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Answer :
We start with the given equation:
[tex]$$
\frac{3b}{2c} = \frac{9}{5}.
$$[/tex]
Notice that the left-hand side can be written as:
[tex]$$
\frac{3b}{2c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]
This means that:
[tex]$$
\frac{3}{2} \cdot \frac{b}{c} = \frac{9}{5}.
$$[/tex]
To find [tex]$\frac{b}{c}$[/tex], multiply both sides by [tex]$\frac{2}{3}$[/tex]:
[tex]$$
\frac{b}{c} = \frac{9}{5} \cdot \frac{2}{3} = \frac{18}{15} = \frac{6}{5}.
$$[/tex]
Next, we want to find the value of:
[tex]$$
\frac{9b}{6c}.
$$[/tex]
We can simplify this expression:
[tex]$$
\frac{9b}{6c} = \frac{9}{6} \cdot \frac{b}{c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]
Now substitute the value we found for [tex]$\frac{b}{c}$[/tex]:
[tex]$$
\frac{3}{2} \cdot \frac{6}{5} = \frac{18}{10} = \frac{9}{5}.
$$[/tex]
Thus, the final answer is:
[tex]$$
\frac{9}{5}.
$$[/tex]
[tex]$$
\frac{3b}{2c} = \frac{9}{5}.
$$[/tex]
Notice that the left-hand side can be written as:
[tex]$$
\frac{3b}{2c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]
This means that:
[tex]$$
\frac{3}{2} \cdot \frac{b}{c} = \frac{9}{5}.
$$[/tex]
To find [tex]$\frac{b}{c}$[/tex], multiply both sides by [tex]$\frac{2}{3}$[/tex]:
[tex]$$
\frac{b}{c} = \frac{9}{5} \cdot \frac{2}{3} = \frac{18}{15} = \frac{6}{5}.
$$[/tex]
Next, we want to find the value of:
[tex]$$
\frac{9b}{6c}.
$$[/tex]
We can simplify this expression:
[tex]$$
\frac{9b}{6c} = \frac{9}{6} \cdot \frac{b}{c} = \frac{3}{2} \cdot \frac{b}{c}.
$$[/tex]
Now substitute the value we found for [tex]$\frac{b}{c}$[/tex]:
[tex]$$
\frac{3}{2} \cdot \frac{6}{5} = \frac{18}{10} = \frac{9}{5}.
$$[/tex]
Thus, the final answer is:
[tex]$$
\frac{9}{5}.
$$[/tex]
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