Unit Definition and 1000 Threads

Given a trapezium ABCD with AB parallel to CD. Show that the line joining the midpoints of the diagonals is parallel to AB & CD (done). Show also that its length is the difference of AB and CD. working: I called the midpoint of AC, E and the midpoint of BD, F Then found that ##...

Homework Statement Let ##\alpha(s)## and ##\beta(s)## be two unit speed curves and assume that ##\kappa_{\alpha}(s)=\kappa_{\beta}(s)## and ##\tau_{\alpha}(s)=\tau_{\beta}(s)##, where ##\kappa## and ##\tau## are respectively the curvature and torsion. Let ##J(s) = T_{\alpha}(s)\dot\...

Homework Statement At what wavelength does a cavity at 6000 degrees Kelvin radiate most per unit wavelength? Homework Equations $$\rho_T(\lambda)d\lambda=\frac{8\pi{hc}}{\lambda^5}\frac{d\lambda}{e^{{hc}/{\lambda{kT}}}-1}$$ The Attempt at a Solution I'm pretty new to this whole...

Homework Statement A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the...

Homework Statement given r(t) = <t, 1/t,0> find T(t) N(t) aT and aN at t = 1 Homework Equations T(t) = r'/||r'|| N(t) = T'/||T'|| aT = a . T = (v . a)/||T|| aN = a . N = ||v x a||/||v|| = sqrt(||a||2 - aT2) The Attempt at a Solution for my T(t) I get <t2, -1 , 0>/(sqrt(1+t4) (I...

Homework Statement We are to assume an infinite transmission line with the following parameters: capacitance: 296 ρF/ft Zc=52Ω inductance: 8.0 × 10-7 H/ft We are told that a 100MHz signal is attenuated 31 dB per 100 feet and asked based on the information, assuming no leakage through...

Homework Statement http://imgur.com/VzZjSEH I took a screen shot so I did not leave anything out. Homework Equations Surface area, and volume of a sphere. The Attempt at a Solution I am trying to find the linear charge density from the charge volume density. I got it explained...

Hello, I am reading Planck's Unit. What I understand is that what is the need for Planck's unit. Kilogram, meter and second are measurement, rather arbitrary measurement, which humans have done in the past. The question is what do we know that is constant throught the universe? We know (1)...

Homework Statement Let ##S = \{ (x,y) \space | \space x=\frac{1}{n}, n = 1, 2, 3,... \}## be a subset of the unit square. Prove ##S## has outer content zero. Homework Equations ##C(S) = inf\{ \sum A_i \} = inf\{Area(P)\}## The Attempt at a Solution There are no answers I can check my work...

Find a two unit vectors that make the angle \pi/3 with the vector \vec{v} = \vec{i} + 2\vec{j} + 3\vec{k}. "That isn't asking much since there are apparently infinite such vectors" - Prof. I get as far as to say that \pi/3 = arccos( 1/2 ) and that \frac{v \bullet w}{|v||w|} = 1/2 but from...

Hi; How to raising a square matrix to the power of a complex number? for example: [1 2;3 4]^(1+i) or mathematics software such as Scilab how solve such problems? -->[1 2;3 4]^(1+%i) ans = - 0.1482039 - 0.2030943 - 0.3046414 - 0.4528453 Thanks in advance...

What is the Unit Normal Vector in Acceleration.\vec{u}_n How would I go about calculating the normal. Wiki and Wolfram Alpha were very vague about calculating the normal of an orbit. I would like to know the normal to the orbit of a mass orbiting a much larger mass not counting any other...

what will happen if static pressure in supply duct is higher than the fan compartment in AHU?? or vice-versa thanks

I have two questions 1) How the radial and traversal unit vectors are vector funcitons of scalar variable θ (angle between the position vector and polar axis. 2) To find velocity and accleration in polar co ordinates why it is need to write the traversal and radial unit vectors by...

Homework Statement The Attempt at a Solution I know that u(t) is a unit step function and holds a value of either 0 or 1. In laplace transform, when we integrate f(t) from 0 to infinity, we take u(t) to be 1. In this case, since u(t) is u(-t), does this mean it holds a value of 0? Does not...

Homework Statement The vector -i+j+k bisects the angle between the vector c and 3i+4j. Determine a unit vector along c. Homework Equations The Attempt at a Solution Taking the dot product of the two vectors (other than c) gives me the cosine of the angle = 1/5√3. This is also equal...

Hello, I'm studying The Theory of Polymer Dynamics by Doi and Edwards and on page 98 there is a tensor, defined as a composition of two identical unit vectors pointing from the monomer n to the monomer m: \hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm} As far as I understood, the unit vectors...

Homework Statement Given that the stretched length of a string is Δx(1+1/2(dy/dx)^2) show that the potential energy per unit length is equal to 1/2F(dy(x,t)/dx)^2 Homework Equations potential energy = kx^2 cos(kx-wt) idk really... The Attempt at a Solution The fact that the...

Is there a smallest possible amount of energy? Like, one where all energy quantities in the universe are a multiple of it and the only way to have less energy is to have none at all? If a photon had that energy, it would be the longest possible EMR wavelength. Or can energy be divided...

i have a problem : A small loop antenna in free space and centered about the origin on the xy-plane is producing a (far-field) radiation electric field (in phasor notation) : http://postimg.org/image/63tm76h5l/ and their solution : http://postimg.org/image/6mdm6roh9/ i don't understand how...

The unit consists of a single, long rectangular chamber. On the inside is a moving wall. On one side of the wall is a vacuum, and the other side is room-temperature air. The moving wall starts much closer to the side with the air and moves slowly in the vacuum direction. As this happens, air...

I have some difficulty understanding how the volume per unit cell for the diamond structure is calculated. I've seen in various websites that this volume is: ##v=a^3 = \left( \frac{8r}{\sqrt{3}} \right)^3## Here ##r## is the radius of an atom. But how did they work out ##a## (the edge of the...

I keep reading about polar unit vectors, and I am a bit confused by what they mean. In the way I like to think about it, the n-tuple representation of a vector space is just a "list" of elements from the field that I have to combine (a.k.a. perform multiplication) with the n vectors in some...

1. Homework Statement Let S be the set of complex numbers z such that |z|=1. Is S a cyclic group? 3. The Attempt at a Solution I think this group isn't cyclic but I don't know how to prove it. My only idea is: If G is a cyclic group, then there is an element x in G such that...

Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane

0. The app does not have the template built in so ill do my best, sorry i don't have a computer right now. 1. This is a personal project, and there is a lot to it but I'm cutting out down to where i need help. Imagine a 2x2 grid of squares (2d for now). The center vector is at (0,0), and the...

Hi Guys, I'm tired of waiting for my tenants to finish their midnight laundry loads. I have a hydraulic sliding door assembly ready but I am having trouble getting parts to create the digital system to tie it all together. I want: 120-240VAC Power Relays (for the washing/dryer machines...

Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...

Homework Statement In fact it is problem 8.5 in Griffiths 3rd ed p357 Consider an infinite parallel plate capacitor with the lower plate carrying the charger density - \sigma , and the upper plate carrying the charge density + \sigma . (a) Determine all nine elements of the stress...

Fist a little bit of background on why I am doing physics 12, I am currently a first year electrician and recently found out in order to get a job with BCHydro physics 12 is a pre req. Unfortunately this is the only science I didn't take in highscool. The job posting for apprentice ships will be...

Let $$x$$ be a real number and let $$M=\frac{3x-1}{1+x}-\frac{\sqrt{\mid x\mid-2}+\sqrt{2-\mid x \mid}}{\mid 2-x \mid}$$. Find $$M$$ and also the unit digit of $$M^{2003}$$.

Homework Statement What is the integral of e-1/z around a unit circle centered at z = 0? Homework Equations - The Attempt at a Solution The Laurent expansion of this function gives : 1 - 1/z + 1/(2 z^2) - 1/(3! z^3) + . . . . . The residue of the pole inside is -1. So the integral...

How would I go about algebraically (not graphically) performing operations on two or more Heaviside function.H(x) = {0, if x<0 ...{1, if x>=0 ex. define the function piecewise and graph. a.) (x+1)*H(x+1)-x*H(x) b.) (x+1)*H(x+1) i'm having a hard time solving this please help me!

Homework Statement a proton moves with a velocity <6*105,3*105> m/s through a magnetic field given by <.2,.2> T a. Find the magnetic force per unit charge on the proton b. Find the work done by this forceHomework Equations Fm=qv x BThe Attempt at a Solution For part a, I used a property of...

Homework Statement Given ε > 0, show that there is a collection of disjoint dyadic squares in the unit disk that has a total area which exceeds π - ε. Homework Equations Define a dyadic interval as an interval of the form [a, b] such that a = p/2k and b = (p + 1)/2k, p and k are integers. A...

If force includes strength/magnitude and direction, then why do we say a Newton or Pound is a unit of force? Isn't it more a unit of the magnitude of force? Please help. Now that i have been thinking about forces always having direction, this is all confusing me. Thanks

Please help -- Efficiency of car engine question... Unit test tomorrow Homework Statement A car's engine is only 12% efficient at converting chemical energy in gasoline into mechanical energy. If it takes 18000 N of force to keep the car moving at a constant speed of 21 m/s, how much chemical...

Homework Statement Consider the following circuit which uses ideal components. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the impedance Z_{2} such that the system output is a unit step function of voltage. Be certain to show all components used to construct...

Is it possible to create a portable steam unit similar to this but without the use of the a heating element from a stove. http://vimeo.com/42042554 If so?, briefly how would one go about this? I would like to create something identical but with it's own heating unit and be hand...

Hi, I was given 1Btu/(h.ft^2.°F) to W/m^2.K with these conversion ratios 1m^3=1000L 1Btu=1.055*103 1m=3.2808ft and Δ1K=Δ1.8°F I can convert most of the units but I'm stumped by the temperature conversion here. Because I'm not converting a change in temperature but the discreet value of...

Hey everyone, the question I am faced with is this: Which of the following expressions involving δ[n] is incorrect? where "m" is a non zero integer and u[n] is the unit step function. A. u[n-m] = δ[n] + u[n-m+1] B. x[n]δ[n-m] = x[n-m] C. δ[n] = u[n] - u[n-1] D. δ[n]δ[n-m] = 0...

Homework Statement \rho(\lambda)d\lambda=\frac{8(\pi)hc}{\lambda^{5}}\frac{d\lambda}{e^{hc/(\lambda)KT}-1} What does this represent? Calculate the number of photons per unit volume in a blackbody from \lambda to d\lambda Homework Equations N/A The Attempt at a Solution I...

When my textbook talks about energy it starts with kinetic and potential. The derivation goes like this. F=ma=m(dv/dt)=-mg then they split the derivative using chain rule (dv/dt)=(dv/dy)(dy/dt) therefore since (dy/dt)=v we get F=mv(dv/dy)=-mg then they write mv dv= -mg dy...

Homework Statement Find the La Place transform of cos(x)*(u(x-\pi)) Homework Equations L{u(t-a)}(s)=(e^(-as))/s The Attempt at a Solution I don't think I can just multiply this by the La Place transform of cos (x), which is s/(s^2) ?

Homework Statement I need to find the mass of a disk with a hole, given inner and outer diameters of 0.10m and 0.30m, respectively. The disk has a mass per unit of 20 \frac{kg}{m^2}. The Attempt at a Solution Since I needed mass units, I thought that I could multiply the mass per unit...

Homework Statement Let ##100!=N\cdot 10^n##. If N is relatively prime with 10 and unit digit of N is d, then n+d is equal to A)26 B)28 C)30 D)32 Homework Equations The Attempt at a Solution I don't think it would be a good idea to expand the factorial and separately write out...

Homework Statement How much energy per unit mass (E/m) must you give a rocket to put it into a geosynchronous orbit three Earth radii above the surface of the Earth? Radius of Earth : 6380 km GM/r = 6.25 x 10^7 m^2/ s^2 Homework Equations U(r) = - GMm/r The Attempt at a...

Homework Statement A 45 kg object is lifted vertically at a constant speed to a height of 9.0m by a 750 W electric motor. If this motor is 25% efficient in converting electric energy to mechanical energy, how long does the motor take to lift the object? Homework Equations The...

So I'm trying to find the DTFT of the following; where u(n) is the unit step function. u \left( n \right) =\cases{0&$n<0$\cr 1&$0\leq n$\cr} I want to find the DTFT of u \left( n \right) -2\,u \left( n-8 \right) +u \left( n-16 \right) Which ends up being a piecewise defined function...

I want to find the unit vector of ## \vec E= \hat x A\;+\;\hat y Be^{j\phi}## ##\hat E=\frac {\vec E}{|\vec E|}## From my work: ##|\vec E|=\sqrt{A^2+(Be^{j\phi})^2}## My question is what is ##(Be^{j\phi})^2##? Do I substitude ##e^{j\phi}=\cos \phi +j\sin \phi##? So...