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This question involves ratios; men : women = 7:2; women : children = 1:3. We need to find a common number to combine the two ratios together. If we multiply the women:children ratio by 2, the ratio become...

In order for two lines to be parallel, they need to have the same gradient (m). The gradient (m) is the coefficient of x in the line equation y=mx+c. Therefore, the gradient of L1 is 3 since 3 is the coef...

Factorisation question: Simplify equation as each function is divisible by 2 then factorise to find roots, roots must = x value when added roots must = constant when multiplied

Differentiating is a process which you can apply to a function which lets you find the gradient (or slope) the function.

The first part of the question is actually a "show that" the equation in the question can be rearranged to the form 10 cot^(x) + 11 cot(x) - 6 = 0. To do this add 11 cot (x) and subtract 16 to/f...