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Express cos(4x) in terms of powers of cos(x)

By quoting De Moivre's theorem, (r(cos(x) + isin(x))) n = r n (cos(nx) + isin(nx)), we can realise that cos(4x) is a result of the real parts of (cos(x) + isin(x)) 4 Using binomial expansion: (where c = cos(...
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Why is phenylamine a weaker organic base than ethylamine?

Phenylamine contains a phenyl group attached to the amine. Phenyl groups have a delocalised system of electrons as a result of p orbitals from the 6 adjacent carbon atoms overlapping and "merging" ...
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Answered by Adam W. Chemistry tutor
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How do you go about differentiating a^x functions?

A key point to remember here is that a^x could mean the base (a) is not “e”-that special number which has a gradient function, dy/dx (the differential), EQUAL to the function itself, y=e^x. When "a&quot...
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Answered by Adam W. Maths tutor
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In terms of reaction mechanisms, what exactly is the rate-determining step?

The easiest way to visualise this is to imagine a line of four dinner ladies serving you different parts of a school meal e.g. the first peas, the second mash potatoes, the third chicken and the fourth gravy...
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Answered by Adam W. Chemistry tutor
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To what extent do the structures and functions of DNA and RNA differ?

Firstly, there are chemical differences between the two nucleic acids. DNA has the following structural properties:-double stranded and anti-parallel polymer held together by (relatively) weak hydrogen bonds...
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Answered by Adam W. Biology tutor
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