Find the value of \( c \) in the equation \( a c^{2}-b^{2}-\frac{d}{2-d}=\frac{1}{4} \) if \( d=9, b=-3, a=1 \) Read Less

Given that the quadratic equation \( p x^{2}-9 q x+9 p=0 \), where \( p \) and \( q \) are constants, has two equal roots. Find \( p: q \). [2 marks.

The value of \( \frac{9^{x}\left(9^{x-1}\right)^{x}}{9^{x+1} \cdot 3^{2 x-2}}\left\{\frac{729^{\frac{1}{3}}}{81}\right\}^{-x} \div \frac{3^{a}-2^{3} \cdot 3^{a-2}}{3^{a}-3^{a-1}} \)

(c) Subtract: \( 31(1-4 m+5 n) \) from \( 4 I(10 n-3 m+21) \) (d) Subtract: \( 3 a(a+b+c)-2 b(a-b+c) \) from \( 4 c(-a+b+c \)

What is the growth factor in the exponential function \( f(x) = 3(2)^{x} \)?

Simplify the expression: \( (x^{1/4}y^{1/2})^{8} \)