If y varier inveersely as x and if y=9 when x=2 find y when x = 3

When \( y \) varies inversely as \( x \), it means that their product is constant. Mathematically, this can be expressed as:

\[
y \times x = k
\]

where \( k \) is the constant of variation.

Given:
- \( y = 9 \) when \( x = 2 \)

First, find the constant \( k \):

\[
k = y \times x = 9 \times 2 = 18
\]

Now, use the constant \( k \) to find \( y \) when \( x = 3 \):

\[
y \times 3 = 18
\]

\[
y = \frac{18}{3} = 6
\]

So, \( y = 6 \) when \( x = 3 \).

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. If \( y \) varies inversely as \( x \) and \( y = 4 \) when \( x = 5 \), what is \( y \) when \( x = 10 \)?
2. Suppose \( y \) varies inversely as \( x \) and \( y = 12 \) when \( x = 3 \). Find the value of \( y \) when \( x = 6 \).
3. If \( y \) varies inversely as \( x \) and the constant \( k = 20 \), what is \( y \) when \( x = 4 \)?
4. Given \( y \) varies inversely as \( x \) and \( y = 8 \) when \( x = 2.5 \), find \( x \) when \( y = 16 \).
5. If \( y \) varies inversely as \( x \) and \( x = 7 \) when \( y = 3 \), what is the constant \( k \)?

**Tip:** When dealing with inverse variation problems, always start by finding the constant of variation \( k \). This will make solving for any unknowns much easier.

Explore how to solve problems involving inverse variation using a detailed example. Understand the concept where y varies inversely as x, with step-by-step calculations and practice questions. Suitable for students in Grades 9-10.

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