FugueDude

If v ≡ v(s, t) express (∂u/∂s)_v in terms of the partial derivatives of u(s, t) and t(s, v).

To gain full marks you must make clear which variables, if any, are held constant

in any partial derivatives which feature in your answer.

Thanks!

f(x) = a_0 / 2 + sum from 1 to infinity of (a_n*cos(nx) + b_n*sin(nx))

What can be said about the coefficients a_n and b_n if f(x) has the following symmetry?

f(x) = f(pi - x)

f(x) is just a general function and there is no other information given in the question.

I have another few questions very similar to this but hopefully seeing someone's solution to just this one will be enough help!

Thanks.

So, I've always thought of work done as being the change in energy of a system (which seems to have worked for solving problems so far), but have just found out the formal definition is that it's just the change in kinetic energy.

What I'm now confused about is that the work done against gravity is mgh - but if you are just raising a mass higher in the gravitational field and bringing it to rest at the top, surely that would mean the work done is zero as it both started and finished at rest?

Thanks to anyone who can help clear this up!

Any help on how to evaluate this sum, using complex numbers, please? Thank you!

OK - here is an example I've been given of using Leibnitz's formula (link below). Could someone please explain how exactly you get from the 3rd line to the penultimate line? Thanks a lot for any help!

http://tinypic.com/r/35hiyja/6

I'm wondering how many peaks the C13 NMR spectrum of this compound would have (http://www.chemspider.com/Chemical-Structure.22987... My guess is 4, but I'm not sure how the non-rotatable C=C bond affects it. Thanks!

More generally for any number N, how many base b digits are needed to represent it if it takes k base c digits?

Thanks for any help!

I know that f'(x)/f(x) integrates to ln|f(x)|, and that the modulus signs are necessary to avoid taking the log of a negative number, but I was just wondering why exactly it's OK to just add the modulus signs in, as I've never actually seen any justification of this... Thanks!

Just a quick question about this sort of problem, involving writing a sum of 2 trig functions as a single one. Let's say I have to write sqrt(3)sin(x) + cosx in the form Rsin(x+a)... I know how to use the usual method to get a = pi/6 and R = 2, but was wondering why you can just dismiss the case R = -2, since the previous step would be obtaining R^2 = 4. Obviously both can't be correct at the same time, but there must be a good reason for ignoring the negative root, I just can't figure out why!

Thanks for any help :)

So, I've just been reading (in "Foundations of Science Mathematics") about the vector equation of a plane, in the form

(r . n) / |n| = (a . (b x c) ) / |n| = D

Where D is the perpendicular distance from the origin to the plane. But I also thought that if a, b, c were coplanar, a.(bxc) = 0 ... so surely this always gives D = 0?!

Thanks for any help you can give, just need a bit of clarification here!

Given that p = logq (16), express in terms of p:

a) logq (2)

b) logq (8q)

(By "logq" I mean log to the base q)

A body of mass 2kg is held in limiting equilibrium on a rough plane inclined at 20° to the horizontal by a force Y acting at an angle of 45° to the horizontal. The coefficient of friction between the body and the plane is 0.2. Modelling the body as a particle find X when the body is on the point of slipping

a) up the plane

b) down the plane

Basically I have tried this 3 or 4 times, I keep getting 10.48N but apparently it's 43N (for part a). I'm trying to resolve horizontally/vertically and my equations are

h: Ycos45 - 5Fsin20 - Fcos20 = 0

v: Ysin45 + 5Fcos20 - Fsin20 - 2g = 0

(R = 5F since F = 0.2R)

So, can anyone help with this - where have I gone wrong?

The gradient function of a curve is given by

dy/dx = a + bx

Find the values of a and b and the equation of the curve given that it passes through the point (0, 2), (1, 8) and (-1, 2).

I'm not necessarily asking for someone to do the whole question but if you could just point me in the right direction I would be grateful!

I know C++ pretty well but just decided to start learning python. I understand that if I want something equivalent to:

for (int i = 0; i < 10; i++)

I would write:

for i in range(10)

But I have 2 questions - firstly, what if I wanted a different increment size... ie, what would be equivalent to:

for (int i = 0; i < 10; i += 2)

And also how would I make the iterator decrement instead - as in:

for (int i = 9; i >= 0; i--)

I've been enjoying using Notepad++ recently, and have found the autocomplete function really useful for the standard functions in C++.

However, I was wondering whether it's possible to somehow get autocomplete for functions in other APIs? In particular I'd like to use the Win32 API.

I'm just a hobbyist programmer and have recently been teaching myself about programming (in C++) with the Windows API and with DirectX... from books, and the internet.

The thing is, when I'm learning the stuff I generally understand what's going on, but don't remember it all because there's just so much code, even just for initialising! Is this anything to worry about?

My question is, does anyone actually memorise all of this code, or do they tend to write some working code and just save it in a file which they can edit when needed? Could a professional who works with DirectX just sit down and write a program without reference?

I'm currently programming a game (just for fun), called "Nucleus", in which you control an atomic nucleus. There will be 20 levels, and in each one you have to collect that number of electrons to become a certain atom (eg in level 3 you have to make lithium). I'm treating each "group" on the periodic table as a "world" in the game, i.e each world has a different colour scheme and different music.

The trouble is I'm having problems coming up with good ideas for enemies / obstacles / pickups etc. At the moment I have little "guns" which fire neutrons at you causing you to decay, and doors which are opened by pressing buttons. But I need more ideas, so I'd appreciate any help I could get!

Here's an example screenshot so you can get an idea of what it's looking like:

http://yelvy.com/fuguedude/Boron.png

Another easy question - I have to solve

0 = 8x + x^-2

And wasn't sure how to do it... Could I just multiply by x^2 and get

8x^3 = 0

x = 0

If not then how would I go about solving it?

I'm a bit stuck on this differentiation question.

The first part was to differentiate x - 6x^-1 + 9x^-3 ,

For which I got 1 + 6x^-2 - 27x^-4 (I'm fairly sure this is right)

I now have to "verify that the graph of y = f(x) has stationary points at x = +-sqrt(3)". I know I have to solve dy/dx = 0 but that's where I get stuck!

Here's where I got up to:

0 = 1 + 6x^-2 - 27x^-4

0 = 1 + 3x^-2(2 - 9x^-2)

Thanks a lot for any help you can give me!