JaKiri

The basic idea behind the question is to solve the problem not through the application of simple differential calculus, but through an algebraic solution working from first principles. We don't need to do anything to your account, unless you really want the email address its bound to back.

You're misinterpreting how chemical reactions work. When you're dealing with metals and nonmetals, you're looking at a change in ionisation state; one becomes a positive ion and one becomes a negative ion. The only real factors, therefore, are how easily one gives away an electron, and how easily the other accepts it; based on the electronegativities (link) we can see that Lithium is the least reactive of all the Group 1 metals, increasing towards Francium. This is varified by simple experiments involving the metals themselves; as YT says, but Li in water and it will fizz, put Caesium in water and it will explode. What the size of the atom does affect is the ionic character of a bond; with something like Francium, the overall charge is the same as Lithium (+1), but because of the distance, because of shielding electrons, the force between the metal ion and the nonmetal ion is much less for the larger ion, meaning that it acts more and more distinctly from its partner, whereas Lithium compounds tend to act strangely (compared to other metal compounds) because they're more covalent in character.

There's so much wrong with this I can't begin to fathom how to start my reply. Most notably the notion that 'This country invaded us, killed and tortured our people, destroyed our power and water supplies and has done most of this SEVERAL TIMES' isn't a one that will provoke people to terrorist actions. Furthermore, the idea that instabilty in Iraq would be localised; people can travel outside their own country you know, and besides, creating another nice theocracy in the Middle East will surely solve all the problems out there.

If our society seems more nihilistic than that of previous eras, perhaps this is simply a sign of our maturity as a sentient species. As our collective consciousness expands beyond a crucial point, we are at last ready to accept life's fundamental truth: that life's only purpose is life itself. -- Chairman Sheng-ji Yang "Looking God in the Eye"

You're covered TO AN EXTENT. I believe you can sue the seller for misrepresentation of goods, but if you're trying to get money back from ebay/paypal itself, then you're only going to get 1/20th or so.

Well, you showed me.

You're tool cool for us, we'd better get off this internet before we're exposed as noncool.

This wasn't exactly unexpected. In other news, I see Afghanistan is a cradle of democracy.

Yes it would, you're putting energy in.

In general, the problems people are having are because you're assuming people are going to make logical leaps; the '1's in the first example, for instance, aren't going to be 'obviously' from the initial coords unless you really understand what's going on, which isn't the target audience. My suggestion would be to do each step in 2 stages; a generic version, followed by subbing in the values, which will give people more of a clue what goes where.

Yeah, editing.

That is most definitely wrong; especially given the universe is expanding at sublight speeds (at the moment, as far as my memory tells me)

Well, the main mistake is that it's not always h+1. It's h+5 in this case, as that's the x coordinate you're working with; so, the numerator should be (1/(h+x)^2) - (1/x^2), or 1/(5+x)^2 - 1/25 and the denominator should be (h+5) - 5, not (h+1)-5.

Where n is the x coordinate of the point you want to find ((d+n)^2 + n^2) / ((d+n) - n) = (d^2 +2nd + n^2 - n^2) / d = (d^2 + 2nd) / d = d + 2n As d -> 0, gradient -> 2n.

It's the english way.

Ding. A man walks into a bar and says 'I'll have a pint of Adenosine Triphosphate please'. The barman says 'Sure, that'll be ATP'

You've explained yourself really badly here. The denominator will always be (where n is the initial x value) (x+n) - n Not (x+1) - 1. This may partially explain people always having 1 as the 'base' value, despite the questions being based around 5.

My eyes need the exercise.

This joke thread is abhorrant to me. It doesn't contain the ATP joke.

I really want to know what an Ackman is, and why there's a huge one about.

I've always wanted to work in the field of Bioterrorism. ALLAH ACKBAH*. *it's a TRAP

Mainly because that doesn't look like the method at all. The method is from setting a point (in the eg. (1,1)) and then finding the gradient of a point 'h' away from it on the x axis, and finding the gradient as h -> 0. You don't set h as a value and solve it, you set the initial value to (5, 125) and solve it, rather than (1, 1). The limit as h -> 0 is the answer, not some crazy subbing with h. SPOILER! (spoiler tags please sayo) ( ((d+5)^3 - 125)/((d+5) - 5) = d^2 + 15d + 75, as d -> 0, approximation of dy/dx -> 75, as required)

Good thinking that man. The Emp's New Mind (Roger Penrose) is mostly about AI, but it touches on literally EVERYTHING ELSE.

Ding ding ding. Weight =! Mass. Weight is the force caused by mass being acted upon by the force called 'gravity'. For the simple version, F = GmM/d^2 (I can't be having with these crazy 'proper equations'), combined with F = ma. F is the force, G is the Gravitational Constant (gravitational constant = 6.67300 × 10-11 m^3 kg^-1 s^-2, thank you google), m is the object's mass, M is the mass of the big object (the earth in this case) and a is the acceleration, in this case the value 'g' (acc. due to gravity). F = mg Therefore mg = GMm/d^2 g = GM/d^2. This shows the accel due to gravity is independent of the mass of the object, as famously demonstrated by Galileo. Back to the topic at hand, energy, Work done = Force x distance = mgd (height moved x force due to gravity) = GMm/d. E = mc^2, on the other hand, has little to do with gravity, and is more of an equivilency when you're changing between 'mass' and 'energy', most usually when you're talking about nuclear binding energy in atomic reactions (well, that's when I've used it the most anyway.)

I think we have that covered as well.