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Question
Complite the following table given that x varies directly as y .
| x | 3 | 5 | 7 | 9 |
| y | ... | 20 | 28 | ... |
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Solution
\[\text{ Here, x and y vary directly } . \]
\[ \therefore x = ky\]
\[x = 5 \text{ and } y = 20\]
\[i . e . , 5 = k \times 20\]
\[ \Rightarrow k = \frac{5}{20} = \frac{1}{4}\]
\[\text{ For x = 3 and } k = \frac{1}{4}, \text{ we have:} \]
\[3 = \frac{1}{4} \times y\]
\[ \Rightarrow y = 4 \times 3 = 12\]
\[\text{ For } x = 9, k = \frac{1}{4}, \text{ we have: } \]
\[x = ky\]
\[ \Rightarrow 9 = \frac{1}{4} \times y\]
\[ \Rightarrow y = 9 \times 4 = 36\]
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