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Euclid's algorithm is really useful to be able to, firstly, see if two numbers are co-prime, in other words to see if they share any common factors, but also to find solutions to equations. Say we have tw...

We start with the definitions of sine and cosine, which are, respectively: sinx = opposite/hypoteneuse and cosx = adjacent/hypoteneuse. We then square the analyzed expressions to get the following: 
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We can easily identify the first term (5)

The common difference can be found by subtracting the n^th term from the (n+1)^th term

7-5=9-7=11-9=2

Therefore:

U...

It will mainly depend on your own interests, so there is no definite answer. In my opinion, the whole calculus section is probably the most significant part of the course as it will take up a significant ...

To calculate the desired probability we need to calculate the number n of arrangements of the kids such that the girls sit together and the bous sit together and then calculate the total number m of arran...