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So this may seem a bit odd at first - like why is it the the more of something there is, the less it costs to buy? But it actually makes a lot of sense when we break down the law of demand. The law of dem...

cos(4x) = cos(2(2x)) = 2(cos^2(2x)) - 1 = 2 (cos^2(x) - 1)^2 - 1 = 8(cos^4(x)) - 8(cos^2(x)) + 1

Diamond- Each carbon atom is bonded to four other carbon atoms with strong covalent bonds in a tetrahedral structure (with bond angles of 104.9 degrees). As all four valence electrons are used for bonding...