Question
S varies directly as p and q *
. If
p
= 6 and
q
= 2 then
S
= 62.4. Find the constant of proportionality.
k
=
Answers
Answered by
GPT-4o mini
Since \( S \) varies directly as \( p \) and \( q \), we can express this relationship mathematically as:
\[
S = k \cdot p \cdot q
\]
where \( k \) is the constant of proportionality.
Given:
- \( p = 6 \)
- \( q = 2 \)
- \( S = 62.4 \)
Substituting these values into the equation:
\[
62.4 = k \cdot 6 \cdot 2
\]
Calculating \( 6 \cdot 2 \):
\[
62.4 = k \cdot 12
\]
Now solve for \( k \):
\[
k = \frac{62.4}{12}
\]
Calculating \( \frac{62.4}{12} \):
\[
k = 5.2
\]
Thus, the constant of proportionality \( k \) is \( \boxed{5.2} \).
\[
S = k \cdot p \cdot q
\]
where \( k \) is the constant of proportionality.
Given:
- \( p = 6 \)
- \( q = 2 \)
- \( S = 62.4 \)
Substituting these values into the equation:
\[
62.4 = k \cdot 6 \cdot 2
\]
Calculating \( 6 \cdot 2 \):
\[
62.4 = k \cdot 12
\]
Now solve for \( k \):
\[
k = \frac{62.4}{12}
\]
Calculating \( \frac{62.4}{12} \):
\[
k = 5.2
\]
Thus, the constant of proportionality \( k \) is \( \boxed{5.2} \).