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4x Two equations are shown, where \( s>0 \) \( s^{2}=\frac{1}{16} \) \( f^{3}=s \) What is the value of \( \ell \) A \( \frac{1}{\sqrt[3]{4}} \) B \( \frac{\sqrt[3]{4}}{4} \) C \( \frac{1}{\sqrt{4}} \)

Ask by Lang Reese. in the United States
Mar 18,2025

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The value of \( \ell \) is \( \frac{1}{\sqrt[3]{4}} \), which is option A.

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To solve for \( s \), we start with the equation \( s^{2}=\frac{1}{16} \). Taking the square root of both sides gives us \( s = \frac{1}{4} \) since \( s > 0 \). Next, we substitute \( s \) into the second equation \( f^{3}=s \) which gives us \( f^{3}=\frac{1}{4} \). To find \( f \), we take the cube root of both sides, yielding \( f = \frac{1}{\sqrt[3]{4}} \). Now, using the provided options, we see that the corresponding value of \( \ell \) is \( \frac{1}{\sqrt[3]{4}} \), which matches with option A, thereby giving us the answer: **A. \( \frac{1}{\sqrt[3]{4}} \)**.

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