1. It is given that \( a=2 n(n-3 k) \). (i) Find \( a \) when \( n=0.5 \) and \( k=-1.2 \). (ii) Express \( k \) in terms of \( a \) and \( n \).

To find \( a \) when \( n=0.5 \) and \( k=-1.2 \), we begin by substituting the values into the given equation: \[ a = 2 n (n - 3k) \] Substituting \( n = 0.5 \) and \( k = -1.2 \): \[ a = 2 \times 0.5 \left(0.5 - 3 \times (-1.2)\right) \] \[ = 1 \left(0.5 + 3.6\right) \] \[ = 1 \times 4.1 = 4.1 \] So, the value of \( a \) is \( 4.1 \). Next, we will express \( k \) in terms of \( a \) and \( n \). Starting from the original equation: \[ a = 2n(n - 3k) \] We can rearrange this to isolate \( k \): \[ a = 2n^2 - 6nk \] Rearranging gives: \[ 6nk = 2n^2 - a \] Now, divide both sides by \( 6n \) (assuming \( n \neq 0 \)): \[ k = \frac{2n^2 - a}{6n} \] Thus, \( k \) can be expressed in terms of \( a \) and \( n \) as: \[ k = \frac{2n^2 - a}{6n} \]