = 3 \), and \( X = 30 \), we can explore a possible relationship.
Let's consider a simple linear relationship of the form:
\[ X = k \cdot Y^a \cdot Z^b \]
where \( k \), \( a \), and \( b \) are constants.
Given the known values:
\[ 30 = k \cdot (2^a) \cdot (3^b) \]
Now, we need to decide on the values of \( a \), \( b \), and \( k \). Without additional information or constraints, there are infinite combinations of \( k \), \( a \), and \( b \) that can represent this relationship.
However, to provide a specific formula, let’s assume a simple case where \( a = 1 \) and \( b = 1 \), which gives us:
\[ X = k \cdot Y \cdot Z \]
Plugging in the values we know:
\[ 30 = k \cdot 2 \cdot 3 \]
This simplifies to:
\[ 30 = k \cdot 6 \]
Thus,
\[ k = \frac{30}{6} = 5 \]
Substituting back, we obtain the relationship:
\[ X = 5 \cdot Y \cdot Z \]
This means if you know \( Y \) and \( Z \), you can find \( X \) using the formula:
\[ X = 5YZ \]
So the relationship between \( X \), \( Y \), and \( Z \) is \( X = 5YZ \).
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