Uniform Definition and 1000 Threads

Homework Statement In space in the absence of gravity, there is a post of "infinite mass," meaning that the post is fixed or "nailed down" and cannot move. A ball of mass m1 is connected to the post by a cable of negligible mass of length L1. A second ball of mass m2 is connected to the first...

The universe is known to be expanding. There is no centre of expanision, since it's space itself that is expanding, rather than galaxies speeding away from us through space. But if the expansion is uniform, wouldn't the space between molecules expand as well as the space between galaxies? If...

Hey everyone! I need some help. Can a non uniform charge distribution exist on a conductor's surface due to some external influence? Please explain bearing in mind that a conductor's surface is equipotential.

Homework Statement Show that if h is continuous on [0, ∞) and uniformly continuous on [a, ∞), for some positive constant a, then h is uniformly continuous on [0, ∞). Homework Equations The Attempt at a Solution I'm thinking of using the epsilon-delta definition of continuity...

Homework Statement A uniform rod of length 0.750 m and mass 1.20 kg is pivoted at one end by a smooth pin as shown below. The rod is released from the vertical position and given a slight nudge to release it from the vertical position of unstable equilibrium...

Homework Statement I am having trouble with calculating the required pump pressure in a horizontal water pipe, 3Km long. i know that the flowrate is 600Kg/s, average velocity 5.6m/s, cross-sectional area of pipe is 0.107143m^2 and losses due to friction average 0.002 per meter Homework...

Hi, I have a problem working out the answer to one part of a type of uniform field question. My answers to the first three parts of the question are correct, but I'll write out those parts as well because I think it's necessary, to understand the second part: An X-ray tube is operated at 25...

Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...

Im wondering if electrons in rectilinear uniform motion will 'feel' an external magnetic field...?

So my teacher said that uniform continuity was a metric space notion, not a topological space one. At first it seemed obvious, since there is no "distance" function in general topological spaces. But then I remembered that you can generalize point-wise continuity in general topologies, so why...

let f is a continuous, real-valued function on [a,b] then, for any e, there exist a polygonal function p such that sup|f(x)-p(x)|<e using uniform convergence, this might be shown... but i cannot figure it out...

Homework Statement Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y? Homework Equations fX(x) = 1/ lambda . exp (-x/...

Homework Statement Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g = (x,y) = sqrt (-2ln(x) . cos(2piy). Since finding the distribution of g(X,Y) analytically is quite tough, I need to generate MATLAB program for 1 - 10,000...

Hello I have been struggling with a simple probability question. Homework Statement We are given that X is a uniformly distributed random variable on [0, 1]. After X is chosen, we take another uniform [0, 1] random variable Y (independent of X) and choose the subinterval that Y falls in. L...

Z = X + Y Where X and Y are continuous random variables defined on [0,1] with a continuous uniform distribution. I know we define the density of Z, fz as the convolution of fx and fy but I have no idea why to evaluate the convolution integral, we consider the intervals [0,z] and [1,z-1]...

I'll be very thankful is someone will tell me where I'm wrong. We know: 1) f is uniform continuous. 2) g is uniform continuous. We want to prove: fg(x) is uniform continuous. proof: from 1 we know -> for every |a-b|<d_0 exists |f(a)-f(b)|<e from 2 we know -> for every |x-y|<d...

Hi all Came across this question which i have attempted to answer but am sure i have gone wrong somewhere, any help would be appreciated... Suppose fn(x):R-->R, where fn(x)=x+(1/n) (n belongs to N). Find the pointwise limits of the sequences (fn), (1/n fn) and (fn2). In each case determine...

Uniform Circular motion problem! Homework Statement A 235 m tall tower is built on the equator. Due to the rotation of the earth, how much faster does a point at the top of the tower move than a point at the bottom (in m/s)? Homework Equations v=w*r (w is omega) The...

Homework Statement A uniform rod 1.1 m long with mass 0.7 kg is pivoted at one end, as shown in Fig. 9-46, and released from a horizontal position. Find the torque about the pivot exerted by the force of gravity as a function of the angle that the rod makes with the horizontal direction. (Use...

Homework Statement So I just took a probability test and I'm having a hard time with the fact that my answer is wrong. I've done some research online and I believe I am correct, I was hoping to get some input. I'm new to using LaTeX so sorry if it's sloppy. Thanks! Problem: Suppose that the...

1. A car initially at rest experiences uniform acceleration of 5m/s2 for 6 seconds. It maintains constant velocity for 14 seconds and is then brought to rest in 5 seconds by a uniform retardation. a. Find out how far the car has travelled. b. Find the total angular displacement of one of the...

Homework Statement For k = 1,2,\ldots define f_k : [0,1] \to \mathbb{R} by \begin{align*} f_k(x) = \left\{ \begin{array}{ll} 4k^2x & 0 \leq \displaystyle x \leq \frac{1}{2k} \\ 4k(1 - kx) & \displaystyle \frac{1}{2k} < x \leq \frac{1}{k} \\ 0 & \displaystyle \frac{1}{k} < x \leq 1...

Homework Statement A neutral metal rod of length 0.35 m slides horizontally at a constant speed of 9 m/s on frictionless insulating rails through a region of uniform magnetic field of magnitude 0.6 tesla, directed into the page as shown in the diagram. Before answering the following...

Homework Statement Two identical, uniform, frictionless spheres, each of weight W , rest in a rigid rectangular container as shown in the figure. Find, in terms of a ratio to W, the forces acting on the spheres due to the container surfaces and one another, if the line of centers of the...

"Let fk be functions defined on Rn converging uniformly to a function f. IF each fk is bounded, say by Ak, THEN f is bounded." fk converges to f uniformly =>||fk - f||∞ ->0 as k->∞ Also, we know|fk(x)|≤ Ak for all k, for all x But why does this imply that f is bounded? I don't see why it...

Homework Statement At x = 1.00 m, the voltage is 4.00 V. At x = 3.00 m, the voltage is also 4.00 V. Assuming that there is a steady, uniform non-zero electric field over this entire region, give four possible directions of that electric field. Homework Equations E = (delta V)/d Ue =...

Homework Statement A uniform plank is supported by two equal 120 N forces at X and Y. The support at X is then moved to Z (halfway to the plank center). The supporting force at Y then becomes? _____________________________ X...Z...c......Y i tried to draw it above. The line is the plank, X...

Homework Statement Homework Equations The Attempt at a Solution This is not graded homework, but optional exercises I found in my textbook. It's days before my exam, but I'm still not sure how to do problems like this. I would really appreciate if someone can teach me how to solve...

Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...

Homework Statement 8. Suppose that X and Y are independent continuous random variables, and each is uniformly distributed on the interval [0,1] (thus the pdfs for X and Y are zero outside of this interval and equal to one on [0,1]). (a) Find the mean and variance for X+Y. (b) Calculate...

1. Homework Statement : It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels. Question: How far would you have...

Homework Statement Theorem: Let (X,d_X),(Y,d_Y) be metric spaces and let f_k : X \to Y, f : X \to Y be functions such that 1. f_k is continuous at fixed x_0 \in X for all k \in \mathbb{N} 2. f_k \to f uniformly then f is continuous at x_0. Homework Equations If all f_k are...

Homework Statement A uniform rectangular coil of total mass 270 g and dimensions 1m x 5m is oriented perpendicular to a uniform 4.00-T magnetic field (the figure ). A current of 2.90 A is suddenly started in the coil. Homework Equations angular acceleration = torgue / moment of inertia...

Homework Statement Define the sequence \displaystyle f_n : [0,\infty) \to \left[0,\frac{\pi}{2}\right) by f_n(x) := \tan^{-1}(nx), x \geq 0. Homework Equations Prove that f_n converges pointwise, but not uniformly on [0,\infty). Prove that f_n converges uniformly on [t, \infty)...

Homework Statement \text{Show that the series }f(x) = \sum_{n=0}^\infty{\frac{nx}{1+n^4 x^2}}\text{ converges uniformly on }[1,\infty]. Homework Equations The Attempt at a Solution I think we should use the Weierstrass M-test, but I'm not sure if I'm applying it correctly: For...

Homework Statement In the experiment that I have performed, the ball was thrown upward and caught once it reached its initial position. The data was recorded using the graphical analysis program. The graph produced is a parabola. The parabolic curve was generated showing the values of three...

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Hi guys, I'm using a composite trapezoidal rule to approximate the integral of functions. Up till now I have been using a uniform composite mesh, ie, there are J intervals, each interval being 1/J wide (since the integral is between 0 and 1). How do I find the most efficient non-uniform mesh...

Homework Statement 1.) Prove that if { f_{n} } is a sequence of functions defined on a set D, and if there is a sequence of numbers b_{n}, such that b_{n} \rightarrow 0, and | f_{n}(x) | \leq b_{n} for all x \in D, then { f_{n} } converges uniformly to 0 on D. 2.) Prove that if { f_{n} } is a...

1. Five equal-mass particles (A–E) enter a region of uniform magnetic field directed into the page. They follow the trajectories illustrated in the figure. Rank from largest to smallest velocity 2. qvBsin(theta) = ma qvB = ma = m(v^2/r) v = qBr/m 3. Based on their...

Homework Statement Is it possible to design a current winding that will produce a uniform magnetic field in a spherical region of space? Homework Equations Well, the literature tells that the equation for the B-field for a uniformly magnetized sphere = (2/3)u_0 * M and also the...

Homework Statement A charge q is uniformly distributed over the volume of a solid sphere of radius R. A spherical cavity is cut out of this solid sphere, and the material and its charges are discarded. Show that the electric field in the cavity will then be uniform, of magnitude...

This page contains one derivation for the potential energy: http://www.shef.ac.uk/physics/teaching/phy205/lecture_4.htm" Result: U=-pEcos\theta where E = magnetic field's magnitude P = dipole moment = d*Q d= distance between + and - charge Q= charges' magnitude \theta = angle between the...

The circular blade on a radial arm saw is turning at 265 rad/s at the instant the motor is turned off. In 12.0 s the speed of the blade is reduced to 85 rad/s. Assume the blade to be a uniform solid disk of radius 0.140 m and mass 0.400 kg. Find the net torque applied to the blade. Relevant...

Homework Statement Note: I will use 'e' to denote epsilon and 'd' to denote delta. Using only the e-d definition of continuity, prove that the function f(x) = x/(x+1) is uniformly continuous on [0, infinity). Homework Equations The Attempt at a Solution Proof: Must show...

This is not homework. I am reviewing all of the calculus that I have forgotten. Howard Anton's Calculus w/Analytical Geometry, 5th ed., section 4.1, prob #32: A police helicopter is flying due north at 100km/hr and at a constant altitude of 1/2mi. Below, a car is traveling west on a...

Homework Statement A uniform electric field of magnitude 325 V/m is directed in the negative y direction. The coordinates of point A are (-0.200, -0.300) m and those of point B are (0.400, 0.500) m. Calculate the potential difference V(B)-V(A). Homework Equations The Attempt at a...

I see in the description of non-uniform circular motion in a textbook, referring to a ferris wheel, that the velocity of an object at the bottom must be twice the velocity at the top, but it is not mathematically shown and it is not immediately obvious to me. Can someone show a simple...

Hi had this question on my last "Statistical Inference" exam. And I still have some doubts about it. I determined that the maximum likelihood estimator of an Uniform distribution U(0,k) is equal to the maximum value observed in the sample. That is correct. So say my textbooks. After that the...

Having trouble getting the formula for this question. 1. During a football games, Igor is 8.0m behind Brian and is running at 7.0m/s when Brian catches the ball and starts to accelerate away at 2.8m/s^2 at rest. Will Igor catch Brian? If so, after how long? How far down the field will...