
Solve the following equation for A*A*. Be sure to take into account whether a letter is capitalized or not.

f, equals, 4, N, A

*f*=

4*NA*​


To solve the equation \( f = 4NA \) for \( A \times A \) (which can be written as \( A^2 \)), follow these steps:

1. **Isolate \( A \) on one side of the equation:**

   \[
   A = \frac{f}{4N}
   \]

2. **Square both sides to solve for \( A^2 \):**

   \[
   A^2 = \left(\frac{f}{4N}\right)^2
   \]

So, the solution for \( A \times A \) or \( A^2 \) is:

\[
A^2 = \frac{f^2}{(4N)^2} = \frac{f^2}{16N^2}
\]

Would you like more details or have any questions?

Here are five related questions to consider:
1. What happens to \( A^2 \) if \( N \) is doubled?
2. How would the solution change if \( f = 4N \times A^2 \)?
3. What if \( f \) were dependent on another variable? How would it affect \( A^2 \)?
4. How does \( A^2 \) behave as \( N \) approaches zero?
5. Can this equation be used to derive a formula for \( A \) in terms of \( f \) and \( N \)?

**Tip:** When squaring both sides of an equation, remember that the square of a fraction involves squaring both the numerator and the denominator.

Learn how to solve the equation A^2 = 4NA to find the value of A. This problem involves algebraic manipulation and the square of a fraction theorem. Suitable for high school students and advanced learners.

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