Unit Definition and 1000 Threads

Say for example v = <3,4> I was taught to divide each component by the magnitude in order to get the unit vector, i.e. 3^2 + 4^2 = ||v||^2 5 = ||v|| So the unit vector of that vector is <3/5,4/5> or 1/5<3,4> But if I forgot that I had to divide the components by the magnitude, I would not...

Suppose you look at all of the equilateral (non-self-intersecting) polygons** with an odd number of sides, and each side length is equal to 1 unit. For examples, the polygon with the fewest number of sides in this group is the equilateral triangle, and then the next one is an equilateral...

I have grammar S → ABaC | BaC | AaC | ABa | aC | Aa | Ba | a A → B | C | BC B → b C → D D → d Can someone please help me to eliminate all the rules of grammar production unit. Thanks for help! :biggrin:

Question: Carbon-14 has a half-life of 5730 years. A bone is found in which \frac{7}{8} of the original [16g of] carbon-14 has decayed. How old is the bone? Formula: C(t)=Co(\frac{1}{2})\frac{t}{H} (it's hard to see but it says \frac{1}{2} to the power of \frac{t}{H}) C(t) - the number at...

Homework Statement Starting with: G = \frac{I}{V}= \frac{-\int_{s}\sigma\mathbf{E}\cdot d\boldsymbol{s}}{-\int_{l}\boldsymbol{E}\cdot d\boldsymbol{l}} Derive the conductance per unit length, G', of a coaxial cable by assuming a line charge of \rho_{l} on the center conductor...

What does the unit "hp" means? I admit that my physics sucks because it has been a long time since I heard the word "physics" but putting that aside, what does the unit "hp" represent/means? I don't remember learning that unit in school. Eg. An engine develops 85hp I'm guessing it's a Power...

Now that other solar systems have been discovered, as well as binary and trinary star systems, is the helio-geocentric Astronomical Unit still useful? Wouldn't it be clearer to use the terms light second, light minute. light day, light year, etc., instead? Obviously, these terms are still...

It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.

1. The problem I need to know what unit I would use for my calculated velocity? 2. Relevant Information T (Relative Time) = 9 years To (Stationary Time) = 2 years U (Velocity) = ? Solution? What unit would I use for the velocity received?

1) I'm not sure how to solve this question A 20MVA induction motor connected at 13.8kV draws a load current of 1.0 p.u, 0.85 power factor lag. Calculate the rated load current in Amps and the real power and reactive power drawn by the motor. Express these quantities in per unit form using...

Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...

I'm on the last chapter of a 1200 page calc book, I'm really psyched. Homework Statement The Attempt at a Solution The method I learned for finding the unit normal of a vector field, n, is take the derivative of the equation and divide that by the magnitude of the...

Hello. Let's say we have the quantity f=1/(1+x) where x has no unit of measure. What is the unit of measure of f, once we take f^t, where t can be in years? Thanks

Homework Statement Two parallel whires, separated by a distance D (midpoint distance), are charged with a current density L (each whire has a radius R). If the whires have the potential +/- X Volts, what is the force per unit length between them? Homework Equations B = μ0*I /(2πr) is...

Homework Statement Show that the function f(z) = z/(1-z) maps the unit circle to an infinite line. Homework Equations Polar form z = rexp(iθ) The Attempt at a Solution I've tried to see what happens, when we let f(z) = f(eiθ) and then get: f(eiθ) = eiθ/(1-eiθ) But I need some...

What are Chords? What is the smallest "unit" in physics? Someone told me they read a Yahoo AP article stating the most basic "building block" of the universe was a sound wave, and upon discovery this had been named a chord(or perhaps cord/kord/etc). Again, this was an AP article, but I...

When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it...

Our teacher taught us a way to represent a force as a unit vector. Suppose a force of 12 N acts along the line 2i+j-2k. The force is written as: F = 12 N (2i+j-2k/√1^2+2^2+2^2) Therefore, F = 8i+4j-8k But, I can't understand why is it so. Please explain.

Hi everyone, It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem: Question "The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is...

Homework Statement Please can someone look at the attached question (I have extracted MS and relevant previous pieces of information) Where do they get the idea that 100 W is produced over 24 hours ?? Homework Equations The Attempt at a SolutionI know power = work done / time but if power...

We're given x^2+2*y^2=1. so x^2=1-2y^2 now using distance formula d^2=x^2+y^2 since x^2=1-2y^2, substituting it in the distance formula we get: d^2=1-2y^2+y^2=1-y^2; differentiating and then setting the eq to 0 we get; 0=-4y or y=0. now x^2=1-2y^2=1 so x=+-1 so point having...

Homework Statement The uranium isotope 235U captures a neutron and undergoes fission to produce 93Rb and 141Cs. Calculate the energy released in this process. The nuclear masses of the relevant isotopes are 235U 235.0439u, 93Rb 92.9217u, 141Cs 140.9195u Homework Equations...

Homework Statement Given vector OP = 2i+3j, OQ = qi+2qj. How can i find the possible value for q? note that PQ is a unit vector. Homework Equations Given (p-1)i + (2p-6)j having magnitude 10, find p The Attempt at a Solution From the formula, i was told that the unit vector...

Let $f$ be a nonconstant entire function that maps the unit circle, $\{z: |z| = 1\}$, into itself. Prove that $f$ maps the open unit disc, $\{z: |z| < 1\}$, into itself. I am having a little trouble starting this one. z in C

Does there exist a holomorphic function f(z) on the unit disc and satisfies f(1/n) = f(-1/n) = 1/n^3 for every n in N?

Why doesn't $1+z^{2^n}$ have zeros on the unit disc?

For better understanding of it's principles, electrotechnics is often compared to hydronics (and, probably, vice versa). But, why having the electrical resistance to a flow of charged particles - with it's basic unit "Ohm", there in general Physics is no unit of measurement of the hydronic...

Let f(z) = \prod\limits_{n = 1}^{\infty}(1 - nz^n) Prove that each point on the unit circle is an accumulation point of zeros of f So we have that z = \sqrt[n]{1/n} . Now where do I go from here? Probably should note that this is a Weierstrass Product.

Homework Statement The diagram provided shows a man pulling a box across the floor. Assume that the force of the friction can be ignored and that the acceleration of the box is 1.27 m/s. Find the angle to the horizontal that the man must pull. 65N figure located on the rope the person is...

Homework Statement I don't know if this is a physics problem per se but its from physics class. So we were supposed to pick out a solar panel and figure out what is the cost per unit of energy for this form of solar energy? I know where supposed to use the data sheet for the panel that we...

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 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...

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...