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In the question we are given that a + b = 20 where a and b are positive integers. Remember this.First let y = a^2 b. This is a good starting point as we have an equality now which we can mess with.We want...

This question is takes from the 2008 STEP I paper (Question 8). We are first given (dy/dx)^2 + x dy/dx + y = 0 where y is a function of x. Differentiating both sides of the equation with respect to x, giv...

Sin, cos and tan are functions that help you work out either, the missing angle or one of the missing lengths of a side in a right angle triangle.To work out the missing angle you need two side lengths, d...

b = (2a + 5)/3 Step 1 - Multiply both sides by 33b = 2a + 5Step 2 - subtract 53b - 5 = 2aStep 3 - divide by 2(3b - 5)/2 = a

There are several approaches to integrating this function, thus making this a valuable exercise for students needing to develop fluency with the various techniques of integration and practise dealing with...