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f(x) = cx + d f(0) = c0 + d = d = -6 => d = -6 f(2) = c2 + d = c2 + -6 = 10 => c2 - 6 = 10 => c = (10 + 6) / 2 => c = 8

Find the value of x in (4⁵⋅x+32²)⋅2⁵=2¹⁶⋅x

First we transform everything into powers of 2 as all the numbers involved in...

There are 4 key steps to this question.

(i) calculate the matrix of minors: you want to find the determinant of each entry and this forms a new matrix. 

(ii) convert this into a matrix of co...

Think about which mathematical theorem you might want to use for this question (Pythagoras: a² + b² = c² )

Draw a diagram of the situation described, and write down...

The natural frequency of a glass can be found by tapping it or making it 'sing' (running a wet finger around the top of the glass till it sings a note. If you emit sound waves at this frequency in the dir...