To solve the problem, we need to keep in mind that \( R \) is inversely proportional to \( A \). This relationship means that \( R \times A \) is a constant value, \( k \).
Given:
- \( R = 12 \) when \( A = 1.5 \)
We first determine the constant \( k \) using the initial values:
[tex]\[ k = R \times A \][/tex]
[tex]\[ k = 12 \times 1.5 \][/tex]
[tex]\[ k = 18 \][/tex]
Now we can use this constant \( k \) to find the required values in the subsequent parts of the question.
### Part (a)
To find the value of \( R \) when \( A = 5 \):
We use the relationship \( R \times A = k \):
[tex]\[ R \times 5 = 18 \][/tex]
Solving for \( R \):
[tex]\[ R = \frac{18}{5} \][/tex]
[tex]\[ R = 3.6 \][/tex]
### Part (b)
To find the value of \( A \) when \( R = 9 \):
Again, we use the relationship \( R \times A = k \):
[tex]\[ 9 \times A = 18 \][/tex]
Solving for \( A \):
[tex]\[ A = \frac{18}{9} \][/tex]
[tex]\[ A = 2 \][/tex]
### Summary
Therefore, the solutions are:
- The value of \( R \) when \( A = 5 \) is \( 3.6 \).
- The value of [tex]\( A \)[/tex] when [tex]\( R = 9 \)[/tex] is [tex]\( 2.0 \)[/tex].
