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First, we need to write cos²x in a form that is easily integrable. We can use the double angle formula cos(2x) = 2cos²x - 1 to see that cos²x = 1/2cos(2x)+1/2. Now, we can...

Often, substitution is used when dealing with quadratic simultaneous equations as the other method, elimination, is more straightforward and can be used to solve linear equations but it cannot be used for...

Draw a probability tree diagram. For this question, only two branches are required (orange and orange). At the start, there are n sweets in total, 6 are orange, so p(O) = 6/n. On our second pick, there ar...

We are given that Karen got 38% in her English test, so all that's left to do is work out the percentage she achieved in her maths test and then compare it with 38%: We calculate the percentage by taking ...

Define the original cost as 100%.

So £16=85% (100-15) of the original cost.

Find 1% of the original cost by dividing both sides by 85. 

16/85=85/85%

To find the orginal cost, 1...