studiot

That is why I prefer exams to continuous assessment. The route is not as important as the destination so the learning process should not be marked so long as you get there in the end. By the way did you understand what I said, and now know which is not Lewis and why?

You learn more from your mistakes than from your successes !

Carbon, hydrogen, oxygen, chlorine. One of these has the wrong number of bonds.

There is a substantial electric field within liquid water. That is why hydrogen bonding is so important in water.

How many times can you test something to destruction ? Not always, no. There are indeed questions mechancial (and other physical) questions that can be asked but have no mathematical formula to answer them. These have to be answered by a (suitable) process. This whole question is self contradictory. There is no exact meaning. Any further the meaning is changing over time. Bacon was different sort of scientist from Newton, who was a different sort of scientist from Thomson who was.... You might just as well ask What does "plumber" mean ? Modern plumbers do very different things and work in a very different way, from plumbers of even just 50 years ago.

Would like to hear how you got on with this one ?

I don't see any justification for the first statement, (Which is think is wrong because of carries as below) I don't understand the second statement at all. The following beginning analysis may help, Start with two nine digit numbers XXXXXXXXX and YYYYYYYYY. Allow all digits 0 through 9 including leading zeros, which will take care of the possibility of the actual numbers having less than 9 digits. The last digit is a zero so consider all possible pairs that can result in a zero. Strike out those that have a factor from the disallowed list. [math]\begin{array}{*{20}{c}} {Pair} \hfill & {Divisor} \hfill \\ {\left\{ {0,0} \right\}} \hfill & 2 \hfill \\ {\left\{ {1,9} \right\}} \hfill & - \hfill \\ {\left\{ {2,8} \right\}} \hfill & 2 \hfill \\ {\left\{ {3,7} \right\}} \hfill & - \hfill \\ {\left\{ {4,6} \right\}} \hfill & 2 \hfill \\ {\left\{ {5,5} \right\}} \hfill & 5 \hfill \\ \end{array}[/math] Hence the last digit (of each number) can be chosen in 2 possible ways (as Tina says ) but However since both add up to 10 there must be a carry to the next digit. Also all possible last digits are now odd so from no on no number will be divisible by 2. Since there is a carry, the two digits must add to 6 or 16 Listing these as before [math]\begin{array}{*{20}{c}} {Pair} \hfill & {Divisor} \hfill \\ {\left\{ {0,6} \right\}} \hfill & - \hfill \\ {\left\{ {1,5} \right\}} \hfill & - \hfill \\ {\left\{ {2,4} \right\}} \hfill & - \hfill \\ {\left\{ {3,3} \right\}} \hfill & - \hfill \\ {\left\{ {8,8} \right\}} \hfill & - \hfill \\ {\left\{ {7,9} \right\}} \hfill & - \hfill \\ \end{array}[/math] Which yields 6 possible pairs, not 3 as Tina hopes I will leave it to you to decide if any further divisors can be eliminated

When ciritcally assessing your sources I suggest you use some simple criteria. For instance you seem to be suggesting that the Himalaya is billions of years old. Yet we know that there are no rocks of this age there. The oldest rocks (in South Africa, Canada and Australia) are a long way from the biggest mountains - the Himalaya, Andes, Rockies.

The point is that prime no prime number greater than 23 is divisible by any of the first 9 primes. So each prime number and its pair which adds to make 223092870 will be candidates for inclusion and so must be checked. and there are a great many prime numbers up to 9 digits long. But added to these are numbers which are not prime yet still not divisible by any of the first 9 primes such as the example 2419 I gave. All of these must also be checked.

Why are you suprised? Yes, you made a valid comment that the problem is ill defined. But you also made an invalid one about irrational numbers in your examples. Yes I also made an invalid one, which joigus picked up and I immediately corrected. We all make mistakes; we all need to admit them. Well this is one very long way to do it since that is only a beginning, not a solution. There are plenty of primes less than your criterion for example the 1,000th prime is only 7919 Further there are other non prime numbers not divisible by your set eg 2419 is not prime nor divisible by your set.

A pity you spent so much effort putting all this wild speculation into a computer without considering the majority of the evidence. This belongs in Speculations at best.

I think you will find it's the Froude number you need. A typical analysis might study the 'force' (called specific thrust) needed to halt the stream at a stagnation point. Fanno and Rayleigh curves can be drawn from this approach.

Counterexample: π is irrational; 1−π is irrational too. but π+1−π=1 . Nice one. +1

pdf files are documents for reading , they are not videos for watching. ph.ed.ac.uk is the postgraduate Physics department of the University of Edinburgh.

I did look at this one, but I am sorry to say that all of us have parts of our subject we like more than other parts. And amongst my personally least liked parts are combinatoric and number theory. There seem to be several problems of this type going around at the moment. On another (maths) forum they have been debating this simpler one for a couple of weeks now. and this is only a four digit number. The one here is a nine digit number so I would expect candidate numbers for addition to be of the form xxxxxxxxx + yyyyyyyyy Which has a lot more combinations. This really is problem that lends itself to a computer solution so I am suprised at Sensei's response, which is incorrect. since the last digit is a zero, there must be a carry so possible choices for pairs in the last positions are [0,0}, {9,1} , {8,2}. {7,3), {6,4} and {5,5} So {x,y} can be selected in 6 different ways. But any number ending in a 5 is divisible by five so the last one can be discounted. Further reduction can be had by noting that any pair containing an even number can be discounted as divisible by 2, another orignal factor. You can work through the digit pairs to find out how many possibilities there are for each other pair. Then multiply these together an see the final result, using the laws of combinatorics. Tina please note this first result and compare with your answer. I don't think there are any two irrational numbers that can be added together to make a rational one. In any case none of these are irrational.

I'm glad to see you came through today's R scale 7 earthquake, hopefully you were not too badly affected. Since your internet is still working here are a bunch of 4 lectures in pdf that should help you with English Maths terminology. https://www2.ph.ed.ac.uk/~ldeldebb/docs/QM2/chap1.pdf Note the chapter numbers at the end. Change these from 1 through 4 to get all 4. Chapter 4 (Rotations) is particularly relevent to this thread. In particular you should note the difference between finite rotations and continuous rotations in dimension theory, vector theory and calculus.

Nice picture +1 sorry I can't offer any corrections, I basically agree with everything you have said. But I can offer some more thoughts. 1) Shock waves are impossible in a truly incompressible fluid since the speed of sound in such a fluid is infinite. Water, of course is not truly incompressible. How ever John's rocketsubmarine would encounter other effects. In particular you would get flow separation between the compression half cycle and the expansion half cycle. In the compression half cycle ice would form around the sub. In the expansion half cycle the solid and liquid would not expand to fill the void. Cavitation is indeed an issue. It is worth noting what a 'shock' wave is. It is a discontinuity in the pressure field across a very narrow region. Such a discontinuity entails an enormous value for [math]\frac{{du}}{{dx}}[/math] so that even for a low friction substance such as water viscoscity effects would be significant. The second law of thermodynamics requires that entropy does not decrease across the shock. Since entropy is proportional to [math]\ln \left( {p{p^{ - \gamma }}} \right)[/math] ift follows that [math]\frac{{{p_2}}}{{{p_1}}} \ge {\left( {\frac{{{p_2}}}{{{p_1}}}} \right)^\gamma }[/math] Finally an alternative view is that of specific energy -- The energy per unit volume (or mass) of the fluid. Consider a flow regime and gradually increase the flow velocity. The specific energy increases as a result. At some 'critical' point the specific energy exceeds the ability of that flow regime to sustain it. So there is an abrupt change to a different regime. In liquids this is responsible for phenomena such as the hydraulic jump, which does not occur in gas dynamics.

Sorry I messed up there. The equation you want is [math]HLB\left( {oil} \right) = \frac{{{W_A}*HLB\left( A \right) + {W_B}*HLB\left( B \right)}}{{{W_A} + {W_B}}}[/math] Where A refers to the first surfactant and B to the second. However the values of HLB you quote give the (not) suprising result that you require no tween at all. Are you sure you posted the correct HLB values ? Trying to look up olive oil values it looks as though your span20 value is too high, you need something below 6 The span and tween components are supposed to be chosen so their HLB values bracket the oil HLB value.

You need to start by finding the required HLB for the combined emulsifier. Have you done this ? - I made it 12.65

Thank you for your thoughts. Perhaps that is why I have never come across a 'permanent battery', except as an idealised voltage source in a circuit diagram. However such a source could indeed be arranged to power a pendulum. I did not take permanent to mean inexhaustible however, I took it to mean fixed in polarity, given the rest of the text. Perhaps I was wrong.

But you posted it here so you are responsible for explaining it here. You also praised Sternglass, whose words I assume you understood. I am simply asking what (you think) is meant by them. Since I don't know what is meant I can't say whether I think that is right or wrong or possible or not. Sorry but those are the rules here.

Edit Nothing you have said is wrong but How does that have any bearing (pun intended) on my question ? I wasn't discussing Friction.

I'm having difficulty understandiing what you mean by this ?

Forth is just one of the reasons I have such a jaundiced view of arguments about programming languages. I've seen them come and I've seen them go And the cycle repeats And each cycle the same mistakes repeat.

Why not ?