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Problems like this usually look something like: Find the differential of (x² e^2x). The product rule is used when we have to differentiate two different functions multiplied by eachot...

The key word in the question is 'shortest'. The shortest distance from a point to a line is always the perpendicular distance. If we calculate the appropriate angles and lengths/distances, we can use trig...

Multiply the second equation by 2 so that the coefficients of y are equal.(4x+y=14) x2 = (8x+2y=28)Now subtract the first equation from 8x+2y=28.(8x+2y=28) - (3x+2y=13)and you get 5x=15.Divide both sides ...

In situations like this I would always find it best to draw a diagram with all the information we know labelled on it. Firstly, however, notice that our measurements are in different units. You can conver...

This question can be treated like a normal binomial expansion question which is commonly seen at A level. The standard binomial expansion is (1+x)ⁿ = 1 + nx + (n(n-1)(x²))/2! where 2...