To determine the constant of variation [tex]\( k \)[/tex] when a quantity [tex]\( p \)[/tex] varies jointly with [tex]\( r \)[/tex] and [tex]\( s \)[/tex], we follow these steps:
1. Understand the Relationship:
When a quantity [tex]\( p \)[/tex] varies jointly with [tex]\( r \)[/tex] and [tex]\( s \)[/tex], it means that [tex]\( p \)[/tex] is directly proportional to the product of [tex]\( r \)[/tex] and [tex]\( s \)[/tex]. Mathematically, we can express it as:
[tex]\[
p = k \cdot r \cdot s
\][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
2. Solve for the Constant of Variation [tex]\( k \)[/tex]:
To isolate [tex]\( k \)[/tex], we need to rearrange the equation. We start with:
[tex]\[
p = k \cdot r \cdot s
\][/tex]
Dividing both sides of the equation by [tex]\( r \cdot s \)[/tex], we get:
[tex]\[
k = \frac{p}{r \cdot s}
\][/tex]
3. Write the Expression:
The expression for the constant of variation [tex]\( k \)[/tex] is:
[tex]\[
k = \frac{p}{r \cdot s}
\][/tex]
Thus, the correct option that represents the constant of variation [tex]\( k \)[/tex] is:
[tex]\[
\frac{p}{r \cdot s}
\][/tex]
