Mean Definition and 1000 Threads

Homework Statement We performed an experiment to see which laboratory glassware was more accurate and which was more precise. Question: (a): Which glassware was more precise and why? (b) Which glassware was more accurate and why? Use the calculations to support your statement. I won't post the...

In the case of lifting a box, I know potential energy is negative because negative work is done by gravity. What does the negative part of -PE denote? Does it denote the direction of the energy or does it mean that energy is being lost? But how is energy being lost if the box gains more...

Homework Statement If ##P(x)\propto e^{x^2/2\sigma^2}##, show that the average ##\langle x^2\rangle = \sigma^2##. Homework Equations ##\langle x\rangle = \frac {\int xP(x) \, dx} {\int P(x) \, dx}## The Attempt at a Solution ##I = \int x^2e^{x^2/2\sigma^2} \, dx = \int (-\sigma^2x)(\frac...

Hi everyone. I'm trying to write a program that reads data from 2 files and then calculates the mean, standard deviation and standard error of both files (separate values for each). I'm struggling to get my head around simple I/O, so excuse the poor attempt, but this is what I have so far: (I'm...

Homework Statement The problem that I am having stems from a problem given in the following way:[/B] "a)Show that for a gas, the mean free path ##\lambda## between collisions is related to the mean distance between nearest neighbors ##r## by the approximate relation ##\lambda \approx...

I saw the sentence " So the contour integral of an analytic function f(z) around a tiny square of size e is zero to order e^2. ". I want to know what " be zero to order " means exactly.

I'm looking at this quote: "The proportions of the phyla Firmicutes and Bacteroidetes were statistically significantly increased in the obese group compared to the normal weight group (p< 0.001, p = 0.003 respectively)." Since I don't know statistics can you please explain how to visualize...

Hello everyone, I have a question regarding the implication of mean free path and pressure acoustics. I have seen several publications on the internet and also calculated the minimum displacement of a wave in air using the formula dp=v * rho * *2*pi*freq. * dx The values of displacement can...

Homework Statement Both images are 2 consecutive pages of my notes . In this theory , i was told to use z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) . However , in the 2nd image , i was told to replace σ with s ( sample...

Hello everyone Help me please... What does"double-infinities" mean?

Homework Statement Homework EquationsThe Attempt at a Solution [/B] A) Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s B) How is part a) different from part b)? I think what Irodov means by mean velocity is mean speed in part a. It is mean...

I suspect the following reasoning is faulty, but I am not sure why. Hence I would appreciate someone pointing out the errors. That is, which, if any, of the following statements are incorrect, and why? 1) Theoretically, albeit not practically due to the large numbers involved, the laws of...

If I construct a set of qubit gates, say {G1, G2 ... Gk ... Gn}, that can act on a state |ψ>, what does it mean for the set of states Gk |ψ> to span the Bloch sphere? As an example, take the set {G1, G2, G3, G4} = { I, X π/2 , Y π/2, Xπ } Here, X π/2 denotes a π/2 rotation about the x-axis, Y...

Homework Statement Accidents at a busy intersection follow a Poisson distribution with three accidents expected in a week. What is the probability that at least 10 days pass between accidents? Homework Equations F(X) = 1- e-λx μ = 1/λ The Attempt at a Solution Let x = amount of time between...

Homework Statement I have problem of obtaining the cross sectional area . Homework EquationsThe Attempt at a Solution Taking section 2-3 as an example , my working is [ (3.3 +4.8) / 2 ]* 5 = 20.25 , but the ans provided is 29.28 , how to get the 29.28 ?

Given two positive numbers a and b, we define the root mean square as follows: R. M. S. = sqrt{(a^2 + b^2)/2} The arithmetic mean is given by (a + b)/2. Given a = 1 and b = 2, which is larger, A. M. or R. M. S. ? A. M. = sqrt{1•2} A. M. = sqrt{2} R. M. S. = sqrt{(1^2 + 2^2)/2} R. M. S. =...

Given two positive numbers a and b, we define the geometric mean and the arithmetic mean as follows G. M. = sqrt{ab} A. M. = (a + b)/2 If a = 1 and b = 2, which is larger, G. M. or A. M. ? G. M. = sqrt{1•2} G. M. = sqrt{2} A. M. = (1 + 2)/2 A. M = 3/2 Conclusion: G. M. > A. M. Correct...

"Ghosts of Departed Quantities" And a host of ones own deity?

Homework Statement I have taken ODE, linear algebra, mechanics, math physics, etc. and we would always go on about how important the homogeneous equation is. To solve for the equation of motion for a harmonic oscillator (for example) we would solve for both the homogeneous and particular...

When they talk about information falling into a black hole, are they referring to the basic defining parameters of the particles falling into the hole?

I think the title speaks for itself: What does "flat" MC samples mean? Thanks.

Hi. I don't understand the meaning of "up to total derivatives". It was used during a lecture on superfluid. It says as follows: --------------------------------------------------------------------- Lagrangian for complex scalar field ##\phi## is $$ \mathcal{L}=\frac12 (\partial_\mu \phi)^*...

Hey guy! I've just started learn physics and i ran into a problem. Can you guy let me know what is d and p mean in this

I can understand force being exerted by an object on another object but I can't understand what all this force between two objects is. Can anyone give the complex and simple explanation, please? I am completely freaking out not being able to understand. Analogies and visualizations are a great...

Homework Statement [/B] A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength μ greater than 1350 kPa. A sample of 100 blocks is produced and...

Homework Statement An airplane of mass 1.2 x 10^4 kg tows a glider of mass 0.6 x 10^4 kg. The airplane propellers provide a net forward thrust of 5.4 x 10^4 N. What is the glider’s acceleration? Homework Equations I The Attempt at a Solution Let T = tension on glider from airplane. M= mass of...

Hello friends. I'm trying to compute an EoS to walecka model of barion interaction, but I'm having trouble to solve this equation by bisection. M*=M-gs²*nb/ms² where nb= (M*)*( kf*Ef- (M*)²* ln (kf+Ef)/M*) , using Ef= sqrt( kf²+(M*)²) and Cs²= gs² M² / ms² = 267.1 I'm using J. D. Walecka...

I was solving the problems given by Griffith in his book 'Introduction to Electrodynamics' and stumbled across this question. "Because sigma (conductivity of the medium) is a function of position, the equation 7.5 does not hold" --i get this point; current density isn't constant and so its...

I intuitively understand macroscopic vibration, but trying to understand what it means for a particle to vibrate doesn't seem to make sense from the classical understanding I have of momentum and energy. First, are particles even said to vibrate or have vibrational energy? If so, how is momentum...

My understanding of the distribution curves is very basic but I do have a couple of somewhat generic questions. I looked up a number of definitions but have had a hard time finding these specific answers: - Is there an agreed on minimum number of samples that one needs to take to deem a result...

hello all i've just started university about a month ago (studying for a single major in mathematics) and in desperate need for some advice from the wiser and older. since I've started at the second semester (you can do that in my uni), we are a relatively small group of people, only about 20-30...

I'm hoping someone can help check whether my final contour plots look plausible based on the surface. I haven't done too much differential geometry but I've needed to work with Gaussian/Mean curvature for a simple 3D gaussian surface. Here's an example: (A = 7, a=b=1/(3.5)^2) It's...

In general relativity, does momentum conservation mean conservation of 4-momentum or 3-momentum

I've seen in books things like "G is mapping of plane into itself", "map of a set into itself" or "map of set/plane onto itself". What exactly to map into/onto itself means? Do this means that when G maps into itself we get G as a result or we can also associate points on G to other points as...

Whats the difference between (4/3) and -(4/3) Why ratio in external division is negative? I have answer for how it is negative but not why? X = (mx2+nx1)/(m+n) ⇒ (mx2+nx1) = X(m+n) ⇒m(x2-X) = n(X-x1) ⇒(m/n) = (X-x1)/(x2-X) From the above equation we can conclude that when division is...

Homework Statement Find the point "c" that satisfies the Mean Value Theorem For Derivatives for the function ## f(x) = \frac {x-1} {x+1}## on the interval [4,5]. Answer - c = 4.48 Homework Equations ##x = \frac {-b \pm \sqrt{b^2 -4ac}} {2a}## ##f'(c) = \frac { f(b) - f(a)} {b-a}## The Attempt...

Hi. Let's say I have data which I have measured. For example I measured a length of an object and the measurment was repeated 5 times. An instrument which I used to measure has an error, value of which I know. My options are to either to just go with the instrument error (probably not, right?)...

I'm reading the paper of the EPR paradox and I'm confused in the meaning of this: "The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements......when the operators corresponding...

Specifically, what does each of the letters denote in this solar sail equation? "The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the Sun (unless extremely close to the Sun[17]), and by the square of the cosine of the angle between the...

To me the state vector represents the following... 1) The number of elements in the state vector is the number of possible outcomes. Call that number n. 2) The value of each element in the state vector is the probability amplitude associated with that outcome. If that is true, then it seems to...

stevendaryl submitted a new PF Insights post Lenses and Pinholes: What Does "In Focus" Mean? Continue reading the Original PF Insights Post.

http://depts.washington.edu/uwptms/research.html In a penning trap where they use sideband detection of the particle, they need to "drive" it. But what does that mean? Is the position of the particle detected anywhere along this process?

Hope this is a valid question. I can't quite understand this very simple thing. Prof Shankar's introduction to relativity on Youtube starting at about 50 minutes has a quick calculation that comes up with the Lorentz transform. I follow the maths, no problem. But he confuses me a bit when...

Homework Statement Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K? Why 273K?

since i am new at learning special relativity, i still miss the concept about how thing move in special relativity. In high school, i am doing several problem about velocity addition, and that word always appear. for example: A is moving with velocity vAO relative to O, and B is moving with...

Homework Statement Find all the numbers c that satisfy the conclusion of the Mean Value Theorem for the functions f(x)=\dfrac{1}{x-2} on the interval [1, 4] f(x)=\dfrac{1}{x-2} on the interval [3, 6] I don't need help solving for c, I just want to know how I can verify that the hypotheses of...

I was wondering if someone would kindly point me to reading material that might help to shed some light on the idea outlined below. I'm looking to understand the related concepts in greater depth. Searching for "dark time" is what brought me to PF in the first place, via this forum, and then I...

What does it mean for the holes to have mass? But they are not physically existent.

d is sometimes used to represent an infinitesimal change in a quantity and sometimes a small amount of a quantity. E.g dx vs dM. dV could mean a small volume element and also an infinitesimal change in volume. How can it be used for two different things? My suspicion is that while converting...

Currently, Earth's eccentricity (orbital shape) is 0.0167086. Zero is a perfect circle whereas One is parabolic escape orbit and any greater becomes a hyperbola. And in the theory of the Milankovitch cycles, Earth's eccentricity varies between 0.000055 and 0.0679 over a period of 100,000 years...