studiot

Perhaps unfortunately, perhaps fortunately the user is not at liberty to take the laws of any universe any way he or she likes. A closed box to simulate an open system? Grow up and read some textbooks before continuing this discussion.

Before you can invoke the laws of thermodynamics you need to define your system and decide whether it is open, closed or isolated. The laws have different implications for these. The issue of whether the universe is a closed or isolated system has been undecided for about two and a half centuries.

If you don't mean filled then I suggest you say "populated with particles such that......."

I'm having great trouble following this. Where did b come from? Do you in fact mean the option you have labelled 2? If the universe is filled with particles how can any of them move? The idea that the second law requires gravity is nonsense. A simple counterexample would be allotropy where substances change their crystal structure and therefore their entropy without reference to gravity. Your title suggests that you also have a beef with the first law, but I cannot decipher your penultimate paragraph or how you get from "we are left with the first law" to your alleged beef with it.

How to perform a quick check of your work? Well boolean variables can take on only two values viz 0 or 1. So assign values to A, B, C, D ...etc and substitute In your case let A=B=C=D=1 your expression comes to 0+0+0+0+0+0+0=0 or let A=B=C=D=0 your expression comes to 0+0+0+0+0+0+0=0 So any equivalent expression must evaluate to the same. However this check is like an accountant balancing the books, it is not perfect. That is if the expressions disagree there is definitely a mistake somewhere, but if they agree there is no guarantee that you have not made self cancelling mistakes.

D'CB is correct. You are getting there. Now what do you see if you add what you got from simplyfying the second and third terms to what you got in post 12? D'C'B + D'CB Can you take the next step with these pairs? ie which variable can you eliminate next? You will then have reduced four of the seven terms to 1. Not bad going. But I must leave you to work on the others a bit we do not do all your work for you here.

The second does not follow from the first, since you have one A' and one A How about trying the fourth and fifth terms?

A,B, C, D, E, F , elephant, monkey, tangerine are all dummy variables the same rules apply to them all. So where I have written A you could write any other variable and the same for B or C etc. The only restrictions to order are as I outlined in my list of rules. So yes, take the first and last if you like, though I recommend seeing what you can make of the last two terms. Can you simplify them together?

Yes indeed. So does that not simplyfy the second and third terms combined? You need to play with this idea and see how far you can simplify things this way. I will be away for about half an hour now so happy playing.

Come on, can you not start collecting terms together and simplifying? You also have a bunch of more basic rules like A.A=A A+A=A A.1=A A+A'=1 AA'=0 (A')'=A A+B=B+A A+B+C=A+(B+C)=(A+B)+C ABC=A(BC)=(AB)C A(B+C)=AB+AC So for instance in your example you have D'C'BA+D'C'BA' =D'C'B(A+A') and what is (A+A')?

Do you know the rules of boolean algebra as algebra? A+AB = A A(A+B)=A A(A'+B)=AB A+A'B=A+B A+BC=(A+B)(A+C) (AB)'=(A'+B') A'B'=(A+B)' The last two make up De Morgan's Theorem. Alternatively you could use Venn Diagrams.or switch diagrams

You will have to ask your dad what the glittery brown stuff is. I would guess that as you compress the powder the shiny grains rub together and rub/grind off some fine powder that coats the grains making them dull. I don't know what your science experiment does all together, but an interesting variation might be to consider what happens with some hard beads that do not squash down. If you look carefully there are large spaces between the beads that you cannot fill unless you have some particles (grains) of different (smaller) sizes to go into the gaps. Between these smaller particles there will be again smaller gaps that need even smaller particle to fill and so on. This process is called grading in earth science. It also appears in materials technology like concrete and in chemistry in crystal structures, so is worth looking into if you are interested. go well with your project.

Gosh it's running so fast now my head is spinning. Do we have to pay extra for the speed? Oh it's free. Well do we get paid extra for rushing about chasing pages at this speed?

Did you not learn the algebraic procedure for extracting square roots in primary or early secondary school? Its comparable to long division. Which is much much easier than finding the third order coefficient of a seven digit number by hand, as you suggested earlier. Interpolation? Who said linear interpolation? I was referring to at least Newton's forward difference method. As a matter of interest there are many right triangles with integral sides containing the right angle that can yield many way points on the table quite simply.

Personally I find it ideally paced. I just go for a nap between webpages. I do like that icon.

So should I edit the post to read 1.3372986 rads? The value was chosen at random. Did you not understand the point I was making?

Is there a difficulty here? I don't see it. However I apologise for not noting that strictly the angles should be measured in radians to use the small angle approximatuion. However the OP did say without a calculator. Series answers are all very well but get quite hairy quite quickly on say 0.3372986 rads. So I would recommend constructing a table like mine with as many known points as possible and then learning to interpolate. This is, of course, the actual method by which tables were originally constructed and used. Series methods are just too laborious.

If you want to let off steam, go down the gym.

Kirchoff's rules have little or nothing to do with bar magnets and induction. That is Faraday's law. Kirchoff's laws enable you to solve (linear) electrical circuits for voltage and current, given the connectivity between components.

The attraction/repulsion effect is due to the magnetic field developed by the travelling charge (electrons). In the case of a wire is takes the form of concentric circles around the axis of the wires. In my sketch the wires are perpendicular to the plane of the screen. I have drawn a couple of circles of the magnetic field lines. Obviously they combine to form a single field. You should draw some for yourself to see how the reinforce in some areas and cancel in others, due to their directions.

It's really the other way round. You have a line of force and define a surface to which that line is normal, and passes through. If you defined any slant surface then the effect (integral) over the that surface would be the same. Gauss theorem relates to the projection of any slant surface onto the normal one as equivalent.

Here is a simple table for basic important angles for sin and cos; tan, of course, is sin/cos. The table values are exact. You can make a more complicated table for multiples of 15 degrees. Remember also that for small angles sinx = tanx = x.

Hello einstein (I've always wanted to say that), Your apparatus does not demonstrate metamorphic rocks I'm afraid. It sounds like it does a good job of demonstrating sedimentary rocks however. Metamorphic rocks are subject to extreme temperature and or pressure. The temperature may be as a result of the pressure or it may be as a result of contact with very hot molten rock coming up from the interior, with little or no pressure involved. Either way the temperature is enough to cause (partial) melting and recrystallisation of the material to form the metamorphic rock. This is usually involve chemical change. Sedimentary rocks, on the other hand are simple compressed material laid down under the pressure of stuff above. It may be that some sort of binding material comes out of solution as lakes or seas evaporate and cements the otherwise non sticky particles together. There are all sorts of iffs and buts, but this is the basic outline.

The original problem was posted as a simple exercise in potential flow theory. But we do not do peoples homework for them, only guide them (hopefully) to a solution. Of course that requires their cooperation. Not all do so.

I did talk about reinforcement. Western structures use reinforcement in general. But carbonation can be a good thing as it leads to a stronger harder mass material, even if that does not protect any steel present. Scientific American did an article a few years back on this, showing some amazingly strong Aztec structures and citing modern research into artificially inducing carbonation in mass concrete by using carbon dioxide injection. Sorry but I don't have the reference any longer but it was in the mid 1990s.