A uniform is a type of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform.
Homework Statement
S solid uniform glass sphere is surrounded by air. The sphere has radius R and refractive index n. As shown in the picture, a light ray traveling in air, parallel to a diameter of the sphere, enters the sphere, reflects off the far side, then exits the sphere traveling in a...
How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?
Homework Statement
If a curve with a radius of 60 meters is properly banked for a car traveling 60 km/hr, what must the coefficient of friction be for a car on the same curve traveling 90 km/hr?
Homework Equations
Fmax = u * Fn
where Fmax = force causing the friction, u = coefficient of...
Homework Statement
Fuzzy dice hang from the rear-view mirror of a car rounding a curve. If the curve has a radius of 275 meters and the dice are hanging at an angle of 12° from the vertical, how fast is the car going?
Homework Equations
a = v2/R
for an acceleration with a constant...
Homework Statement
A uniform bar AB of length l and weight W is hinged to the wall at its end A and supported by means of a string of length a which is tied to the wall as shown. Find the angle \theta that the bar will make with the wall corresponding to the position of equilibrium...
Homework Statement
A purse at radius 1.90 m and a wallet at radius 2.60 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2) + (4.60 m/s2). At that instant and in...
Homework Statement
A Machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for $3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the...
Homework Statement
Which, if any, of the following statements about a particle in uniform circular motion is/are true?
Its acceleration vector is a constant.
Its velocity and acceleration vectors are always perpendicular.
The direction of its acceleration is toward the center of...
Homework Statement
A non-uniform surface charge lies in the xz-plane. At the origin, the surface charge density is (sigma)=3.01C/m^2; other charges are present in the vicinity as well. Just to the right of the origin the y-component of the electric field is 520,000N/C. What is the y-component...
Homework Statement
The graph shows the potential energy of an electric dipole which is in a constant electric field; only the electric force is acting on the dipole. Consider a dipole that oscillates between +/- 51 degrees.
What is the dipole's kinetic energy when it is aligned with the...
Homework Statement
We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box?
Homework Equations
The Attempt at a Solution
I have an...
Homework Statement
An 80kg person is preparing to dive into a pool. The diving board is a uniform horizontal beam that is hinged to the ground at point A and supported by a frictionless roller at D. B is the point directly under the center of gravity of the person. The distance between A to B...
Homework Statement
Alright, here is the problem. Given a compact metric space X, and a sequence of functions fn which are continuous and f_{n}:X->R (reals), also f_n->f (where f is an arbitrary function f:X->R). Also, given any convergent sequence in X x_{n}->x, f_{n}(x_{n})->f(x). The problem...
Homework Statement
Does the following series converge uniformly?
[sum from n=1 to inf] \frac{e^{-nx}}{n^2} on [0, inf)
Homework Equations
I know I need to use the M test or Cauchys Principle of uniform convergence. My tutor suggests using the former if there is uniform convergence...
Homework Statement
A uniform thin rod 7.0 cm long with a mass of 40.0 g lies on frictionless horizontal table. It is struck with horizontal impulse at right-angle to its length, at a point 2.0 cm from one end. If the impulse is 8.5 mN*s: describe the resulting motion of the stick...
Homework Statement
Accelerating voltage of 2500V is applied to an electron gun producing a beam of e- originally traveling horizontally north in a vacuum toward a viewing screen 25cm away. a. What are the magnitude and direction of the deflection caused by Earth's gravitational field? b. What...
Homework Statement
How to calculate the expected value of the log of a uniform distribution?
Homework Equations
E[X] where X=ln(U(0,1))
The Attempt at a Solution
integral from 0 to 1 of a.ln(a) da where a = U(0,1)
= -1/4
However I know the answer is -1
Homework Statement
[edit]: In case anyone didn't get a clear picture, in a nutshell the experiment involves us releasing a glider down an air track within a fixed distance x, where the time, t taken is then recorded down. Sorry for not mentioning this before if it's of any use.
To determine...
I would like to determine the MLE for k in U(0,k) where U is the uniform pdf constant on the interval [0,k] and zero elsewhere. I would like this estimate in the case of missing data. To be specific, what is the MLE for k given the three draws X={1,3,*} where * is unknown.
Homework Statement
a) What is the value of an electrostatic potential V, a distance r from a point charge Q?
b) A uniform line of charge, of linear charge density (\lambda), extends along the x-axis from x = 0, to x = a.
i) By considering the contributions from the infitisimal elements...
A function is pointwise bounded on a set E if for every x\in E there is a finite-valued function \phi such that |f_n(x)|<\phi(x) for n=1,2,....
A function is uniformly bounded on E if there is a number M such that |f_n(x)|<M for all x\in E, n=1,2,....
I understand that in uniform...
hi everyone
I was reading one example about Uniform continuity, say that the polynomials, of degree less than or equal that 1 are Uniform continuity, my question is, for example in the case polynomial of degree equal to one Which is \delta, that the Uniform continuity condition satisfies...
Homework Statement
We know that f is uniformly continuous.
For each n in N, we define fn(x)=f(x+1/n) (for all x in R).
Show that fn converges uniformly to f.
Homework Equations
http://en.wikipedia.org/wiki/Uniform_convergenceThe Attempt at a Solution
I know that as n approaches infinity...
<p> and <p^2> for uniform "psi"
Homework Statement
What is <p> and <p^2> for state:
\begin{array}{l}
\psi (x) = {\rm{constant for x}} \in {\rm{[ - a,a]}} \\
\psi (x) = {\rm{0 for x}} \notin {\rm{[ - a,a]}} \\
\end{array}
...that is: a "psi" that is constant within...
Hi.
I'm curious, how would a charged particle, let's say an electron, move in a simple uniform electric field?
My first guess would be that it would follow Newton's second law of motion and move with a constant acceleration:
$ \dot{x}=\frac{Eq}{m} $
where E is the fields intensity, q the...
Homework Statement
A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source?
Just a simple answer check to see if my answer is reasonable.
Homework Equations
\beta = 10 db log (I/I0)...
Hello guys. I am taking an introductory course in computer programming. For one assignment I was to make up a word problem, then write a program to solve it. I wrote a program to calculate the radius of a circular orbit based on the orbiting object's current velocity, and other parameters. Can...
Here the extra credit question I'm stuck on:
A square loop (perimeter of 4L and hinged along one side) is made of a wire that has a mass per unit length of 0.1000 kg/m and carries a current of 5.000 A. A uniform magnetic field of 10.00 mT directed perpendicular to the hinged side exists in...
Homework Statement
Which of the following is not true in relation to an object moving in uniform circular motion?
a. KE of the object is constant
b. net force is zero
c. net work is zero
d. the magnitude of acceleration is constant
e. momentum is non-constant
The Attempt at a...
Homework Statement
Determine the dipole moment, \mathbf{p}, of a sphere of radius R with a uniform volume charge, total Q, with respect to its center. Homework Equations
\mathbf{p}=\int \mathbf{r} \rho(\mathbf{r}) d\tauThe Attempt at a Solution
I know that \mathbf{p}=\mathbf{0}, but I have a...
Homework Statement
The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates.
If the plates are moved closer together
A X and Y will both remain...
Let y_n be a sequence of functions in \mathcal{C}([0,1], \mathbb{R})
Suppose that every subsequence of y_n has a subsequence that converges uniformly. Prove that they all converge to the same limit.
1.kn (x) = 0 for x ≤ n
x − n, x ≥ n,
Is kn(x) uniformly convergent on R?
I can show that it is uniformly convergent on any closed bounded interval [a,b], but I don't think it is on R. Could anyone please give me some hints how to prove it?
2.Fix 0 < η < 1. Suppose now...
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...
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...