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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
4323 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
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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
7291 Views

What are buffers and how do they work?

Buffers are solutions of acid and base which work to minimise changes in pH following the addition of small amounts of acid or base. Ideal buffers are made of a weak acid (i.e. one which does not fully disso...
SJ
Answered by Samuel J. • Chemistry tutor
8483 Views

Which compound has a higher boiling point and why: water (H2O) or methane (CH4)?

Water has a higher boiling point because the hydrogen bonds that form among water molecules are stronger than the Van der Waals interactions among methane molecules, thus more energy must be provided in orde...
MD
Answered by Maria D. • Chemistry tutor
43437 Views