Make g the subject of the formula M = 2fg/(g-c).
Understand the Problem
We need to rearrange the formula M = 2fg/(g-c) to isolate 'g' as the subject of the formula. This involves algebraic manipulation to get 'g' by itself on one side of the equation.
Answer
$$ g = \frac{Mc}{M - 2f} $$
Answer for screen readers
$$ g = \frac{Mc}{M - 2f} $$
Steps to Solve
- Multiply both sides by $(g-c)$
To eliminate the fraction, multiply both sides of the equation by $(g-c)$:
$$ M(g-c) = 2fg $$
- Expand the left side
Distribute $M$ on the left side of the equation:
$$ Mg - Mc = 2fg $$
- Gather terms containing 'g' on one side
Move all terms containing $g$ to one side of the equation. Subtract $2fg$ from both sides:
$$ Mg - 2fg = Mc $$
- Factor out 'g'
Factor out $g$ from the left side of the equation:
$$ g(M - 2f) = Mc $$
- Isolate 'g'
Divide both sides by $(M - 2f)$ to isolate $g$:
$$ g = \frac{Mc}{M - 2f} $$
$$ g = \frac{Mc}{M - 2f} $$
More Information
The formula $g = \frac{Mc}{M - 2f}$ expresses $g$ in terms of $M$, $c$, and $f$. This rearrangement is useful if you need to calculate $g$ directly from known values of $M$, $c$, and $f$.
Tips
A common mistake is not distributing $M$ correctly in step 2, or making a mistake when moving terms around in step 3, especially with the signs. Also, be careful when factoring out $g$ in Step 4.
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