Unit Definition and 1000 Threads

Homework Statement Ok so using the standard equation v = Sqrt(T/Mu) I want to find Mu as a gradient for the first fundamental. I've made it into F x lambda = sqrt(T/Mu) Then f x 2l = sqrt(T/Mu) Then f= sqrt(T/4l^2 Mu) As I'm having the tension held by a mass suspended over a pulley. f=...

So I am given the vector 1...but I need to find vector 2 and 3, in order to find U=(v1, v2, v3), and U is a unitary matrix. Vector 1 is: (1/2+1/2i 1/2 1/2i)^T The example from my notes shows me how to find U, but I am also given a matrix S to start with... Any clue where to start?

Homework Statement see attached file Homework Equations The Attempt at a Solution ok so I get that the answer is B but is it because they have the same q/m ratio?

Homework Statement If \phi(x,y,z) = x3 + 2xy +yz3 find \nabla\phi at the point P=(1,1,2) and direction of the unit normal to the surface \phi(x,y,z) = 11 at P. Homework Equations The Attempt at a Solution Worked out \nabla\phi to be 5i + 10j + 12k Got |\nabla\phi|= √256 so the...

hey, i've been trying to work out how to determine the sign of cross products of unit vectors, for example in cylindrical, r x z = - theta theta x z = r r x theta = z i can't figure out the sign, r x z = |r||z|sinβ theta where β is the angle between them, which is 90°...

Homework Statement Evaluate the matrix elements x_{nn'} = \left<n\left|x\right|n'\right> and p_{nn'} = \left<n\left|p\right|n'\right> and map the energy eigenstates \left|n\right> to Cartesian unit vectors. Homework Equations x = \sqrt{\frac{\hbar}{2m...

Homework Statement The problem is given as a piece-wise function f(t)={1, 0≤t<4; 0, 4≤t<5; 1, t≥5}. I am asked to write the function in terms of unit step functions and then find the Laplace Transform of the function. I can do the Laplace if I could ever get the unit step function...

Hi, I am a bit confused about the units of L = (0.9λ)/(βcosθ) the Scherrer equation used in powder diffraction. My idea is λ= radiation wavelength with unit (angstrom) β= FWHM with unit (radians) θ= braggs angle with unit (degrees) L= particle size with unit (angstrom) Am I right in...

Homework Statement let f(z) be a 1-1 analytic mapping of unit disc |z|<1 onto itself with two fixed points in |z|<1 Show that f(z)=z Homework Equations none The Attempt at a Solution I'm thinking there has to be a theorem or something that I am missing for this.. But I'm not...

To find the eigenvalues \lambda of a matrix A you solve the equation det |A - \lambda I| = 0 eq(1) but now what if you add e I to the matrix A where e is a constant? Then you have to solve the equation, det |(A + eI) - \lambda_{new} I| = 0 eq(2) which is the same as solving...

I am trying to understand this example: Let H be the upper half plane. The map $$ f:z\mapsto\frac{z - i}{z + i} $$ is an isomorphism of H with the unit disc. proof: Let $w=f(z)$ and $z=x+yi$. Then $$ f(z) = \frac{x + (y-1)i}{x+(y+1)i}. $$ Since $z\in H$, $y>0$, it follows that...

Prove that the most general analytic isomorphism of the open upper half plane, $\mathcal{H}$, onto the open unit disc is of the form $$ T(z) = e^{i\varphi}\frac{z - a}{z - \bar{z}} $$ for some $\varphi\in\mathbb{R}$ and some $a\in\mathbb{C}$ with $\text{Im}(a) > 0$ I need some guidance here...

Homework Statement I'm having trouble with part b and part d, where there is some kind of ramp function involved http://img845.imageshack.us/img845/7507/76500775.jpg The Attempt at a Solution For part b, I calculated the gradient of that ramp, and the intercept which gives y = -x...

Homework Statement Define a pseudometric on the unit sphere S^{n} in ℝ^{n+1} that makes the set of lines in ℝ^{n+1} through the origin into a metric space. Homework Equations Pseudometric (X,\rho) is where \rho satisfies all conditions of a metric except that \rho(x,y) = 0 need not...

I have a very simple question We all know that high frequency light has more energy than low frequency What IS oscillating, though? What are the units of the x and y axis?

Homework Statement Let R be a ring with multiplicative identity. Let a, b \in R. To show: 1-ab is a unit iff 1-ba is a unit. The Attempt at a Solution Assume 1-ab is a unit. Then \exists u\in R a unit such that (1-ab)u=u(1-ab)=1 \Leftrightarrow u-abu=u-uab \Leftrightarrow abu=uab. Not...

Homework Statement I am reading about electrodynamics, and in different formula, there is a SI form and a Gaussian form. Homework Equations What is the relationship in the different unit system for c or B or E and other relative variables? The Attempt at a Solution sometimes...

Dear all, My aim is to get the density of states (DOS) per unit area for monolayer (bilayer) graphene. I have done this using mathematica. I have set a sampling k grid with 22500 points and computed the expression: DOS=(1/Nk)*Ʃ δ(E-Ek) where the sum is over the k points in the reciprocal...

Homework Statement http://img828.imageshack.us/img828/1149/70833278.jpg Now this is a part of the solution that was given I was having difficulty understanding. The Attempt at a Solution i(0) = 0 - understood u(t -1) for 0 < t < 1 = 0 I can understand why the voltage from...

Homework Statement y'' + 4y' + 2y = u_pi(t) + u_2pi(t) y(0) = 0 and y'(0) = 0.Homework Equations the step function equation: u_c(t) = u(t-c) --> (laplace) --> e^-cs/sThe Attempt at a Solution i am having major probs with getting my head around step function probs wrt laplace transforms. What...

Homework Statement Could someone please explain this to me? I have read several notes on it, but do not really follow the reasoning: The Attempt at a Solution When t = 0, -1/s*e^-st = -1/s because e^0 = 1. When t goes to infinity is the part I do not fully understand. Why...

Homework Statement Let Y_i be standard normal random variables, and let X be an N vector of random variables, X=(X_1, ..., X_N) where X_i = 1/{sqrt{N}} * Y_i. I want to show that as N goes to infinity, the vector X becomes "close" to the unit sphere. Homework Equations The...

In my Trig class, we learned about the unit circle and its relationship to the various trig functions (sin, cos, etc.). I am curious to know why the unit circle works the way it does, and the how it was "derived" so to speak. More specifically, why does radius of the circle have to be 1 for...

Homework Statement http://imgur.com/LDx7IHomework Equations http://en.wikipedia.org/wiki/Snell%27s_law The Attempt at a Solution I'm not really sure on the approach to take for this question. Since it proves 2 angles, Snell's Law could prove to be beneficial. Thanks for the help!

Homework Statement A cylinder rotating uniformly about the x' axis of S' will seem twisted when observed instantaneously in S, where it not only rotates but also travels forward. If the angular speed of the cylinder in S' is ω, prove that in S the twist per unit length is yωv/c(squared)...

Homework Statement Let c(t) be a path of class C1. Suppose that ||c(t)||>0 for all t. Show that c(t) dot product with d/dt((c(t))/||c(t)||) =0 for every t. Homework Equations I am having trouble with the derivative of (c(t)/||c(t)||) and how to show that when its dotted with c(t) that...

Hello Forum, a lattice is a set of points. We can place a basis at each set of points. The basis can be one atom or a group of atoms. I thought that a translation of the basis would produce the whole crystal... How is a basis different from the unit cell? Are they the same thing...

Hi, I want to rotate vectors through 120 and they are unit vectors so they lie on a unit spheres. So basically the tails of the vectors are at the origin and given one vector with spherical coordinates (1,θ,∅), how do I obtain the coordinates of the unit vectors that make 120 degrees with the...

how do you calculate the amount of water that can be supplied to pvc pipe with an exact number of holes drilled into it to feed plants water 3/32" diameter hole in 1/2 pvc pipe each pipe has 29 hole 5 pipes approx 88" long connected to a 1" pvc pipe manifold water fed through drilled holes must...

Homework Statement long solenoid of n turns per unit length is wound upon a cylindrical core of radius a and relative permeability. The current I through the solenoid is increasing with time t at a constant rate. Obtain expression for the rate of increase of stored energy per unit length...

Someone give me a crash course on Unit Step Laplace Transform and Inverse Laplace Transform. Need help on the formula: U(t-a)f(t-a) to (e^-as)F(s) from what i can deduce, the way to use it is (Laplace) - Find a from U(t-a) - group (t-a) together - replace (t-a) with ____ (?) What...

Write f(x) in terms of the unit step function u(x). $u(x)=\left\{ \begin{array}{rcl} 1\ &\text{if}& \ x\geq 0 \\ 0\ &\text{if}& \ x<0\end{array} \right.$ $f(x)=\left\{ \begin{array}{rcl} 1\ &\text{if}& \ 2n\le x\le 2n+1 \\ 0\ &\text{elsewhere}\end{array} \right.$

If you already have one of the two coordinates?

Dear all, I have a simple question for you. Any help will be very appreciated. ==Assumptions=== I have a 2x2 matrix, with real entries: |A B| |C D| Such matrix has unit determinant, AD-BC=1. (For those of you in group theory: the above is a representative of SL(2,R))...

Ok I can do the integral and see that it is equal to 2∏i, but thinking about it in terms of 'adding up' all the points along the curve I feel like every every point gets canceled out by its antipode, e.g. 1/i and -1/i.

Homework Statement Question: "Find the unit tangent, normal and binormal vectors T, N, B, and the curvature of the curve x = 4t, y = -3t^2, z = -4t^3 at t = 1." Answer: T = 0.285714285714286 i - 0.428571428571429 j - 0.857142857142857 k N = -0.75644794981871 i + 0.448265451744421 -...

Analytic in the unit disc $z^7$ yes $|z|$ no $\frac{1}{z}$ yes Correct?

I have a query of supplying pumps namely electricity operating pump 500 GPM, 7 bar, diesel engine driven backup pump 500 GPM, 7 bar and a jockey pump 50 GPM, 8 bar to be used for making fire fighting pumping unit (FFPU). Please guide/tell how to design the unit (FFPU) from these?

I originally wanted to post this in the EE forum, but after seeing the sticky there, I decided that this might be a better place. 1. I got the whole thing about unit conversions (like from V to kV, move the decimal point 3 to the left -- the number becomes smaller by 10^3). Right now, we're...

Does anyone know exactly what kind of mathematical object a unit (like meters, coulombs, etc.) is? Or what kind of algebraic structure units are elements of?

Homework Statement For a particular material the density varies with position as ρ(r)=x2yz Find the total mass of a unit cube with one edge in the origin made by a such a material.Homework Equations We have dm = ρ(r)dV = ρ(r)dxdydz So we want to calculate the volume integral (all from 0 to 1)...

Homework Statement Let c(t) be a path and T the unit tangent vector. What is \int_c \mathbf{T} \cdot d\mathbf{s} Homework Equations The unit tangent vector of c(t) is c'(t) over the magnitude of c'(t) : \mathbf{T} = \frac{c'(t)}{||c'(t)||} The length of c(t) can be represented by ...

Homework Statement Find the unit tangent vector at the indicated point of the vector function r(t) = e(19t)costi + e(19t)sintj + e(19t) kT(pi/2) = <___i+___j+___k>Homework Equations r'(t) / |r'(t)| The Attempt at a SolutionAnswers: 19e(19*∏/2)(cos(∏/2)-sin(∏/2)) /...

Homework Statement Find two unit vectors that are normal to the plane determined by the points A(0,-2,1), B(1,-1,-2), and C(-1,1,0) I found the cross-product of the two position vectors then i got 8i+4j+4k then i divided that by the magnitude to get the unit vector but how do i find the other...

Find unit vector with a given angle to two other vectors in 3-space Homework Statement We are given the vectors <1,0,-1> and <0,1,1>, and are told to find a unit vector that shares an angle of (pi/3) with both of these vectors. Homework Equations a(dot)b = |a||b|cosθ The...

Homework Statement A radium nucleus decays by emitting an alpha particle. The speed of the recoiling nucleus is small compared to the speed of the alpha particle. This is because the: A force acting on the recoiling nucleus is smaller than the force acting on the alpha particle B...

2 unit negative chargees and a positive charge +q are along the same line. what should be the magnitude of charge q and in which position must it be placed so that the three charges remain in equilibrium...

Hello! I'm just asking for a clue on how to make a unit hydrograph Reservoir Level - Storage Curve for a Dam. I have been searching information on internet, but I could not find anything about that. I would appreciate any idea or suggestion. Thanks!

Homework Statement If u is a unit vector, find u.v and u.wHomework Equations I assumed that unit vector means u=<1,1,1> u.v=|u||v|cos60 My knowledge of unit vectors is very limited. I know that a unit vector is i=<1,0,0> j=<0,1,0> k=<0,0,1> The Attempt at a Solution Since the triangle is...

The deciBel is probably the most commonly used unit for sound, but why isn't there an SI unit? Also, what is a logarithmic unit? Thanks.