studiot

Good on you. +1 It was noted in the experimental link that Do you agree with this ? If so or not why ? Whay was the lift angle chosen to be 30 degrees ? What difference does it make if any ? The pendulum is one of those experiments that can offer much more insight than just verifying the period formula. Why was twine used as the suspension method and would other methods perform differently ? Note pendulums clocks often have rigid bar support arms. Other aspects of this experiment are being discussed here. Scroll down the page to the sketch.

I wondered if you would notice that so wel spotted. If you will indulge me until next time we will return to the more difficult uses of sigma and its whys and wherefores. I mentioned vectors and einstein last time so please take a look at this webpage which is the source of this picture about vectors in 3 dimensions and their components, using XYZ axes http://emweb.unl.edu/negahban/em223/note4/note4.htm There lots of useful graphics, but can you spot the difficulty (clumsiness really) they get into using XYZ ? Don't worry about the rest of the maths, but it is a good page to refer to in the future. Note they make use of sigmas. We can then return to answer your question about r2 and also see if we can improve on the XYZ issue. We can use it

Alas, Alac, poor Joe His voice we'll hear no more. For what he took for H2O Was H2SO4

Ah I see, thank you I will give it some thought.

I see you are a new member so welcome. 😀 Can you elaborate on what you want ? The standard works for these are Roark's Formulae for Stress and Strain and Kleinlogel Rigid Frame Formulae. How many handbooks and textbooks contain shorter tables eg Fiona Cobb The Structural Engineers Pocketbook

The usb interface was designed to be safe for hot disconnection/connection with the original devices it was designed for such as cameras, printers, scanners.. which have safe reset on powerdown/up. It was not designed for hard drives. So hot connection/disconnection capability depends upon the connected device. And as you say hard drives should be 'ejected' properly. +1

I'm not being awkward, but what you are attempting is still not clear to me. Classical geometric construction is not coordinate geometry. It starts with a blank sheet. So what do you mean by the centre is known ? And what do you mean by I don't have a ruler ? I'm only trying to help after all.

Don't worry, it is tricky. So I haven't told you all of it. I am trying to do it in bite sized chunks. When you get to the level of Einstein you can dispense with the sigmas altogether, using what is known as the einstein convention. Sadly this is where you will most likely come across the need. Anyway. Yes you can use any letter, but n is by far the most common, followed by i. Remember they are the index, which tells you how many terms you are adding up or how many times you are repeating the formula with differnt values. That is why they have to be integers. Yes the bottom one is the start point (0 is often acceptable but adding zero doesn't add much) And the top one is the last or end one (unless it is infinity where this is no end) Yes that is correct, Gold star point. I will come onto vectors because that is your most likely use. No it is simply a number, but I call it after the sigma not infront of (ie not before) Yes they do end up with a single output, but you will see when I do vectors the formulae are more complicated. I wish . I did invent one once and actually thought about going into production. But there are too many obstacles in blighty. https://editor.codecogs.com/ or https://www.sciweavers.org/free-online-latex-equation-editor

Chemistry is messy. What a suprise. 😀

Well yes the tangent is perpendicular to the line joining the centres. So it can be constructed as a perpendicular line anywhere along the common centreline. Two things. Firstly constructed using a ruler and compass has two variations. The otiginal strict meaning was that the ruler could only be used as a straight edge, not for linear measurement. These days many relax that and allow the use of the ruler as a scale device. Secondly you haven't mentioned if you know the diameters of at least one of the circles ?

Physicists like atoms whereas chemists like molecules. This book about the story of the molecule is fascinating. John Buckingham is an organic chemist and a pharmacist.

OK so the symbol is the greek capital letter sigma and represents what is called a continuous sum. It is really an instruction not an equation by itself, although it can form part of an equation. Some examples might help. [math]\sum\limits_{n = 1}^4 {formula\;involving\;n} [/math] This is an instruction to form the sum of the squares of the foirst 4 integers ( 12, 22 ,32 and 42 ) [math]\sum\limits_{n = 1}^4 {{n^2}} \;which\;is\;1 + 4 + 9 + 16 = 30[/math] n is an index for the formula and runs from n = 1 through to n = 4 Lazy folks may abbreviate this a bit to [math]\sum\limits_1^4 {{n^2}} [/math] This is a finite sum (n is finite) comprising only 4 terms. Sigma may also be used to symbolise an infinite sum or sum to infinity. [math]\sum\limits_{n = 1}^\infty {formula\;involving\;n} [/math] This sum may be used in an equation if there is a formula that gives you the answer directly [math]\sum\limits_{n = 1}^4 {{r^2}} = \frac{1}{6}\left( n \right)\left( {n + 1} \right)\left( {2n + 1} \right)[/math] Note capital sigma should not be confused with little sigma which is used for an entirely different purpose. Sigma is for summation. There is similar symbol for multiplication called continuous products. This uses the greek capital letter pi insteat of sigma, but works in the same way. I am using the star to indicate multiplication [math]\prod\limits_{n = 1}^4 {{n^2}} \;which\;is\;1*4*9*16 = 576[/math]

Did you mean this ? Not quite sure what you mean, but yes I did say that waves could travel through material objects. Incidentally the word particle has special significance in Physics. Very many different areas on Physics have models or theories that rely on the interactions of huge numbers of very tiny elements which are called particles. They are the smallest bodies or bits of the subject theory that we can consider as acting as individuals and interacting with each other to produce the observed physical phenomena. These theories don't inquire as to what is inside the particle, just how it interacts with the others. We spent nearly 2000 years developing th idea that the smallest piece of matter is called an atom. Then at the end of the 19th century scientists began to realise that the atoms may be made up of yet smaller bits., which became known as sub atomic particles. That is the famous history. But in the 1930s a quiet revolution occured that is not so famous but perhaps even more startling and revolutionary. They found out that there are 'particles' small enough to be sub atomic, but that never appear as part of an atom.

Not a good way to think of it. It takes two to tango. Gravity is a phenomenon that takes place between two or more objects. Since most objects have an actual size, the various parts of that object display that phenomenon between each other. Gravitational Potential is an imaginary field that records the strength and direction of that phenomenon at any point in the field, were we to place a material object there. But until we do it remains imaginary, which is why it is called potential.

Thanks you have taught me a new word and facts about I subject I am pretty ignorant of. +1

Firstly can we be assured that this is neither for a competition, homework or coursework ? Given that, A cone is surface generated by a pencil of lines passing through a fixed point and intersecting a fixed closed curve. There is a closed form analytical formula for the cone in 3D when that curve is a conic. Since a conci is a plane curve, you can take advantage of that by splitting the cone into two parts along the lines that genady has already mentioned. You need to make your splitting plane parallel to the Z axis. Then the conic is a circle in the xy plane. The radius may then be found by using the fact that the radius equals the Y coordinate at Z = 0, in this plane. Ref: Longchamps Problemes de Geometrie Analytique vol3

You should read him G I Brown's book for bedtime reading. 😀

Clearly there is a glitch in the translation from Russian to Emglish. A trick question (which is what is I said) is designed to mislead or trick. A tricky question is more simply a difficult one in some way. So I repeat my assertion that any intention to mislead would be challengeable in English. Your AI (or LLM ) is just plain incorrect. It is indeed a maths question not general parlance, and was posted as such. However in mathematics Incidentally it was too difficult to access your scoop link.

I certainly agree. +1 In any mathematics course I have ever attended a question in which the provided diagram did not match the wording would be considered ill posed and void. I have seen 'trick' questions like this in psychologcal evaluations though. But of course the evaluator is not interested in the real answer, just the reaction of the candidate.

Well sort of. Density functions like charge density and mass density are not Lorenz invariant. Suppose an observer is at rest relative to a row of charges or mass points, strung out along a line at equal spacing. This observer will observe exactly that. A line of charges or mass points. The stationary observer does not see a magnetic field in either case. Now consider an observer passing the line at speed. The travelling observer sees the same number of points but, because of length contraction, sees the charge density or mass density differently. With the elctric field the travelling observer experiences a sideways force that he interprets as magnetic in origin. The two mirrors is not a bad 'guess', although you only need one mirror. Actually the wave can either penetrate the matter (refraction) or reflect off it like a mirror or a bit of both. It can also transfer momentum to the matter or be absorbed by it. Anyway your thoughts are more like a physicist so well done. I am trying to divert you from mentally roaming the universe, guessing solutions to twenty five intractable questions before breakfast. No one can do that - it is counter productive. 😀

There is already a standard symbol for this purpose - another greek letter epsilon. Since the same epsilon concept is also used for other purposes in Analysis (eg the epsilon - delta process) what benefits does uisng upsilon bring ? You upsilon is not an infinitesimal in the strict sense of the word and again there is standard symbolisn for infinitesimals, which have the advantage that they can distinguish what quantity or quantities is being referred to when the algebra of infinitesimals is being used. For the purposes of decimal expansions of real number you need to refer to Archimedes Condition which states that Given any positive real number x there exists an integer n such that 1/10n < x (Note that none of these are infinitesimals.) This condition is used twice to create a decimal expansion of any real number. More detailed analysis of that expansion of say 0.9 recurring and 1.0 leads to the proff I referred to earlier.

I don't know what your background in mathematic is but have you seen the proof that 0.9 recurring and 1.0 refer to the same decimal number ? This proof is part of a first year university 'foundations of mathematics' course.

Interesting question. You might be suprised to learn that the answer is even more interesting. This is because it is like in a police drama or a gangster movie, where there is a knock at the door and a vocie says "Are you Mr Smith ?" Because the answer "depends upon who's asking. Who want to know ?" also applies in Physics. This is a direct result of relativity. Collisions are also interesting. Being scientific about it you can ask what happens when two (or more) something or anothers collide. When matter alone is involved damage, deflection, chemical action, coalescence and many other results occur. On the other hand when two waves collide, the waves can pass right through each other and come out the other side, undeflected, undamaged and apparantly unaffected. So what do you think might happen if a wave collides with some matter ?

Well I don't see that a negative vote is a good welcome to a potential new member who might have other worthwhile comments to make. So I have balanced it with a +1 Thank you jeremy. I believe it is legitimate to post links to sites which offer a free calculator or other processor or data even if they would like visitors to venture further and buy something from them as with your link. Google will alo find many free plotters.

Pour evaluer le AI vous avez besoin de travailler en francais. 😀