To solve the ratio \( x^3 = y^4 \) for the new value of \( x = 15 \), we can rearrange the equation to find \( y \).
Start with the equation: \[ x^3 = y^4 \]
Substituting \( x = 15 \): \[ 15^3 = y^4 \]
Now calculate \( 15^3 \): \[ 15^3 = 15 \times 15 \times 15 = 225 \times 15 = 3375 \]
So now we have: \[ y^4 = 3375 \]
To find \( y \), we take the fourth root of both sides: \[ y = (3375)^{1/4} \]
Calculating the fourth root of 3375:
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First, factor 3375:
- \( 3375 = 3^3 \times 5^3 \)
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Taking the fourth root: \[ y = (3^3 \cdot 5^3)^{1/4} \] \[ y = 3^{3/4} \cdot 5^{3/4} \]
To express this in a simpler numerical form, we can approximate:
- \( 3^{3/4} \approx 2.279 \)
- \( 5^{3/4} \approx 3.169 \)
Calculating their product: \[ y \approx 2.279 \times 3.169 \approx 7.22 \]
Thus, the approximate value of \( y \) when \( x = 15 \) is: \[ \boxed{7.22 \text{ units}} \]
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