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Prove the identity: sin^2(x)+cos^2(x) = 1

This is one of the most commonly used A level identities which can be proved using only GCSE maths! Firstly, take an arbitrary right angle triangle with Hypotenuse h, and angle x between h and the adjacent s...
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Answered by Sean O. • Maths tutor
5357 Views

If the highest frequency a song is 10 kHz and it is encoded at 16 bits per sample what is the minimum number of bytes needed to encode the 3 minute song?

The key to this question is to remember the Nyquist rate of a signal. This is the lowest sample rate which can be used for a signal without losing valid frequencies or gaining incorrect frequencies. This is ...
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Answered by David M. • Physics tutor
7076 Views

Differentiate the function f(x) = x*sin(x)

This function is the product of the two functions 'x' and 'sin(x)'. Therefore we use the product rule, which says that the differential of a product of two functions is the differential of the first multipli...
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Answered by Dylan B. • Maths tutor
6269 Views

When red light is shone on a metal, regardless of the intensity of this light, no current will flow. However if blue light is shone on this metal a current will flow. Why does this occur?

This problem can be solved by first considering the energy of a photon e = hf. ​A photon of red light lacks the sufficient energy to free an electron. However a photon of blue light has a higher frequency an...
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Answered by Jonathan P. • Physics tutor
7061 Views

When and how do I use integration by parts?

Integration by parts is used when you would like to find the integral of a composite function made up of two functions of the same variable as which you're integrating with respect to. The formula for this t...
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Answered by Craig Y. • Maths tutor
6169 Views