Question

It x and y vary inversely, fill in the following blank:

x	9	...	81	243
y	27	9	...	1

Answer 1

\[ \text{ Since x and y vary inversely, we have: }  \]
\[xy = k\]
\[\text{ For x = 9 and } y = 27\]
\[9 \times 27 = k\]
\[ \Rightarrow k = 243\]
\[\text { For y = 9 and k = 243, we have } : \]
\[xy = k\]
\[ \Rightarrow 9x = 243\]
\[ \Rightarrow y = \frac{243}{9}\]
\[ = 27\]
\[\text{ For x = 81 and k = 243, we have: } \]
\[xy = k\]
\[ \Rightarrow 81y = 243\]
\[ \Rightarrow y = \frac{243}{81}\]
\[ = 3\]