Mathematics

Hello everyone, im new here seeking an answer and hopefully more in the future. I'm in a dilemma, there is a way of calculating the fundamental frequencies, i.e the resonance of a string, however i need o work out the resonance of an object. for example, if you ping a wine glass, itl give you a frequency (usually about 500hz) and if you play that frequency to the glass, it'l begin to move and eventually shatter because of the wave pressure "match" the frequency of the glass thus resonating with it. ive included the formula for the resonance frequency, however i have no idea how to apply this to mass and density of object, as apposed to the tension and length and mass…

I derived this system of differential equations this week as I was researching possible profiles for water diffusers & nozzles, used when joining pipes with different bores. Mathematics: Solve this system of differential equations. \[ x' = y^{-2} \] \[ y' = - \sqrt {(t+1)^2- y^{-4}} \] \(x'\) and \(y'\) are derivatives with respect to \(t\). I have obtained a numerical solution (which was non-trivial because of the numerical instability of the Euler method with this system of differential equations) but I am curious to know "does an analytical solution exist?", which would be more efficient and convenient to use. Derivation of the syst…

I'm really bad at this sort of thing and this is not homework, just curious about learning how to do this type of problem. 80 is the represented number of 25% of the people Find the other represented number for 75% of the other people

Front side: Progress Sums:-1,-2,-3,-4,-5... 1,2,3,4,5... We express the formulas:Sn= (a₁n2+n)/2, ; Sn-1=(a₁n2-n)/2,. (n - Number of summing members, a₁ - first member of the progression. With a negative or positive value n. Expressions Sn-1, Sn-2 should be understood: subtraction from the number of the member taken). First option: Example: Sn= (a₁n2+n)/2. For n = -5 we have: (-1*(-5)2+(-5))/2=-15; For n = 5 we have: (1*(5)2+5)/2=15. Example: Sn-1=(a₁n2-n)/2 For n = -5 we have: (-1*(-5)2-(-5))/2=-10 For n = 5 we have: (1*(5)2-5)/2=10. Triangular: Progress Sums:-1,-3,-6,…

Hello everyone, I'm new here and I have a question; So we know that π is a circle's circumference/diameter So 2 rational numbers dividing and cames out as irrational. Can you explain me how is this happening and is there any examples like that? Sorry for bad English btw.

I found a formula for a magic square that guarantees 5 out of the 9 numbers to be perfect square numbers (the 4 corners and the center) for any value of (x,y) And before Microsoft Excel succumbed to rounding errors, I found four specific values of (x,y) which bring this up to 6 out of 9 (the 4 corners, the center, and one of the 4 sides) (1,3) with a central value of 125^2 = 15,625 and a right-hand value of 95^2 = 9,025 (1,10) with a central value of 1,105^2 = 1,221,025 and a right-hand value of 529^2 = 279,841 (1,59) with a central value of 35,405^2 = 1,253,514,025 and an upper value of 2,831^2 = 8,014,561 (3,41) with a central value of 86…

I heard once of an equation that was proved in a simple way and then the solution was lost. This happened some hundreds of years ago, I think. Does anyone know this equation ? I forgot the exact context.

I had some arguments with my calculus teachers about limits and integrals, that I obviously lost, but never did I understand the principle. If the whole idea of an integral is to determine the tendency of a tiny slice with which you can then describe the whole by multiplying the slice by the number of slices, then "tending toward zero" is a characteristic of your slice size to begin with. If you need to look at the thing and as you consider your formulae, you make the determination that this or that term is tending to zero...how can you, or at what point is it proper to "call it zero"? Regards, TAR Where this comes into LIGO is the fact that in order to sense…

I'm going to try for the "Mathematics" forum for this topic but no worries if the mods decide to move this to "The Lounge". I've posted this image which I've described as a "Three-spoke dovetailing tile tessellation". Trispokedovetile tessellation by Peter Dow, on Flickr which is a tessellation of this tile shape, Trispokedovetile by Peter Dow, on Flickr Check my Flickr page for the preceding design iterations and inspiration. I've named the shape Trispokedovetile which is a contraction of "tri-spoke dovetailing tile". "tri-spoke" because the shape is similar to a 3-spoke motorcycle wheel with three bites taken out of it. "dovetailing" because t…

Hello Everyone, I'm about to transfer to University at Albany for FALL 2017. I'm a Meteorology Major and Chemistry Minor. I'm writing this because I want to know what's the best scientific calculator in the store right now. The calculators I'm looking at are TI- 36X Pro and Casio FX-115ESPLUS. Also FC-200V I was wondering if these are the strongest calculators in the market right now. I want one that can be good for my Calculus 2 and 3 classes. Also for Ordinary Differential Equations and possibly in the future Partial Differential Equations. Also, I'm taking Physics 1 next semester, any suggestions? Thank you

Correct me if my thinking is wrong. I have a series of independent events; in each of those the probability of a desired outcome is 0.1, for example. I need to find out the probability of getting a desired outcome at least once in a random series of n events. It's been a while since I'd done any probability theory. The only way of not getting a desired outcome is if all n events produce a non-desired outcome. The probability of a non-desired outcome in my example is (1-0.1)=0.9, therefore failing n times will have the probability of 0.9n and then finally the probability of at least one desired outcome will be (1-0.9n). a) Is this correct? b) If events are ent…

Let us say you have a ruler laid out on the floor, with the spacings arranged such that 1 increment = 1 meter. You are standing at 0. You start flipping a coin an infinite number of times. When you get heads, you move 1 meter forwards (positively) on the ruler. When you get tails, you move 1 meter backwards. If you flip tails at 0, you stay at zero. Let's say that you flipped the coin once and it landed on heads, so you are now standing at 1 meter. With a potentially infinite number of coin tosses, what are the odds of eventually arriving at 0? How different would it be if the ruler was infinite as opposed to finite? --------------------------------------------------…

I've been fooling around with the Gregory series: [latex]\sum_{k=1}^{\infty} \frac {(-1)^{k+1}}{2k-1}[/latex] and brought it into the following form (since the series converges, I believe I can partition the Sum as I wish, I think. At least when I simulate it for [latex] n = 10^7[/latex] terms it still converges towards [latex]\frac {\pi}{4}[/latex]). [latex]\frac{1}{2}\sum _{k=1}^n\frac{1}{\left(16k^2-16k+3\right)}[/latex] Which sorta reminds me of the Geometric series, though it is quite different. My question is if the series of the following form is always transcendental: [latex]\frac{1}{2}\sum _{k=1}^n\frac{1}{\left(16k^2-16k+w\right)}[/latex] whe…

I've been working on a solution for one of the millennium prize problems (the Navier-Stokes Equations and Smoothness problem), but one of the finalizing things I need is a formal definition of 'smoothness'. The problem asks for proof which involves a smooth, divergent free vector field, a smooth function for a force, and a smooth function for pressure.

Say, I was rolling a dice and need to get a 6. I know that my probability of rolling a 6 on any single throw will be 1/6. Now, let's say I'm rolling the dice every 2 seconds for 1 minute, therefore getting 30 rolls. What would be the correct way to calculate expected number of sixes I will roll? Part of me wants to simply say, that it's 5, but something tells me it might not be that simple.

I'm asking it here because I don't even know HOW to ask this! Basically, I'm looking for some identities regarding the "tends to" part of the limit. So for instance: [latex]\lim_{x\rightarrow b} f(x) = \lim_{x\rightarrow 0} f(x+b)[/latex] Is the above expression correct? If so, is it always correct, at least for Hilbert spaces? What else can you do with the "tends to" part, can you rename variables there? References are welcome.

F² . M~H _____ = TIME R² AcceLeRATion e' SONA&ZioNative 8106 (Wait & See:) Sounds: when Frequention rise our Mass M~H = Enligh10ment, we come conscious aware time is LESSon due uplifting AcceLeration & Frequency wAves enhighers us to come aware of our Oura, & our brain, become IQed Our Body movement becomes quicklier & feels 2bc, walking on clouds. {(F².M~H)/(R².∆T)}=1 So1 can Timetravel when (F².M~H)=(R²)! = Keygen JwsHe' 'ETernity Sciences & We'L7 I Am WhoIAm&I am ME AL YC! IT¥NoTa Who We are &A way We do;& note '40-2 'What was been;4)grace(' & What will Be, &We thank Y 4support! E=H.F! Behold …

This site (in French & English) has published (open source) 18000 pages of mathematician Alexander Grothendieck archives, out of the 28000. (copyright issues) For those interested (and who can understand) https://grothendieck.umontpellier.fr/archives-grothendieck/

{(FF.M~H)/(RR.∆T)}=1 So1 can Timetravel when (FF.M~H)=(RR)! = Keygen JwsHe' 'ETERNAL life = Proove, because ourA Conciousness or our Soul can never perish. E=H.F! Sos Have Fun!) Behold E=C ;)C = H.F whereinby C = Conciousness(;&its D1! {(E . C)/(F . M)} = 1 & ((E.C)/(F) = M) & M = Ev/C² & Light = The Frequention from our Conciousness. Conciousness = F . M / E Once F rise7Light fastens YeaH be'be'!) F²=F² & C²=F.C (0,261121 MeV = {(∆T.FF)/(RR)}) ©® becuz 1 Ev = 0,511 MeV Watt do JouLE Think!?!) Throughby acceleration of An Electron came AL in shape in the beginning and last forever continuED!) {(F². ∆T)/( Ev². R²)} = 1 …

Can anybody prove that eight is the only cube which is one less than a square?

Recently i learned about Quadratic Inequallities and i can't understand when i should flip the > or < sign. Can anyone help me with that?

Is it possible or easy at all to calculate mathematically? If you considered only the initial landing position and ignored the physics that happened thereafter, would it just be surface area of the sides X and surface area of the width Y where the odds would be 1 in (X:Y)? Of course, if you included actual physics, that would reduce the odds as there is a considerable chance that the coin would flip over after landing vertically due to momentum, angle, etc. Also, while I'm at it, another question (but pls answer the first): I've read a few times a supposedly true fact that the coin has a 2% higher chance of landing on the upper side due to that side being upw…

Just messing around with primes+30 to give next primes, some +30's do not equal a prime, but if not, they always equal a prime x's a prime? when this happens, I add 30 again, which gives a prime, unless it is once again a prime x's a prime. Example: Prime 19 + 30= 49, not a prime, but a prime x's a prime =7x7=49, but then add 30 again will give me prime 79. So no prime x's prime can equal a prime? why does adding 30 to a prime, always give a prime, unless the answer is a prime x's a prime, but adding 30 again gives a prime? prime plus 30 prime x prime 5 35 5x7 +30=65 = 5x13 +30=95 = 5x19 +30=125=25x5 +30=155 =3…

How do you explain the formula tan(20) = B/(A-C). In which Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 ?

Let's say i have two random vectors, X and Y, both of length n*. The elements of either vector are not independent, and X and Y themselves are not independent. All elements are non-negative. I want to explore the behaviour of the inner product of X and Y as . Not sure where to begin though: does anyone know of any good references/advice to get me started? I'm sure i once saw a paper that showed if the RVs are independent then the inner product converges to zero, but can't for life of me dig it up: that'd be a good start. Cheers. *Edit: i meant of n dimensions.