Mean Definition and 1000 Threads

Homework Statement Let ###f## be double differentiable function such that ##|f''(x)|\le 1## for all ##x\in [0,1]##. If f(0)=f(1), then, A)##|f(x)|>1## B)##|f(x)|<1## C)##|f'(x)|>1## D)##|f'(x)|<1## Homework Equations MVT: $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ The Attempt at a Solution I first tried...

If something hat has no volume and no mass can exist ,what does it mean to say that something physical exists?

Also, what about f(2x)? I am confused about how to enter 2 multiplied by the function in a ti-84 calc. I am wondering if its because I am mixing up function notation. I am learning about transforming graphs. What does 2f(x) mean in words? Also what does f(2x) mean in words? thanks

Hi, I am trying to get up to speed on electrical schematics and how to read them and I am getting stuck with a particular symbol. I understand that the following symbol represents a link; However, I cannot seem to find what the following one means? I believe that it is meant to represent...

Hi there! I am currently building a simulation to model the propagation of radio waves in seawater in terms of its propagation loss. I have previously discussed the models I've looked at but have settled on a model which depends primarily on the propagation distance ##r##, the carrier wave...

Hi, I often hear people say that a certain program (i.e. computer science, maths, etc) is better at one school than at another. For example, here in Canada a lot of people say that if you want to enter into computer science you should go to the University of Waterloo, because they have a...

Hi all, I am currently reading a paper and they have this statement in the abstract: "If the supermassive black hole Sgr A* at the center of the Milky Way grew adiabatically from an initial seed embedded in an NFW dark matter (DM) halo, then the DM profile near the hole has steepened...

1. hi there I am a bit confused, I am doing a survey of 100 respondents. ive asked them 5 colors to choose from ( red, green, blue, yellow and black) ive got these results from my survey of 100 respondents red = 21 green = 36 blue = 19 yellow = 10 black = 142. is my sample size 100? or 5? how...

I am stuck with this question: why can't we use the equation c(rms)=√(3RT/M) for problems when no of moles is not 1? Because I think the mole will be deduced as c(rms)=√(3nRT/nM) =√(3RT/M) For instance I found this problem, given atmospheric pressure is 10^5 Pa, molecular mass of Nitrogen...

I was looking at the attached picture, where it gives the Higgs Mass obtained from the two different channels from ATLAS and CMS. Let's only talk about the diphoton channel : H\rightarrow \gamma \gamma From the ATLAS the mass value is: m_{Ah} =126.02 \pm 0.51 and the CMS: m_{Ch} =124.70 \pm...

What does v equals dx/dt mean? I interpret v as: the limiting value as a vanishingly small value for time t (dt) goes to 0. Or lim as dt-->0 of dx/dt.

I've always thought that when people say exponential growth, they mean e^x. But other times I hear people just say that the quantity doubles 2^x every time. So which is it? And if it's just doubling, why don't we say that 3^x or 4^x is exponential growth as well, since that's what those...

Homework Statement I wanted to ask anyone willing to check my proofs to two problems, so that I may know if I am making any mistakes or assumptions. Let the function f be continuous and strictly monotonic on the positive real axis and let g denote the inverse of f. If a_1\lt a_2\lt...\lt a_n...

Homework Statement Let f(x) = 1 - x2/3. Show that f(-1) = f(1) but there is no number c in (-1,1) such that f'(c) = 0. Why does this not contradict Rolle's Theorem? Homework EquationsThe Attempt at a Solution f(x) = 1 - x2/3. f(-1) = 1 - 1 = 0 f(1) = 1 - 1 = 0 f' = 2/3 x -1/3. I don't...

what does this --> ∫ mean and what how do you use it? Thanks.

This is a very basic question, but one that's vexed me for a while. Are these two fragments equal:-In C, with c and t as integers [FONT=Courier New]c = t < 0 and in Java, also with integers [FONT=Courier New]if (t < 0) { c = -1; } else { c = 0; } Reason I ask is that...

In the MVT for Integrals: ##f(c)(b-a)=\int_a^bf(x)dx##, why does ##f(x)## have to be continuous in ##[a,b]##.

Probably an ignorant question, but if gravity is or can be quantized, does that mean that time must be quantized too? I guess I'm thinking of energy- definitely quantized. Gravitational energy... hmmm. Makes me wonder, if space-time truly is smooth (general relativity), then there must be a...

It's pretty clear by the title... what does it mean to say something like (check http://arxiv.org/pdf/hep-ex/0606027v1.pdf pg5 ends of left column) "a momentum-weighted charge of the decay products of the second b..." ? I don't understand why someone would use momentum-weighted variables and...

Mean Value Theorem Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather...

As I know: Velocity of sound = wavelength x frequency. If frequency increases wavelength decreases. So even if you shout loudly the velocity of sound won't change only that you will hear a louder voice. So does that mean that louder voice has higher frequency?

Potential for infinity? According to Inflation theory, (Big Bang type models) The observable Universe can be measured. We put a specific size on space/time of 13.8 billion years based on expansion from some Singularity. My question. When we speak of 'infinity' are we speaking about infinity...

If I know the mean and standard deviation, but I don't have an original data set, is it possible to reverse calculate a data set that has this known mean and std dev? Is there an excel function I could use to do this easily? I know there could be multiple correct datasets and that's fine, I'm...

If I know the mean and standard deviation, but I don't have an original data set, is it possible to reverse calculate a data set that has this known mean and std dev? Is there an excel function I could use to do this easily? I know there could be multiple correct datasets and that's fine, I'm...

Sorry if this is in the wrong section. I didn't know which homework section I should use. 1. Homework Statement Human subjects are involved in a medical study to represent certain segments of the population in terms of blood lead concentration, PbB. First, assume the normal distribution...

In rigid body rotation, there is some question. First, problem give me Lagrangian. And, I have to compute Hamiltonian. Then, problem said that "Reduce the system to quadratures (i.e., write the solution in the form of a one dimensional integral whose integrand is an explicit function of the...

In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'? For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c'...

Hello, I'm having a little trouble figuring out the following problem: Consider the set of number a, 2a, 3a, ..., na where a and n are positive integers. (i) Show that the expression for the mean of this set is \frac{a(n+1)}{2}. So far the only work I've been able to muster up is: Mean =...

I am in Calculus 3, and I do not under stand what it means when they ask to find the relative extrema of f|S? The problem is usually something like f:R^n=>R, (x,y,z) |=> (some function) , S= {(x,y) | x e R} What does f|s mean? How does this relate to Lagrange multipliers? The book does not...

Hi. I know how to work with potentials and how to solve problems involving them, but what exactly does it mean that we connect something (say, a spherical shell) to a potential V0? What is "actually" happening? My guess is charges are "pumped" from some source to the material until an electric...

Define energy as E=T+U. For anyone using different terminology, by rheonomic (time dependent constraints) I mean that if a system has N degrees of freedom, the position vectors of each particle of the system are given by ##\vec{r}_i(q_1,q_2,...,q_n,t)##. Where ##q_i## are generalized...

What is the relation between p max and mean effective pressure inside the cylinder

In the quest of searching what are the basic ingredients of quantum theory that provide exponential speed-up to some quantum algorithms, a basic question that is pursued in the literature is when a quantum circuit (or algorithm) can be classically simulated efficiently. One example is this paper...

This is with regards to the principle of least action. I understand that an action is a functional (a function where functions have values assigned to them, I believe?) When trying to figure this out, I understood minimising as finding the true path of the principle of least action. But that...

I am really confused about it.Suppose we add 5 moles of acetic acid in 1 litre of water..The molarity of solution will be -(5 moles)/volume of solution?Or it will be -(the number of moles of acetic acid dissociated/dissolved)/volume of solution

Not a homework question, I'm just curious, I know this has been asked a few times, but what exactly is happening when you move dx over to the other side of dy/dx=f'(x), is it like the point slope form ∆y=m∆x, or is it applying the differential to both sides, I've always been told a rigorous...

Once you've integrated, dx and dy just indicate what variable you've integrated in terms of, correct?

Is there redundancy in the phrase ‘an isolated free particle’? Do not the words ‘free’ and ‘isolated’ imply each other? Any help is much appreciated. Thanks

Let's try something simple and hope this goes better than my last two threads. :( The problem can be stated thusly: ---- Given thermal neutrons emitted at a source S interacting with a mean interaction length of L and an evaluation point P distance d away from S, what is the average number of...

Is the expection value of expession in left hand side of motion equation of field(example: Klein-Gordon,Dirac...equations) equal zero or not?(left hand side of the equation equals zero when we put condition of mimimizing the action).If not,why we can say when expectation value of divergence of...

What does it mean by maximum work of an isothermal, reversible expansion of a perfect gas from initial volume Vi to final volume Vf at temperature T? I understand that heat enters the system during this expansion to ensure that no internal energy is lost but it doesn't really help in anyway...

My understanding: When we draw a triangle on a flat piece of paper and measure the angles using a protractor, the sum of the angles is ##180^\circ##. So we conclude that the universe is locally flat. Suppose we draw a very big triangle that spans across galaxies (say, using lasers and mirrors)...

Hi everybody, I was doing one asignment form class, I was tasked to prove that in one system, the arimetic mean of FD and BE distributions is equal to MB's distribution for undishtingable particles. After doing the numbers I found out that it actually was, but I don't know why this happens, can...

Hello! :) I just want to ask how, did the encircled portion come about? It says that it equates the $\hat{i}$ and $\hat{j}$ components. but when I tried that, this is what I get $0.5447F_{1}=F_{3}(\sin(\theta)-\cos(\theta))$ ---> This expression doesn't ring a bell. It doesn't make any sense...

Einstein wrote in a letter to Max Born that he feels that QM is not the true Jacob, quote: "Quantum mechanics demands serious attention. But an inner voice tells me that this is not the true Jacob. The theory accomplishes a lot, but it does not bring us closer to the secrets of the Old One. In...

Homework Statement If the energy ##E## of a system behaves like ## E = \alpha |x|^n##, where ## n =1, 2, 3, \dots ## and ## \alpha > 0##, show that ## \langle E \rangle = \xi k_B T ##, where ##\xi## is a numerical constant. Homework Equations $$ \langle E \rangle = \frac{ \int_{- \infty}^{...

I have been watching a few explanations of the Higgs boson/ Higgs field. From what I can understand is that all space if filled with a sea of Higgs bosons which create the Higgs field. Is the Higgs field a property of space and does it give space energy? As more space is created with the...

We know that Fourier Transform F(W) of function f(t) is summation from -infinity to +infinity product of f(t) and exp^{-j w t}Here, what does the exponential term mean?

If I have three sets of numbers A is numbers between 0 and 0.09 B is numbers between 0.091 and 0.011 C is numbers between 0.011 and 0.1 where the number of elements in A are say, 37, B are 16 and C are 178. So the three arrays have different numbers of points and different distances, plotting...

Homework Statement Devise the mean voltage and current in controlled and uncontrolled single device rectifier circuits with R-L series loads. Single circuit series circuit given of an AC voltage source, a uncontrolled diode, resistor, inductor. V = 240 v, F = 50 Hz, R = 10 ohms, L = 50 mH...