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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...

Light from the sun is white. As it passes through the Earth's atmosphere, the different wavelengths of white light (i.e. the visible spectrum of colours) are scattered by gas and dust particles. Colours w...