Answer:
[tex]p =4[/tex]
Step-by-step explanation:
Given
Variation: Inversely
[tex]p = 12[/tex] when [tex]q = 45[/tex]
Required
Determine p when [tex]q = 135[/tex]
First, we need to determine the relationship between p and q
Since, it is an inverse variation.
The relationship is:
[tex]p\ \alpha\ \frac{1}{q}[/tex]
Convert to an equation
[tex]p= k *\frac{1}{q}[/tex]
[tex]p= \frac{k}{q}[/tex]
Where k = constant of variation
Make k the subject
[tex]k = p * q[/tex]
When [tex]p = 12[/tex] and [tex]q = 45[/tex]
[tex]k = 12 * 45[/tex]
[tex]k = 540[/tex]
To solve for p when q = 135
Substitute 135 for q and 540 for k in [tex]p= \frac{k}{q}[/tex]
[tex]p = \frac{540}{135}[/tex]
[tex]p =4[/tex]
