8 It is given that \( c=\frac{b x^{2}}{a}+8 \). (a) Find the value of \( c \) when \( b=0.2, x=-3 \) and \( a=6 \). \[ \left(=\frac{(0 \cdot 2)(-3)^{2}}{6}+8\right. \] (b) Express \( x \) in terms of \( a, b \) and \( c \).

To solve the problem, we will address each part separately. ### Part (a) We need to find the value of \( c \) when \( b = 0.2 \), \( x = -3 \), and \( a = 6 \). The formula given is: \[ c = \frac{b x^{2}}{a} + 8 \] Substituting the values into the equation: 1. Calculate \( x^2 \): \[ x^2 = (-3)^2 = 9 \] 2. Substitute \( b \), \( x^2 \), and \( a \) into the equation: \[ c = \frac{0.2 \cdot 9}{6} + 8 \] 3. Calculate \( \frac{0.2 \cdot 9}{6} \): \[ 0.2 \cdot 9 = 1.8 \] \[ \frac{1.8}{6} = 0.3 \] 4. Now, substitute back to find \( c \): \[ c = 0.3 + 8 = 8.3 \] Thus, the value of \( c \) is: \[ \boxed{8.3} \] ### Part (b) We need to express \( x \) in terms of \( a \), \( b \), and \( c \). Starting from the original equation: \[ c = \frac{b x^{2}}{a} + 8 \] We can rearrange this equation to isolate \( x^2 \): 1. Subtract 8 from both sides: \[ c - 8 = \frac{b x^{2}}{a} \] 2. Multiply both sides by \( a \): \[ a(c - 8) = b x^{2} \] 3. Divide both sides by \( b \): \[ x^{2} = \frac{a(c - 8)}{b} \] 4. Take the square root of both sides to solve for \( x \): \[ x = \pm \sqrt{\frac{a(c - 8)}{b}} \] Thus, \( x \) expressed in terms of \( a \), \( b \), and \( c \) is: \[ \boxed{x = \pm \sqrt{\frac{a(c - 8)}{b}}} \]