Unit Definition and 1000 Threads

I have an integral of aΘ cos(Θ) dΘ a is the unit vector for Θ. I'm not sure what to do with it in the integration. I know the unit vector equals a/abs(a) but that would give a mess of an integral cause of the abs(a).

I am a little confused by an elementary point. Something must be wrong with the following: On one hand, a Hermitian operator (which is not necessarily unitary) takes one state to another state. Hence a state need not be represented as a unit vector; its norm can be greater (or less than)...

Homework Statement Calculate ##\int _Kz^2exp(\frac{2}{z})dz## where ##K## is unit circle.Homework Equations The Attempt at a Solution Hmmm, I am having some troubles here. Here is how I tried: In general ##\int _\gamma f(z)dz=2\pi i\sum_{k=1}^{n}I(\gamma,a_k)Res(f,a_k)## where in my case...

Hello Homework Statement Show that for an ideal gas: n(E)dE=2πn/(kπT)3/2 *E1/2 exp(-E/kT) dE where n(E) is the number of particles for each element of volume whose energy is between E and E+dE Homework Equations The Attempt at a Solution Really don't know where to start...

Hi everyone, I've some points I want to make sure of. 1- When converting a "POINT" from a coordinate system to another, I'll just use the derived equation to convert (e.g. (1,2,3) from cartestian to cylindrical: \rho=\sqrt{x^{2}+y^{2}}, \phi=tan^{-1}\frac{y}{x}, z=z 2- When converting an...

Homework Statement I need to convert from a fv in units of Jy to fλ in units of erg s^-1 cm ^-2 A^-1 fv = 1.0254e-2 Jy Homework Equations fv dv = fλ dλ fλ = fv dv/dλ and because v = c/λ... fλ = fv*c / λ^2 Also 1 Jy = 10^-23 erg cm^-2 s^-1 Hz ^-1 The Attempt at a Solution...

Homework Statement The power available (output) is measured by the velocity at which you are moving and the thrust required to create that movement. NOTE: Conversions for proper units are provided below equation. Power Available: Pout = Tc * v where: Pout = power available (watts) Tc...

Homework Statement a and b are vectors in R^3 s.t. a=(1,7,-4) and b= -3j-4k 1. Find ||3a-3b|| (magnitude of 3a-3b) 2. Find unit vector u in direction of 3a-3b, write answer in form (u1,u2,u3) 3. Find vector of length 8 in direction of a (write answer in form "-") Homework Equations...

Homework Statement $$Let\quad n\quad =\quad the\quad number\quad of\quad hours\quad I\quad run\quad a\quad 40\quad kilowatt\quad generator.\\ Assume\quad that\quad it\quad costs\quad $0.08\quad for\quad 1\quad kWh.\\ Revenue\quad from\quad generator=\frac { $0.08 }{ kW\cdot hours } \quad...

I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...

Follow the 1st ideia: \\ d\vec{r} = dr \hat{r} + r d\theta \hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \frac{dr}{dr} \hat{r} + r \frac{d\theta}{dr}\hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \hat{r} and now: \\ \frac{d\vec{r}}{dr} = \frac{d\vec{r}}{dt} \frac{dt}{dr} = \frac{d\vec{r}}{dt}...

I have the following question: Given that ø = (x^2)y + cos(z) find the unit vector n which is both tangent to the surface of constant ø at (1,1,∏/2) and normal to the vector b = x + y - 2z (where x y and z are the unit vectors) I have calculated ∇ø = 2x + y - z (again where x y and z are...

Homework Statement Hi, I am having trouble with the following problem and I can't seem to find any examples: I am trying to determine reactions at points A and D of the redundant structure below using the unit load method, there is a 10kN load at the top left point (B), all lengths are...

Homework Statement Hi. I am currently doing a lab where I need to convert mm Hg to atmospheres. When I try to use an online converter to do this, it gives two options for atmospheres, technical and standard. Which would be the best to use for a laboratory calculation...

how can this integral be calculated: ∫[e^(−2mx) θ^2(x)+2θ(x)θ(−x)+e^(−2mx)θ^2(−x)]dx from -∞ to ∞ where θ(x) is the unit step function with its amplitude 0 everywhere before x=0 and θ(−x) is the unit step function with its amplitude 0 everywhere after x=0In Introduction to Quantum Mechanics...

Hi everyone, I've two vectors in cylindrical coordinate - (-1,\frac{3\pi}{2},0),(2,\pi,1) - and I want to find the perpendicular unit vector of these two vector. Basically I'll use the cross product, then I'll find the unit vector by \hat{u}=\frac{\vec{u}}{||\vec{u}||}. But do you I...

like for example digital unit measurement for clear images in devices is ...pixel

Hi everyone, Just want to know how does the the unit vector become in that form: \vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{x \vec{i}+y \vec{j}}{4}

Hello, I have a relatively simple question. after being unable to find it through google I have decided to ask you guys if you know what the Laplace transform of a unit step function that looks like this would look like Us(t-2) From tables, the Laplace transform for a regular units step...

Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've...

Homework Statement You are given that with x = (x1,x2), y = (y1,y2), the formula (x,y) = [x1 x2] [2 1;1 2] [y1;y2] (where ; represents a new row). is a inner product for the vectors in R2 Using this inner product, find a unit vector perpendicular to the vector (1,1) Homework Equations The...

Hi all, Im trying to think of a way of generating non-intersecting randomly oriented cylinders within a unit cell volume for micromechanical analysis. Several research papers suggest a monte-carlo approach was used by displacing cylinders by vectors until the "condition was satisfied" -...

I previously asked a question about this problem. I think I found the answer myself, and I want to know how I did. I'm pretty new at this proof thing and have been working through the textbook Real Mathematical Analysis by Charles Chapman Pugh. Any criticism would be appreciated! Problem...

Hi all, I read The unit cell is the smallest structure that repeats itself by translation through the crystal. Some says premitive unit cells contains atoms only at the corners while a unit cell may contain extra atoms in between(like bcc or fcc). At one place I found this: For each...

The following problem is from the textbook "Real Mathematical Analysis" by Charles Chapman Pugh. Given ##\epsilon > 0##, show that the unit disc contains finitely many dyadic squares whose total area exceeds ##\pi - \epsilon##, and which intersect each other only along their boundaries. I...

As the title inquires, I am curious as to how or why the Sin function represents y coordinate on the unit circle.

Homework Statement When a vector A is dotted with a unit vector, the result is... Select one: a. zero b. the magnitude of the unit vector in the direction of A. c. the magnitude of A. d. the angle between A and the unit vector. e. the magnitude of A in the direction of the unit vector...

Homework Statement Homework Equations I know the equations. See question below. The Attempt at a Solution I am just wondering with this problem, how is it that they go from that derivative to the magnitude at the bottom of that image? I know the formula, but what I mean is...

Homework Statement Say for example, a particles velocity was given by the following equation: \vec{V}(t) = (2t2-4t3)\hat{i} - (6t +3)\hat{j} + 6\hat{k} If I wanted to find the displacement of the particle between t=1s and t=3s, could I just integrate like this? \int \vec{V}= (2t3/3...

Homework Statement The dot product for two.parralel pointing.unit.vectors is ? A. 1 B. 0 C. -1 D. Undefined [b]2. Relevant equation The Attempt at a Solutionsince they are unit vectors they have a magnitude of 1,this implies that the dot product is 1,since the angle between...

hi friends, can anybody clear my concept about the following sentence. " if we use substrates with higher permittivity, like quartz or GaAs that has been used in previous successful experiments, the unit cell will have smaller unit-to-wavelength ratio".

Before anyone thinks I didn't numerous attempts before opening this topic, take a look at my rough draft of mathematics in the annex. So, a simple question. How derivate an unit vector wrt any variable? I can derivate any unit vector wrt θ or φ, obivious, but how derivate the vector φ wrt to x...

I an ideal gas how do I calculate the number of collision per unit area? By collision I do not mean collision between the atoms but rather it is a problem where I know that a nucleation cluster of area A is in my gas, and I want to find the probability that it will get hit by an atom. I know the...

Below is the typical diagram of a Substation in which MIL and MIR are with TR-1 and TR-2 respectively. Where TR-1 and TR-2 are the transformers whose function is to step down the voltage. I have also confusion about the flow(path) of the electricity with in substation. The confusion is that...

Homework Statement the first derivative of a vector of constant magnitude is the cross product of the angular velocity of the vector(i.e , the angular velocity of the moving coordinate system ) and the vector itself.)Homework Equations di/dt= w x i , here w is the angular velocity and x is...

Homework Statement So this isn't really a specific homework question, it's more of a general one. What is the difference between ax and i(hat)? I thought they were the same thing. Can someone please explain the difference? Homework Equations The Attempt at a Solution

Homework Statement Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 4.713 g, is pressed into a leaf of 6.549 μm thickness, what is the area of the leaf? (b) If...

I have a nice table that shows the dot product between unit vectos (see annex). I'd like know how is the cross product between unit vectos of all basis. Do you have a table with such information?

As a particle orbits around a circle, the unit vector of the velocity and acceleration component is constantly changing, so, how do I determine the unit vector?

Homework Statement Consider the sphere x2 + y2 + z2 = 1 Find the mean and variance. Homework Equations The Attempt at a Solution Mean = 0 (Symmetry) Variance Probability = \frac {dV}{\frac{4}{3} \pi R^3} = \frac {4 \pi r^2 dr}{\frac{4}{3} \pi R^3} = 3 \frac {r^2}{R^3} dr Variance =...

\bar{}Homework Statement Hi, I want to show that \frac{\partial}{\partial \phi} is a Killing vector on the unit sphere with metric ds^2 = d\theta^2 + \sin^2 \theta d \phi^2 Homework Equations I compute the Christoffel symbols to be \Gamma^\theta_{\phi \phi} = -\sin \theta \cos...

I am a bit confused about what the difference is between the two? To give some specific context where it has thrown me off, say if I were to define a charge with a vector r and compared that to a unit vector r hat, what exactly is the difference between what each of those tells me? I have...

Is it necessary for a unit sum composed of unit fractions to include 1/2? Doing maple runs this seems to be the case, but it is not evident to me how this could be Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia But...

Dear All, J/K into m/s ? Or kgJs/m into kg? thanks for your help! Rajini.

When i is defined by an equation which has 2 solutions, how does it make sense to do algebra with complex numbers?

If all columns of a matrix are unit vectors, the determinant of the matrix is less or equal 1 I am trying to prove this assertion,which i guess to be true. can anybody help me? Thank's in advance

Does the curvature of spacetime have a unit?

(Skip to the bottom for my questions). I'm just sounding off my thoughts above. Homework Statement Find the density of aluminum, which crystallizes in a face-centered cubic unit cell. The atomic radius is 143 pm. Homework Equations edge length of FCC is (4/sqrt2)r. The Attempt at a...

I am asked to show that when \(\hat{e_r}\), \(\hat{e_\theta}\), and \(\hat{e_\phi}\) are unit vectors in spherical coordinates, that the cartesian unit vectors $$\hat{i} = \sin{\phi}\cos{\theta}\hat{e_r} + \cos{\phi}\cos{\theta}\hat{e_\phi} - \sin{\theta}\hat{e_\theta}$$ $$\hat{j} =...

Homework Statement b_{k} = {4, 1, 1, 4} x[n] = 2u[n] Write your answer using scaled unit impulse sequences and scaled unit step sequences. Write explicitly. Homework Equations The Attempt at a Solution 4114 2222222... ------------ 8228 8228 8228 8228 8228 ... ------------...