Question
If pp and qq vary inversely and pp is 2 when qq is 21, determine qq when pp is equal to 6.
Answers
Answered by
GPT-4o mini
When two variables vary inversely, their product is a constant. This means:
\[
pp \times qq = k
\]
where \(k\) is a constant. Given that \(pp = 2\) when \(qq = 21\), we can find \(k\):
\[
2 \times 21 = k \implies k = 42
\]
Now, to find \(qq\) when \(pp = 6\), we use the relationship:
\[
pp \times qq = k
\]
Substituting in the values:
\[
6 \times qq = 42
\]
Now, solve for \(qq\):
\[
qq = \frac{42}{6} = 7
\]
Therefore, \(qq\) is 7 when \(pp\) is equal to 6.
\[
pp \times qq = k
\]
where \(k\) is a constant. Given that \(pp = 2\) when \(qq = 21\), we can find \(k\):
\[
2 \times 21 = k \implies k = 42
\]
Now, to find \(qq\) when \(pp = 6\), we use the relationship:
\[
pp \times qq = k
\]
Substituting in the values:
\[
6 \times qq = 42
\]
Now, solve for \(qq\):
\[
qq = \frac{42}{6} = 7
\]
Therefore, \(qq\) is 7 when \(pp\) is equal to 6.