m = (z/f - g) / (z/f) * 100

What is the formula for z?

To find the formula for \( z \) from the given equation \( m = \left( \frac{z/f - g}{z/f} \right) \times 100 \), follow these steps:

1. Start with the given equation:
   \[
   m = \left( \frac{z/f - g}{z/f} \right) \times 100
   \]

2. Simplify the fraction:
   \[
   \frac{z/f - g}{z/f} = 1 - \frac{gf}{z}
   \]
   Hence, the equation becomes:
   \[
   m = \left(1 - \frac{gf}{z} \right) \times 100
   \]

3. Divide both sides by 100:
   \[
   \frac{m}{100} = 1 - \frac{gf}{z}
   \]

4. Isolate the fraction involving \( z \):
   \[
   \frac{gf}{z} = 1 - \frac{m}{100}
   \]

5. Simplify the right-hand side:
   \[
   \frac{gf}{z} = \frac{100 - m}{100}
   \]

6. Invert both sides to solve for \( z \):
   \[
   \frac{z}{gf} = \frac{100}{100 - m}
   \]

7. Finally, multiply both sides by \( gf \):
   \[
   z = gf \times \frac{100}{100 - m}
   \]

Therefore, the formula for \( z \) is:
\[
z = \frac{100gf}{100 - m}
\]

Would you like any more details or have any questions?

Here are 8 related questions to expand your understanding:
1. How do you derive a formula for \( f \) given the other variables?
2. What happens to \( z \) if \( m \) approaches 100?
3. How does changing \( g \) affect the value of \( z \)?
4. Can this formula be simplified further under certain conditions?
5. What is the physical meaning of each variable in a real-world context?
6. How does the relationship between \( z \) and \( m \) change if \( f \) is very large?
7. Can you graph \( z \) as a function of \( m \) for fixed \( g \) and \( f \)?
8. What if \( m \) is negative? How does it affect \( z \)?

**Tip:** When manipulating equations, always perform operations symmetrically on both sides to maintain equality.

Learn how to derive the formula for z from the percentage equation m = ((z/f - g) / (z/f)) * 100. Step-by-step solution with fraction manipulation and percentage formula. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation