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For this sort of question, the easiest approach is to make an educated guess at the correct answer, and prove that this must be correct by contradiction. As taking the root of something has a large effect...
The problem seems to be hard as the equation involved both cosx and sinx But we can relate the two as (cosx)^2 + (sinx)^2 = 1, so we can rearrange this as 0 = 2(sinx)^2 - 7sinx + 3. This quadratic in sinx...
The number of 0's at the end of a number is the same as the number of factors of 10 that the number has. So consider the prime factor decomposition of 100! and note that every factor of 10 has prime facto...
As for part III you only need to use the process of elimination. Notice, that there are only three possible situations, since at east one of Alice, Bob, and Charlie has a white hat; namely: one of them ha...
First of all, an integer is a whole number, i.e. a not a fractional number, that can be positive, negative or zero. To find the range of values r and s for which the above fraction is an integer we can st...
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