Final answer:
When 'R' is inversely proportional to 'a', and 'R' is 12 when 'a' is 1.5, we find the constant of proportionality (18). Then, to find 'a' when 'R' is 9, we solve by dividing 18 by 9, which equals 2.
Step-by-step explanation:
The question at hand relates to the concept of inverse proportionality in mathematics. When we say that 'R is inversely proportional to a,' it means that as 'a' increases, 'R' decreases and vice versa, according to the formula R = k/a, where k is the constant of proportionality. Given that R is 12 when a is 1.5, we can find the constant k by multiplying them: 12 × 1.5 = 18. Now, to find the value of 'a' when R is 9, we set up the equation 9 = 18/a and solve for 'a'. Multiplying both sides by 'a' and dividing both sides by 9 gives us a = 18/9 = 2.