Mean Definition and 1000 Threads

Homework Statement I and J are open subsets of the real line. The function f takes I to J, and the function g take J to R. The functions are in C1. Use the mean value theorem to prove the chain rule. Homework Equations (g o f)' (x) = g'(f (x)) f'(x) MVT The Attempt at a Solution [/B] I know...

Homework Statement in the second photo , why the velocity inside the hose is relatively low ? If it is low , the water wouldn't be able to move out of the hose , am I right ? Homework EquationsThe Attempt at a Solution

Homework Statement Let f is differentiable function on [0,1] and f^{'}(0)=1,f^{'}(1)=0. Prove that \exists c\in(0,1) : f^{'}(c)=f(c). Homework Equations -Mean Value Theorem The Attempt at a Solution The given statement is not true. Counter-example is f(x)=\frac{2}{\pi}\sin\frac{\pi}{2}x+10...

Hello again guys. I've been reviewing stuff from electromagnetism and I just recently read about voltage. I know it is a difference of potential, electric potential more precisely. Electric potential is just a property of electric fields and it is measured in Joules per Coulomb. 1 Joule per...

in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched. eg mass attached to a vertical spring.

Homework Statement Air enters a diesel engine with a density of 1.0 kg/m3. The compression ratio is 21 .At steady state ,the air intake is 30 x10-3 Kg/s and the net work output is 15 kW .The mean effective pressure (in kPa) is ... Homework Equations Pm= W.D/ Vs...

Exactly as stated in the title. What does ph(z) mean?

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

So: what does "<>" mean?

I am self learning Physics From a course I read the following : " .. d^2x/dt^2 = -k/m x The left hand side is an acceleration so k/m must have dimensions of (time)−2 .. " I understand that the left hand is acceleration but why does it imply that k/m must have dimensions of (time)−2 ? I...

Links for [1] and [2] are below. Please have a look here section 12.6 [1]. It says here that Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations of motion. It is most useful to obtain solutions that can be interpreted as...

I am not sure what intensity actually looks like and means for light. Does this mean that ex red photon, that there are more than one photon that are superimposed on each other hitting the same spot?

Homework Statement I am given a table of ~3000 measurements for the number of decays from some radioactive substance within some period T. I want to estimate the mean number of decays per period. Homework Equations Poisson distribution How to calculate mean. The Attempt at a Solution My...

I run an algorithm that outputs a normally distributed random number with unknown mean and variance. I need to know the mean of those numbers. To do that, i repeatedly run that algorithm to obtain many numbers, then I calculate the mean and the confidence interval for the mean. Over the last...

Its one specific phrase that is confusing me and its from Samuel Johnson's Preface to Shakespeare. I bolded the exact words that are giving me problems and I also provided the sentences before and after to provide context. (I understand what he is saying wrt how Shakespeare mixes comedy and...

Homework Statement If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=360K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m−3 Homework Equations K=CVvsl l...

Hello. I am an intro Physics student and this is my first post here. In Coulomb's law the charges are said to be stationary. I need some clarification about what does it mean for two charges to be stationary: A. Does it mean that the charges are not moving with respect to each other? (But...

Anyone can explain to me What does it mean for a language not to be complete? for example P has 2 languages are not complete for P ø and {0,1} are not complete for P.

Does the function satisfy the hypothesis of the mean value theorm On the given interval, give reasons for your answer $$f\left(x\right)=\sqrt{x\left(5-x\right)},\ \ \left[0,5\right]$$ The graph of this is the top half of a circle My answer was It is continuous at all points on the...

I was studying in my math textbook about these two methods to measure dispersion and variability in data. I was able to understand mean deviation that it's the average by how much a quantity deviates from mean but I was unable to understand standard deviation. Also, as standard deviation squares...

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

Homework Statement A random sample of size n = 81 is taken from an infinite population with the mean μ = 128 and the standard deviation σ = 6.3. With what probability can we assert that the value we obtain for the sample mean X will fall between 126.6 and 129.4?The Attempt at a Solution z =...

hi all... i have payment schedule with parameter like this : e.g. original price $\$$5000 - if i pay in <=6 months i have penalty (add penalty) 1% from original price - if i pay in >6 months i have penalty (add penalty) 10% from original price e.g. my problem is : i have $\$$5000 and...

The interior of a conductor can have no excess charge in the static situation. What does excess charge mean here?as far as I know there can be no net charge at all in the interior of a conductor.So,is net charge same as excess charge?

Electron is usually imagined as a simple point charge, but in fact it is a very complex entity: https://dl.dropboxusercontent.com/u/12405967/electron.png - being electric charge itself means singular(-like?) configuration of electric field - E behaves like 1/r^2, - it is also magnetic dipole...

Any help would be much appreciated. The problem lies in the non-Gaussian distribution of the sample. If we take the entire data set of total fish catch, the skewness statistic equals 7.463 with a std. error of skewness of 0.39. Accordingly, the Z dist. (7.463/0.39)=19.14. Overall, the...

Homework Statement A system's state of spin 1/2 is represented at t=0 by C*exp[-a2(p-p0)2]*{{1,0},{0,1}} where the density matrix is represented in the base of eighenvalues of Sz and the spatial vector is represented in the continuum base of statesPx, Py, Pz. Find <X>, <Px> and <ΔX>, <ΔPx>...

Homework Statement suppose that 50 random samples of size n = 10 are to be taken from a population having the discrete uniform distribution f(x) = 1/10 for x = 0,1,2,...,9 0 elsewhere sampling is with replacement so that we are sampling from an infinite population. we get 50 random...

For instance, at a point 1 meter from a 1 nC charge the voltage (potential difference) from the formula V = Kq/r, is given as 9 volts, 9 J/C. So what does it then mean to call a battery 9V, 9 J/C? Is this a battery capable of taking a 1 C charge from infinity and pushing to within 1m of a 1 nC...

The distance covered by a car at time t=0 is 0 / at time t= 1 is 10 km/ at time t= 5 is 50 km, With this example can you explain, what is function of what? f(d) or f(t),

A culture contains 1200 bacteria initially and doubles every 30 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes. P(t) = A e^(kt) = B^(2t/C) , where A = 1200 k = 0.0231 B = ? C = ...

Hi I was wondering how you would account for mean stress (such as using with goodman equation) using von mises with miners rule due to variable loading Thank you

Homework Statement [/B] Calculate \widehat{Y^{2}} (i.e., the mean of the square of Y. Homework Equations Y=\sum_{k=0}^{N-1}y_{k} where y_{k}=e^{-\gamma t}e^{\gamma \tau k}G_{k} and t=N\tau The quantities y_{k} (or G_{k}) are statistically independent. The Attempt at a Solution...

QUESTION: In general: when a flow is considered steady does that mean all properties of the flow are steady? Or: can a flow have steady and unsteady properties?

I wans't sure on where I should post this question. So, if this place is inappropriate, please move it to a proper section. The question is as its posed in the title of this topic. What we mean by foundations of physics? when someone talks of the foundations of physics, what is he/she talking...

Homework Statement find μ and σ^2 for the following probability density f(x) = x for 0<x<1 f(x) = 2-x for 1 <= x < 2 f(x) = 0 elsewhere Homework Equations μ = ∫xf(x)dx σ^2 = ∫x^2 f(x)dx - μ^2 The Attempt at a Solution first we find the mean. we split up the integral into sums of different...

In interpretations where the wave function is real, what does that mean? does it mean that the wave function has physical meaning?

So the equation is f(x,t) = f(x-vt,0) = A sine k(x-vt). Now Since x is displacement of wave from origin, t is time taken for that,wouldn't 'x-vt' always be equal to 0 ? If x-vt is 0, Y = A sine k(x-vt) will also be zero. So am I writing the equation wrong?

Homework Statement I must prove that the mean of one number and its absolute value is superior or equal to 0 but inferior or equal to the absolute value of the number Homework Equations I must prove this by the method of case. The Attempt at a Solution I know that the first case is : x>=0...

Given this magnetic circuit: With these dimensions: With this equivalent circuit: If I am using F = HL to calculate the mmf drops in RcoreAB(see equivalent circuit) and RcoreBCDA(see equivalent circuit) then how would I calculate L in the formula ?

Homework Statement [/B] The problem on where the photon will hit a screen, after passing through a single horizontal slit. I know the wavelength, slit width, magnitude of momentum of incoming photon (calculated), and distance between screen and slit. Homework Equations I just don't...

This is a simple question. I know that for any number or expression we can multiply it by 1 and maintain the same expression. However, x / x also equals 1. But if we multiply it by another expression, the expression changes such that we can no longer use 0. So if the domain of an expression...

Hey! I'm reading a book Intermediate Physics for Medicine and Biology In it, there is a section that is describing shear forces and it says this as a side note: In general, the force F across any surface is a vector. It can be resolved into a component perpendicular to the sur- face and two...

In the context of surface science and materials science, what does it exactly mean when a surface is, say, "metal-decorated"? By reading plenty of journals, I am assuming that it means that the atom is adsorbed on the surface, which means that the atom that "decorates" the surface is bonding on...

So last year, I was told by a friend that no Acceleration means no Force, Mathematically, this makes sense (500 Kg * 0 m/s^2 = 0 N), but intuitively, I can't wrap my head around it. Maybe this is because of language and the way we use the word force in normal conversation, but in physics it is...

Homework Statement What does it mean to say that an object undergoes a deceleration? Can this term be used without ambiguity? Edit (That was straight from the book poorly written: Should say object decelerates not undergoes a deceleration) Homework Equations v(t)=v0+a⋅t The Attempt at a...

Someone please explain what the colors mean in QCD. Are different colors different quarks? Are different colors the same quark with different amounts of energy? Is it something else entirely? Does it apply to leptons?

Hi. I have a couple more questions in my quest to self-study GR. 1 - I have some notes where the Kretschmann Invariant is defined as Rk = RabuvRabuv and is given in Schwarzschild coordinates as Rk = 48u2/r6 . My notes say this is an invariant field so that its value at any point as evaluated in...

I'm trying to figure out what the vertical bars in |A∪B| mean given that A and B are both sets. I tried searching for it, and can't seem to find the meaning of it. Is it supposed to be absolute value of all the elements of the union of sets A and B?