Uniform Definition and 1000 Threads

Homework Statement Show that the function ##x^2## is not uniformly continuous on ##\mathbb{R}## Homework Equations Delta - Epsilon Definition: ##\exists \epsilon > 0, \ \forall \delta >0, \exists x \in S [|x-x_0|< \delta \text{and} |x^2 - x_0^2| \ge \epsilon ].## The Attempt at a...

Homework Statement Let \left[a,b\right] be a closed bounded interval, f : [a,b] \rightarrow \textbf{R} be bounded, and let g : [a,b] \rightarrow \textbf{R} be continuous with g\left(a\right)=g\left(b\right)=0. Let f_{n} be a uniformly bounded sequence of functions on \left[a,b\right]. Prove...

Two independent random variables X and Y has the same uniform distributions in the range [-1..1]. Find the distribution function of Z=X-Y, its mean and variance. =Using change of variables technique seems to be easiest. fX(x) = 1/2 fY(y) =1/2 f = 1/4 ( -1<X<1 , -1<Y<1) Using u =x -y...

Homework Statement A ball of mass 4 kg on a string of length 1.5 m is being swung in a circle in the vertical plane at a constant speed of 10 m/s. Find the tension in the string at the bottom and top of the balls path Homework Equations ƩF = m(v^2/r) The Attempt at a Solution This is how I...

I'm struggling with the concept of uniform continuity. I understand the definition of uniform continuity and the difference between uniform and ordinary continuity, but sometimes I confuse the use of quantifiers for the two. The other problem that I have is that intuitively I don't...

Alice and bob each choose a number at rndom between zero and two. We assume a uniform probability law under which the probability of an event is proportional to it sarea. Consider the following events: A: The magnitude of the difference of the two numbers is greater than 1/3 B: At least one of...

Continuous Uniform MGF is M_{x}(z) = E(e^zx) = \frac{e^{zb} - e^{za}}{zb - za} \frac{d}{dz}M_{x}(z) = E(X) Using the Product Rule \ U = e^{bz} - e^{az} \ V = (zb - za)^{-1} \ U' = be^{bz} - ae^{az} \ V' = -1(zb - za)^{-2}(b - a) \frac{dM}{dz} = UV' + VU' \frac{dM}{dz}...

Homework Statement Consider a two-ended laser spinner; that is a pen-like laser acting as the arrow mounted on a pin at the center of a spinner. Suppose the center of the disk is one meter away from a wall of infinite extent marked with a linear scale, with zero at the point closest the center...

Homework Statement A satellite is orbiting 600km above the Earths surface. The free fall speed is 8.21 m/s^2. The radius of Earth is 6400km. What is the satellites speed, and the time interval for one orbit around Earth. Homework Equations v = ((2)(PI)(r))/T ac = rw^2 w = (2)(PI)...

Homework Statement Imagine that you've been invited to try out a new "hoversuit," and here's how it works: Someone has set up a large flat sheet, many kilometers across, somewhere on the Earth, and they've charged the sheet up to a uniform charge density σ = +2 x 10^-6 C/m^2. You are...

Homework Statement The Attempt at a Solution So I just want to ask any of you who know physics pretty well if I am on the right track on this question, so it is asking for the magnitude of the acceleration of the car, and the direction. The magnitude of acceleration is (v^2/R) v = velocity and...

Uniform Circular Motion "A Jet Pilot" Hi, my apologies if this has been posted before. I was just wondering if someone could help look over this question for me and confirm if I did it correct or not. It is a written homework rather than online so I can't check my answer to see if I did it...

Homework Statement A charged particle moves through a region of space that has both a uniform electric field and a uniform magnetic field. In order for the particle to move through this region at a constant velocity, A)The electric and magnetic fields must point in the same direction B)The...

Homework Statement I am trying to make sure I am using the Weierstrass test correctly. So, on the following expression: $$f_n(x) = \frac{x}{1+nx^2}, -1 \le x \le 1$$ I looked at it this way. First I checked to see what happens at -1 and 1. The "plug in" test gets me a limit of 1/2 at x=1...

If i measure a weight on Earth without moving in any direction, it weighs 10kg. Suppose I'm moving upwards in a uniform velocity 5m/s , how much would object weigh now ??

So i can see by symmetry arguments why The electric field inside a uniformly charged spherical shell would be zero inside. But what about a non uniformly charged spherical shell. Say most of the charge is located on one side, why is the electric field still zero? I can see that the flux...

Homework Statement A subway train starting from rest leaves a station with a constant acceleration. At the end of 7.8 s, it is moving at 11.778 m/s. What is the train’s displacement in the first 5.6394 s of motion? Answer in units of m Homework Equations a= velocity final - velocity...

Homework Statement . Let ##f: (X,d) → (Y,d')## a uniform continuous function, and let ##A, B \subseteq X## non-empty sets such that ##d(A,B)=0##. Prove that ##d'(f(A),f(B))=0## I've been thinking this exercise but I don't have any idea where to or how to start, could someone give me a hint?

On the plane z=0 there is a superficial charge distribution such that \sigma is constant. Near to the plane, there is a bar, charged uniform with total charge q. At the extremities the bar has two constraints, so it can't turn. If I want to find the constraints force and the force momentum...

As part of a Griffiths problem, I have a charged capacitor placed in a uniform magnetic field which points in +x direction. the capacitor plates are parallel to xy planes. Suddenly, the B field starts decreasing in magnitude...what is the direction of the induced E field? It makes most sense...

Homework Statement Upload Problem 2.3 and I uploaded the question in a reply belowHomework Equations D/2ε E=KQ/R^2 E=E1+E2+E3 The Attempt at a Solution I would upload my work but I am in a location where I can't right now but I can type what I did hopefully it will be clear enough. When r is...

Here is the question: I have posted a link there to this topic so the OP can see my work.

1. Problem statement. 2. Known equations. E = k § dq/r^2 Lamda = Q/L 3. Attempt. I am having trouble figuring out the dq in this situation. I know that lamda = Q/L, and since those 2 are the variables that are changing I take the derivative of them so it looks like Lamda = dq/dL I...

Just started this Analytical Mechanics class, so I figured this question should go here... I've been pretty stuck with a problem. I felt like I totally knew what I was doing but I've become very stumped. We're given the vector for general circular motion...

Homework Statement An infinite line charge of uniform linear charge density lambda = -3.1 mu or micro CC/m lies parallel to the y-axis at x = -1 m. A point charge of 0.7 mu or micro CC is located at x = 2.5 m, y = 3.5 m. Find the x- and y-components of the electric field at x = 3.5 m, y = 3.0...

Homework Statement So there's a rectangular region in the xy plane subjected to a magnetic field B with strength 0.06T pointing in the -z. A proton moving in the xy plane enters the region with velocity v such that the velocity components are initially vx = v*cos(24), vy = v*sin(24). It...

Hi all, My classmates and I have been at this problem for some time, and it doesn't look like we're getting anywhere. We'd really love any help in the right direction! Homework Statement A lawn sprinkler is made from a spherical cap (max angle  = 45\) with a large number of...

If an electron is placed in a uniform electric field it moves from a lower potential to a higher potential.So does it's potential energy decrease.In other words,is PE_{f}-PE_{i}<0? This is confusing me.

why are we considering speed is constant to find velocity a particle in uniform circular motion, is it possible for a particle in a circular motion to have constant velocity?

Homework Statement A uniform rod of mass 1.2 kg and length 1.2 m is pivoted in the horizontal position as shown (black point). The rod is at rest and then released. The acceleration due to gravity is g = 9.8 m/s2. What is the angular speed (in rad/s, but do not include units) of the rod as...

If i took my pencil to a place in space without gravity or air resistance and i spun it, would it spin forever? I mean its undergoing a centripetal acceleration, so energy has to come from somewhere to keep it spinning right? (and of course this is not meant to be an idea for perpetual motion, i...

√ωHomework Statement A uniform rod of mass 1.2 kg and length 1.2 m is pivoted in the horizontal position as shown (black point). The rod is at rest and then released. The acceleration due to gravity is g = 9.8 m/s2. Part 1. Find the rotational inertia of the rod relative to the axis...

Homework Statement A 0.60 kg sphere rotates around a vertical shaft supported by two strings, as shown. If the tension in the upper string is 18 N, calculate the tension in the lower string. Homework Equations ƩFR = maR FT = m * (v2 / r) I am not sure about this, but I also...

What is the difference between Lipschitz continuous and uniformly continuous? I know there different definitions but what different properties of a function make them one or the other(or both). So Lipschitz continuity means the functions derivative(gradient) is bounded by some real number and...

Homework Statement A uniform ladder of weight (W) is leaned across a rough wall and on a rough floor. The reaction at the wall is (S) with frictional force (G)(upward direction) while the reaction at the floor is (R) with frictional force (F)(away from the wall direction). Frictional forces...

Help slove pls!:( A uniform smooth sphere P,of mass 3m, is moving in a straight line with speed u on a smooth horizontal table.Another uniform smooth sphere Q, of mass and m and having the same radius as P, moving with speed 2u in the same straight line as P but in the opposite direction to P...

Homework Statement Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center. Homework Equations ##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}## ##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy'...

Why is there only a radial component of acceleration present if a body is undergoing uniform circular motion whereas in non uniform circular motion both tangential and radial component of acceleration are present?

Why are centre of mass of all uniform symmetric bodies at there geometric centre? We know the following result: "Consider a system of point masses m1,m2,m3... located at co-ordinates (x1,y1,z1), (x2,y2,z2)...respectively. The centre of mass of this system of masses is a point whose co-ordinates...

This began as homework that our Physics teacher set us. However, for some reason he decided no to collect it. I am curious as to whether or not this display my understanding of the topic well as communication is main area my teacher believes I need improvement in. Homework Statement Write a...

In uniform circular motion only a radial component of acceleration is present i.e centripetal acceleration. So why doesn't the particle following uniform circular motion go radially inwards due to radial acceleration?

Hi, One of the boundary conditions when solving for the potential, \Phi, outside a dielectric sphere placed within a uniform electric field is \lim_{r→0}\Phi(r,θ)<\infty Can anyone explain/prove why this so. Thanks,

Homework Statement Cletus is traveling at 30.0 m/s as he passes a trooper hidden behind a billboard. Four seconds later, the trooper begins his chase for Cletus with a constant acceleration of 2.00 m/s2. How long does it take the trooper to intercept Cletus? Homework Equations x...

Homework Statement An object is in uniform circular motion. As the time passes by, its mass decreases. ( It has Co2 in it, and it evaporates) What will happen to the object's velocity and angular momentum? Homework Equations F = mV²/r, L = mvr The Attempt at a Solution...

Hello everyone, I'm trying to solve a problem but I want to find a simpler way if possible. The basic idea is that I would have one waveguide, for simplicity I will just take a slab waveguide. However instead of being constant there is a point at which the distance between the slab suddenly...

Uniform Circular Motion Question Please Help! (Mechanics/Physics I) A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.10. The length of the arc ABC is 200 m, and the car completes the turn in 34.0 s. (figure attached as...

Hi, I have the next RV: $$\underline{W}=\frac{\underline{X}}{\frac{||\underline{X}||}{\sqrt{n}}}$$ where $$X_i \tilde \ N(0,1)$$ It's a random vector, and I want to show that it has a uniform distribution on the n-sphere with radius $$\sqrt{n}$$. I understand that it has this radius...

Direction of force acting on a body in uniform circular motion?? Hello Sir/Ma'am I'm a a novice. I joined this forum to clear my doubts and improve my physics. Here is my question.. " We generally say, frictional force always acts in a direction, opposite to the direction of motion of a body...

Homework Statement A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency? Homework Equations τ=rFsinθ f=(1/2π)√(k/m) F=kx...

http://gyazo.com/b031e9d54f9512e5a583a4ed0ea28a0a the answer is 2/3: my attempt: one side X~U[1,7] the longer part of this side, call Y, where Y~[4,7] P(Y>6) = 1/3 don't see how they got 2/3, they have 3 different methods in the answers, but none doing my method. I'm...