Uniform Definition and 1000 Threads

In Baby Rudin, Theorem 7.25 states: If K is compact, f_n \in C(K) for n=1,2,3,... and if {f_n} is pointwise bounded and equicontinuous on K, then (a) {f_n} is uniformly bounded on K The theorem continues with point (b), which I understand. My question is, whether point (a) needs the...

A charge q and a charge 3q are released in a uniform electric field. If the force this field exerts on 3q is F, the force it will exert on q is: i think the answer is F/3. is this right? i used E=F/q.

Homework Statement I have a solution to the following problem. I feel it is somewhat questionable though If fn converges uniformly to f, i.e. fn\rightarrowf as n\rightarrow∞ and gn converges uniformly to g, i.e. gn\rightarrowf as n\rightarrow∞ , Prove that fngn...

Homework Statement If U is uniform on [−1, 1], find the density function of U^2. Homework Equations f(u) = 1/(b-a) The Attempt at a Solution I actually solved the problem already, but I am having trouble defining what the boundaries are for U^2. My work is uploaded in paint...

Homework Statement A crystal contains N atoms which posses spin 1 and magnetic moment \mu. Placed in a uniform magnetic field B the atoms can orient themselves in three directions: parallel, perpendicular, and antiparallel to the field. If the crystal is in thermal equilibrium at temperature...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Homework Statement A charge q is released from rest at the origin, in the presence of a uniform electric field and a uniform magnetic field \underline{E} = E_0 \hat{z} and \underline{B} = B_0 \hat{x} in frame S. In another frame S', moving with velocity along the y-axis with respect...

Hi, Can someone please help me solve the following: Find the distribution of xy/z where x, y, z is independent and uniformly distributed from 0 to 1 Thanks for the help

Homework Statement http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/S2%202008-06.pdf Question 1(d) Homework Equations The Attempt at a Solution So I know this is a conditional probability question. Now I would have said P(X>8) / P(X=5) because it...

I had to calculate the distance a car traveled in a given time given its starting speed and acceleration. Would this formula x=Vo.t+ (Vf-Vo)/2.t Where Vf= a.t +Vo Be correct?

I thought the external magnetic field had to vary within an object in order for that object's magnetic moment to line up with the field.

Homework Statement An electron is fired at 4.0x106 m/s horizontally between the parallel plates as shown, (see diagram) starting at the negative plate. The electron deflects downwards and strikes the bottom plate. The magnitude of the electric field between the plates is 4.0 x102 N/C. The...

Does this actually happen in outer space? Do things actually move in uniform motion relative to each other? How would this work for the Earth considering it's rotating? Can the Earth ever be considered an inertial frame because it's always rotating?

thanks!

Homework Statement This isn't really a problem but it is just something I am curious about, I found a theorem stating that you have two metric spaces and f:X --> Y is uniform continuous and (xn) is a cauchy sequence in X then f(xn) is a cauchy sequence in Y. Homework Equations This...

If you were to pick two random numbers on the interval [0,1], what is the probability that the sum of their squares is less than 1? That is, if you let Y_1 ~ U(0,1) and Y_2 ~ U(0,1), find P(Y_1^2 + Y^2_2 \leq 1). There is also a hint: the substitution u = 1 - y_1 may be helpful - look for a beta...

Homework Statement A uniform rod AB has a length l and a weight W0. End A is in contact with a rough wall, but it is not fixed. A massless cord connects end B and is fixed to the wall at point C. The rod AB is now horizontal and the angle formed between the cord and rod is θ as shown in the...

Homework Statement http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/Solomon/Solomon%20B.pdf Questions 3c and 3d Homework Equations The Attempt at a Solution ok so for Qc) it must be between 6 and 10 cm from the bottom and 8 and 12 cm from the left d) it...

Homework Statement If X and Y are independent uniformly distributed random variables between 0 and 1, what is the probability that X^2+Y^2 is less than or equal to one. Homework Equations P(Z<1) = P(X^2+Y^2<1) For z between 0 and 1, P(X^2<z) = P(X < √z) = √z The Attempt at a Solution...

Homework Statement Find the center of mass of figure , of uniform density Homework Equations X = m1 x1 + m2 x2 + ... / m1 + m2 ... The Attempt at a Solution i broke the figure in 4 rectangles and got individual center of masses my answers comes out to be (13b/8 , 5b/2)...

Homework Statement See attachment! A plank is 4m long and has a weight of 500 N. It is pivoted frictionlessly about a nail which is driven through the center of the plank. When a 200 N weight is hung as shown in the figure (attached), the plank is horizontal and in equilibrium. Suppose...

Find the moment of inertia of a uniform solid sphere of mass,m and radius,a about an axis through its centre. I have tried to solve it but I get the different answer, I don't know where I have done mistake. Please! check and correct my solution below:- Consider a volume element, dv of the...

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Homework Statement A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that are inclined at an angle \phi above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude is directed downward in the figure B. The bar is...

Homework Statement 'Figure 2 shows a uniform rod of length L= 0.2m and mass m=0.2kg pivoted at one end. The other end is attached to a horizontal spring with spring constant k =3.0 N/m. The spring is neither stretched nor compressed when the rod is perfectly vertical. You can also assume...

Homework Statement I am told that X is a random variable with uniform distribution over [0,1] I need to find the mean and variance of log(X) 2. The attempt at a solution I assume I must find the pdf of log(X) so I did this as follows; Let Y=log(X) Then to find the cumulative...

1. Homework Statement Question This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough...

Assume we have a particle lying in the xy-plane with an initial velocity in the x-direction. If an external, constant and uniform magnetic field is applied in the z-direction, the particle, assuming it has a positive charge, will begin to do circular clockwise laps. However, it seems to me...

Consider that we have a macroscopic, electrically charged, point object tracing out a circular path in a uniform magnetic field in the usual way due to the Lorentz force. Now we very slowly raise the overall strength of the magnetic field (slow enough that on one orbit, the object sees the same...

Homework Statement A bar of length L supports a mass, m2 at the end. It is fastened by a pivot at one end to a wall which is at an angle θ to the horizontal. The bar is supported by a cord a distance x from the wall. The mass of the uniform bar is m1. I already solved for the...

I'm working on a problem for my analysis class. Here it is: Let f be differentiable on an open subset S of R. Suppose there exists M > 0 such that for all x in S, |f'(x)| ≤ M, i.e. the derivative is bounded. Show that f is uniformly continuous on S. I'm not too sure that this question is...

I am given the moment of inertia of the system ( a fan) and the question asks for me to find the angular acceleration "after the fan is turned on, it takes t = 3.6 s and a total of 12 revolutions to accelerate up to its full speed" ? How I went about solving is that.. I simply converted the rev...

Probably is a silly question, but how could I prove that the function (expressed in polar coordinates) \left(\rho^4\cos^2{\theta} + \sin^3{\theta}\right)^{\frac{1}{3}} - \sin{\theta} converges to 0 as rho->0 uniformely in theta (if it is true, of course)?

Two masses connected by a string uniform circular motion. HELP! :) Homework Statement A puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless, horizontal table. The other end of the string passes through a small hole in the center of the table...

Arnold is jogging west at 5 kph along a trail. Ivan is jogging east on the same trail at 3.75 kph.If they are 0.5 km apart, how long will it be until they meet? Help Pleaseeeeeeeeeeee! I need it now. Thank you!

Why some functions that are continuous on each closed interval of real line fails to be uniformly continuous on real line. For example x2. Give conceptual reasons.

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Homework Statement A function f:(a,b)\to R is said to be uniformly differentiable iff f is differentiable on (a,b) and for each \epsilon > 0, there is a \delta > 0 such that 0 < |x - y| < \delta and x,y \in (a,b) imply that \left|\frac{f(x) - f(y)}{x - y}-f'(x)\right| < \epsilon. Prove that...

Homework Statement Find the potential and force on a mass m outside and inside the Earth in terms of g, the acceleration due to gravity, assuming Earth has uniform density and radius R.Homework Equations For a mass m, the potential energy of it in the gravitational field of a spherical shell of...

Hey all, been struggling through this question all afternoon, was wondering if someone could shine some light on the subject please? QUESTION: If a uniform lateral pressure of 80MN/m (2), is applied to the four sides of the bar, in addition to the axial load, find the contraction on the...

This isn't so much of a homework problem as a general question that will help me with my homework. I am supposed to prove that a given function is uniformly continuous on an open interval (a,b). Since for any continuous function on a closed interval is uniformly continuous, I am curious...

Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M

I am given f_n(x)=\frac{nx}{nx+1} defined on [0,\infty) and I have that the function converges pointwise to 0 \ \mbox{if x=0 and} 1\ \mbox{otherwise} Is the function uniform convergent on [0,1] ? No. If we take x=1/n then Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5...

Homework Statement Find the minimum number required (value of n) for the average deviation of the Fourier Series to fall below 2% Homework Equations Use the Uniform Convergence of Fourier Series. Where Sm is the partial sum of the Fourier Series. C is constant. Here C is ∏^2 So...

Homework Statement A light string can support a stationary hanging load of 25.0kg before breaking. An object of mass m = 3.00kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.800m, and the other end of the string is held fixed. What range of...

Homework Statement A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum? Homework Equations The Attempt at a Solution

Please look at the picture... It is of a blue object in four locations that is swung around with a rope ( red line ) in a circle with constant velocity... I wanted to know if my diagrams are correct for each separate location... and I was hoping someone could check my work below to tell me...

Homework Statement A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.01 m/s in a horizontal circle, as illustrated in the figure. If the angle the string makes with the vertical is 38°, and the tension of the string...

The problem statement Let f:[a,b]→\mathbb{R} be differentiable and assume that f(a)=0 and \left|f'(x)\right|\leq A\left|f(x)\right|, x\in [a,b]. Show that f(x)=0,x\in [a,b]. The attempt at a solution It was hinted at that the solution was partly as follows. Let a \leq x_0 \leq b. For all x\in...

Homework Statement I'm being given problems regarding the center of mass of a uniformly dense object, and I am told by the textbook to use: \frac{1}{V}\int x dV I have no idea what to do with that. I'm pretty sure I won't be learning anything about multiple variable integrals for two...