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Degree: BA Geography (Bachelors) - Durham University
|Geography||A Level||£20 /hr|
|Further Mathematics||GCSE||£18 /hr|
Oliver (Student) May 11 2016
By quoting De Moivre's theorem, (r(cos(x) + isin(x)))n = rn(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(x) and s = sin(x))
(cos(x) + isin(x))4 = c4 + 4c3is + 6c2(is)2 + 4c(is)3 + (is)4
= c4 +4c3is - 6c2s2 - 4cis3 + s4
The real parts of this are c4, -6c2s2 and s4
Therefore, cos(4x) = c4 - 6c2s2 + s4
s2 = 1 - c2
6c2s2 = 6c2(1-c2) = 6c2 - 6c4
s4 = (1 - c2)2 = 1 - 2c2 + c4
By substituting these in:
cos(4x) = c4 - 6c2 + 6c4 + 1 - 2c2 + c4
= 8c4 - 8c2 + 1see more
By recalling that eln(a) = a, you can rewrite 32x as e2xln(3).
Then, you can differentiate this like any other e function, by using the product rule.
d/dx (e2xln(3)) = e2xln(3) x d/dx (2xln(3))
d/dx (e2xln(3)) = e2xln(3) x 2ln(3)see more
Countries they operate in
+ Provide employment opportunities in developing nations - Coca-Cola factory in Egypt employs 12000 people and created 120000 indirect jobs
+ Help developing nations enter the global market through FDI - Coca-Cola $1.5bn in Brazil and $1.5bn in Russia
+ Bring communities closer as factories in rural parts of the country may employ the majority of the surrounding towns' people.
- Harm ecosystems for the sake of profit - Coca-Cola factory in Kerala, India shut down due to contamination of local water sources
- Exploit cheap labour - poor conditions recorded in Foxconn factories (Apple's manufacturing partner) in China, such as poisoning via LCD screen cleaner.
+ By outsourcing big business, leaves more space for local businesses to thrive and grow.
+ Countries which the TNC operates in will more easily become trading partners
- Tax avoidance (e.g Amazon) by basing company headquarters elsewhere.
- Fewer jobs in home nation due to outsourcing of labour - Dyson moved their main factory to Malaysia, 800 workers lost jobssee more