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At first this equation seems tricky, but we can perform a clever substitution to simplify it. We notice that if let y = 2^x, then we can rewrite this as: 8(y^2) - 9y + 1 = 0 This now becomes a simple quadrat...

This question relies on knowledge of algebraic expressions and highest common factors. What is the highest common factor which goes into the expressions 8y and 4y^2. The answer is 4y. This is then taken on t...

Complex numbers have three primary forms: the general form, z=a+ib; the polar form, z=r(cosθ+isinθ); and the exponential form, z=rexp(iθ). To convert from the general form to either form you need to find r a...

A stationary point is where the gradient is exactly zero - the curve is neither increasing or decreasing. This means that we need to differentiate y to find dy/dx and then set this equal to 0. Doing this, us...

Write the equation and balance it. CH4 + 2O2 --> CO2 + 2H2O Assign the enthalpies of formation and the sign of the energy value with the corresponding molecule (Will demonstrate my technique if needed). e...