Search over 10,000 free study notes

The sphere has radius Y, so the volume of the sphere is 4/3 (pi) Y³ , The volume is the same for the cyclinder so we know the volume of the cylinder in terms of Y. Cyclinder volume = area of ci...

First of all, we need to show that the statement is true for the base case n=1. For this case the expression becomes: 1+p≥1+p, which is clearly true as both sides are equal and hence solve the inequality....

Pythagoras's theorem is used to calculate the lengths of the sides of right-angled triangles. The theorem can be used to find the length of the third side of a right-angled triangle, as l...

Here, f(x)=x³e^2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(...

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the f...