Make m the subject of the formula: P = (m/4m)^(1/3)
Understand the Problem
The question requires us to rearrange the given formula to isolate 'm' on one side of the equation. First, we need to isolate the term containing 'm' by raising both sides to the power of 3. Then, we solve for m.
Answer
No solution for $m$ in terms of $P$. $P = \frac{1}{\sqrt[3]{4}}$
Answer for screen readers
There is no solution for $m$ in terms of $P$, since the 'm' terms cancel out in the original equation. $P = \frac{1}{\sqrt[3]{4}}$
Steps to Solve
- Write down the given formula
We are given the formula:
$P = (\frac{m}{4m})^{\frac{1}{3}}$
- Cube both sides of the equation
To eliminate the cube root, we raise both sides of the equation to the power of 3:
$P^3 = (\frac{m}{4m})$
- Simplify the fraction on the right side
We can simplify the fraction by canceling out the 'm' terms:
$P^3 = \frac{1}{4}$
- Solve for m
Notice that 'm' cancelled out. This means the original equation does not depend on 'm' at all. The value of P is always the cube root of $\frac{1}{4}$ regardless of what 'm' is (as long as $m \neq 0$). There is technically no solution for $m$ in terms of $P$. The value of $P$ is fixed.
There is no solution for $m$ in terms of $P$, since the 'm' terms cancel out in the original equation. $P = \frac{1}{\sqrt[3]{4}}$
More Information
Since $P = (\frac{m}{4m})^{\frac{1}{3}}$, we have $P = (\frac{1}{4})^{\frac{1}{3}}$. This represents a constant value for $P$, approximately $0.63$. Consequently, we cannot express 'm' as the subject of the formula in terms of $P$, as 'm' cancels out during simplification.
Tips
A common mistake would be to attempt to manipulate the equation further after cubing both sides, not realizing that the variable 'm' cancels out.
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