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A metal Sphere of radius Ym is melted down and remade into a cylinder of the same volume with height Ym with circular ends of radius 3m, find Y

The sphere has radius Y, so the volume of the sphere is 4/3 (pi) Y 3 , The volume is the same for the cyclinder so we know the volume of the cylinder in terms of Y. Cyclinder volume = area of circle face x h...
JC
Answered by James C. • Maths tutor
3508 Views

Given that p≥ -1 , prove by induction that, for all integers n≥1 , (1+p)^k ≥ 1+k*p.

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. Ne...
EB
6412 Views

What is Pythagoras's theorem?

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 long as the lengths o...
SJ
Answered by Samuel J. • Maths tutor
4305 Views

How would I differentiate a function such as f(x)=x^3(e^(2x))?

Here, f(x)=x 3 e 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'(x)+u'(x)v(x). The firs...
LB
Answered by Lauren B. • Maths tutor
3887 Views

Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

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 frac...
OG
Answered by Omar G. • Maths tutor
7275 Views