1. $y$ is inversely proportional to $x$. If $y=12$ when $x=5$, find $k$ in $y=k/x$.

Answer: $k=60$.

2. $y$ is inversely proportional to $x$. $y=8$ when $x=3$. Find $y$ when $x=12$.

Answer: $y=2$.

3. $y$ is inversely proportional to $x^2$. $y=18$ when $x=2$. Find $y$ when $x=6$.

Answer: $y=2$.

4. 4 identical taps fill a tank in 15 minutes. How long do 6 taps take at the same rate?

Answer: 10 minutes.

5. H. $p$ is inversely proportional to $q$. $p=9$ when $q=4$. Write $p$ in terms of $q$.

Answer: $p=36/q$.

6. $y=72/x$. Find $x$ when $y=9$.

Answer: $x=8$.

7. $P$ is inversely proportional to $d^2$. $P=20$ when $d=3$. Find $P$ when $d=6$.

Answer: $P=5$.

8. For $y=24/x$, find $y$ when $x=8$.

Answer: $3$.

9. 5 workers take 18 days to complete a job. How many days would 15 workers take at the same rate?

Answer: 6 days.

10. For inverse proportion, what happens to $y$ when $x$ is doubled?

Answer: $y$ halves; for example, $y=60/x$ changes from 30 to 15 when $x$ doubles from 2 to 4.

11. A light intensity is inversely proportional to distance squared. It is 80 units at 2 m. Find it at 4 m.

Answer: 20 units.

12. Explain why the graph of $y=30/x$ does not pass through the origin.

Answer: At $x=0$ the formula is undefined, so the graph cannot contain the origin.

13. Choose the direct or inverse model for each relationship: $y=8x$ and $z=8/x$. Work out both values when $x=4$. Which value halves when $x$ doubles, and why?

Answer: $y=32$ and $z=2$. The inverse model halves because doubling $x$ doubles the denominator.