4x Two equations are shown, where $$ s0 $$ $$ s^{2}=\frac{1}{16} $$ $$ f^{3}=s $$ What is the value of $$ \ell $$ A $$ \frac{1}{\sqrt[3]{4}} $$ B $$ \frac{\sqrt[3]{4}}{4} $$ C $$ \frac{1}{\sqrt{4}} $$

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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 $$ \frac{1}{\sqrt{4}} $$

UpStudy AI · Accepted Answer

To find the value of $$ \ell $$, we need to solve the given equations step by step.

Given:
1. $$ s > 0 $$
2. $$ s^2 = \frac{1}{16} $$
3. $$ f^3 = s $$

From equation 2, we can find the value of $$ s $$:
$$ s^2 = \frac{1}{16} $$
$$ s = \pm \frac{1}{4} $$

Since $$ s > 0 $$, we take the positive value of $$ s $$:
$$ s = \frac{1}{4} $$

Now, we can find the value of $$ f $$ using equation 3:
$$ f^3 = s $$
$$ f^3 = \frac{1}{4} $$
$$ f = \sqrt[3]{\frac{1}{4}} $$

Finally, we can find the value of $$ \ell $$ using the given options:
A. $$ \frac{1}{\sqrt[3]{4}} $$
B. $$ \frac{\sqrt[3]{4}}{4} $$
C. $$ \frac{1}{\sqrt{4}} $$

Let's calculate the value of $$ \ell $$ for each option.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{\left(\sqrt[3]{4}\right)}$$
- step1: Remove the parentheses:
  $$\frac{1}{\sqrt[3]{4}}$$
- step2: Multiply by the Conjugate:
  $$\frac{\sqrt[3]{4^{2}}}{\sqrt[3]{4}\times \sqrt[3]{4^{2}}}$$
- step3: Simplify:
  $$\frac{2\sqrt[3]{2}}{\sqrt[3]{4}\times \sqrt[3]{4^{2}}}$$
- step4: Multiply the numbers:
  $$\frac{2\sqrt[3]{2}}{2^{2}}$$
- step5: Reduce the fraction:
  $$\frac{\sqrt[3]{2}}{2}$$
The value of $$ \ell $$ is approximately 0.629961.

Therefore, the correct option is:
A. $$ \frac{1}{\sqrt[3]{4}} $$
The value of $$ \ell $$ is $$ \frac{1}{\sqrt[3]{4}} $$, which is option A.

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 \( \frac{1}{\sqrt{4}} \)

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