If n is inversely proportional to m and n=29 when m=9, express n in terms of m.

1. Break Down the Problem

Since $n$ is inversely proportional to $m$, we can express this relationship mathematically as: $n \propto \frac{1}{m}$ This means that there exists a constant $k$ such that: $n = \frac{k}{m}$

2. Relevant Concepts

From the given information, we know:

• $n = 29$ when $m = 9$.

Using this information, we can find the constant $k$.

3. Analysis and Detail

Substituting the known values into the equation: $29 = \frac{k}{9}$

To find $k$, multiply both sides by 9: $k = 29 \times 9$ $k = 261$

Now, substitute $k$ back into $n = \frac{k}{m}$: $n = \frac{261}{m}$

4. Verify and Summarize

We verified $k$ by substituting back the given values for $n$ and $m$. The relationship holds, confirming that our calculations are correct.

Final Answer

Thus, $n$ expressed in terms of $m$ is: $n = \frac{261}{m}$