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Firstly differentiate the function V with respect to x (dV/dx)=pi*(40-2r-3r^2). Set dV/dr =0 and solve to find r. Divide both sides by pi and divide both side by -1 so that the r^2 term is positive (I per...

To sketch any modulus function, we begin with the sketch of the function itself, y=ln(x). Notice that the question asks for the graph of y=ln(|x|) and not y=|ln(x)|, this is an important distinction.recal...

We can see that (3x + 7)² is a 'composite function'. We can rewrite this as g(f(x)), where f(x) = 3x + 7 and g(x) = x². As you will have learnt, you will need to use the chain rule f...

Last digit of n determines last digit of n^4. All even numbers divide by 2, so are not prime. Any number ending in 5 is a multiple of 5 so is not prime. Primes > 5 end in 1, 3, 7 or 9. If n ends in 1, ...

Many students at first will incorrectly separate the fraction into two fractions in the form of A/(x + b) + B/(x + b). If we then multiplied the two back together we will find that it does not equate to t...