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\( W=4 \pi y \) for \( y \)

Ask by George Valdez. in the United States
Jan 26,2025

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Tutor-Verified Answer

Answer

To solve for \( y \) in the equation \( W = 4\pi y \), divide both sides by \( 4\pi \): \[ y = \frac{W}{4\pi} \]

Solution

It looks like you're working with the equation: \[ W = 4\pi y \] If you want to solve for \( y \), you can rearrange the equation as follows: \[ \begin{align*} W &= 4\pi y \\ y &= \frac{W}{4\pi} \end{align*} \] **Solution for \( y \):** \[ y = \frac{W}{4\pi} \] **Explanation:** 1. **Starting Equation:** \[ W = 4\pi y \] 2. **Isolate \( y \):** - Divide both sides of the equation by \( 4\pi \) to solve for \( y \): \[ y = \frac{W}{4\pi} \] **Example Calculation:** Suppose \( W = 100 \) (units consistent with \( y \)), then: \[ y = \frac{100}{4\pi} \approx \frac{100}{12.566} \approx 7.9577 \] So, \( y \approx 7.96 \) units. **Additional Context (If Applicable):** If this equation arises from a specific context (such as geometry, physics, etc.), providing that context could help in offering a more detailed explanation or in addressing related questions you might have. Feel free to provide more information or ask further questions if you need assistance with a particular application of this equation!

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Bonus Knowledge

To solve the equation \( W = 4 \pi y \) for \( y \), simply isolate \( y \) by dividing both sides by \( 4 \pi \): \[ y = \frac{W}{4 \pi} \] Now you have \( y \) expressed in terms of \( W \), which shows how \( y \) changes with respect to \( W \). This relationship is particularly valuable in mathematical modeling, physics, or engineering problems where quantities often relate linearly. This formula can be applied in various contexts, from calculating the radius of a circle in geometric situations (where \( W \) might represent an area or circumference) to understanding wave functions in physics. Just make sure to keep the units consistent when substituting values for \( W \)!

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