Unit Definition and 1000 Threads

Hello everyone, I've just begun a lesson on cyclic sets, but I am having problems determining a few concepts. One question will ask me to find the generators and the units of a cyclic set Z8. I have become confused and realized that I did not understand the difference between a generator and...

This whole unit thing of mols is somewhat tricky and interesting. if one mol of Na is 23g, then wouldn't 100.3g of NaCl be one Mol as well. I am under the impression from my lecture notes in class that the grams of a substance is the same a s a mol. I was asked a school of thought question by...

Hello, A bit of background, I intend to major in physics and mathematics, and I am currently in second year. As it stands at the moment I am only enrolled in three units, and I was wondering If I should do, normally a third year unit, Introduction to Geometric Topology, (i can apply for an...

Hello, Could someone please review my work and see if it is correct. Thanks :smile: Homework Statement Find two unit vectors orthogonal to both given vectors. i + j + k, 3i + k Homework Equations The Attempt at a Solution So I used cross product and got A x B= i+2j-3k...

Homework Statement What are the x- and y-components of the polar unit vectors \hat{r} and \hat{\theta} when a. \theta = 180° b. \theta = 45° c. \theta = 215° Homework Equations The Attempt at a Solution Please check if I'm correct, i'll just show my answer for a since the process is...

Homework Statement if \vec{e_{1}} = 5\hat{i} - 3\hat{j} + 2\hat{k} what is the unit vector \hat{e_{1}} Homework Equations The Attempt at a Solution here is my answer,, please confirm if I'm correct. |\hat{e_{1}}| = \sqrt{\vec{e_{1}} . \vec{e_{1}}} |\hat{e_{1}}| =...

Homework Statement Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8). Homework Equations u = PQ = Q - P v = PR = R - P ans = uXv = PQ X PR The Attempt at a Solution so I did...

Find the unit vector that makes an angle θ=-3∏/4 with the positive x-axis I know to find a unit vector you divide the given vector by its magnitude, so I guess my problem is finding any vector that makes that angle with the positive x axis. I figured if that angle was the slope of a line, then...

Homework Statement Suppose that f is holomorphic in an open disc U and that Re(f) is constant in U. I have to show that f must be constant in U. Also what is the essential property of the disc U that it used here? Give an example of an open set U for which the conclusion fails.Homework...

Homework Statement Question 6: http://www.xtremepapers.com/Edexcel/Advanced%20Level/Physics/2008%20Jan/6754_01_que_20080121.pdf "On one type of theme park ride, a..." Homework Equations The Attempt at a Solution So at the bottom of the loop the ride is at its fastest GPE =...

Why is the number of charge carriers per unit volume is inversely proportional to resistance?If there is more charges carrier, it doesn't increase the collision between free electron which causes in increase of resistance?sorry for my unclear concept of Electricity circuit.I hope there will be...

Homework Statement Simulate the system to look at the output response with a unit step input applied i.e. use the step command. Confirm the values of K and τau from the simulated response are the same as those you have entered into the simulation. Note that the step command can be used with...

Homework Statement Consider a small portion (area=A) of the inside wall of a container full of gas. Show that the number of molecules colliding with this surface in a time interval Δt is PAΔt/(2mvx avg), where P is the pressure, m is the average molecular mass, and vx avg is the average x...

Homework Statement Prove that the unit vector r{hat} of two-dimensional polar coordinates is equal to r{hat}= x{hat}cosθ + y{hat}sinθ and find the corresponding expression for θ{hat}. all I need is the last part... I'm just not sure what θ{hat} is? How do I go about doing this? Nothing in my...

Homework Statement Calculate the density in lbm/ft3 with the given formula: ρ=p/RT where p=35 psi, R=1716 ft-lbf/slug-°R, and T=100°F. We have access to a table with basically any unit conversion we would need. The Attempt at a Solution 100°F=37.78°C=310.9278K (35 lb/in2)(144 in2/1...

The problem A bubble of kryptopn (Kr) gas is formed underwater. The bubble has a volume of 2.14x10-6m3 and contains 1.70x1020 krypton molecules each of mass 1.39x10-25kg. The pressure of the gas inside the bubble is 300kPa. Calculate the relative molecular mass.The attempt at a solution When...

I've shown that the unit square, [0,1]^2 , is a smooth 2-manifold in \mathbb{R}^2 . But it has a corner at the point (1,1). I thought smooth manifolds weren't suppose to have corners, cusps, etc. So what exactly is special about the unit square?

Hi all, I have a question. I have been asked to estimate the size (thickness/gauge) and specific material of two L-Brackets that will be used to mount a condensing unit on the side of a building. As I am at work and don't have any of my school/ME books at my disposal I am wondering if...

I learned Potential but could not understand what Potential Difference is. Some define it as Work Done per unit charge. I am confused what per unit charge is. Does that mean electrons or protons ? As much as I know, electric current is the flow of negatively charged electrons to the positive...

Change the forum if this is in the wrong place but I was doing some math (multiplying hertz and watts) and I came with 4.8912 × 10^12 m^2 kg / s^4, I don't know what unit that is, so can anybody tell me if there even is one?

What is "unit", when we speak about ∏? The video says that we are taking a 1 unit circle and if we want to find the diameter of this unit circle then we just use the ruler as shown in the video. And now the length of the diameter of this circle is called as PI (∏), which is approximately 3.14...

Homework Statement http://store.aqa.org.uk/qual/gce/pdf/AQA-BIOL4-W-QP-JUN10.PDF Question 7eii) asks "What conclusions can you draw from the data in figure 3 about the effect of human disturbance on the animals living on the seashore. Explain The mark scheme...

Hi, exam question: My doubts start where it comes up with: S=75(0.8-j0.6) and Vr = 0.97 p.u. Its easy to determine that 75 comes from 60/0.8, but where is the part in the brackets coming from ? Also how was the 0.97 determined ? Thanks in advance.

Homework Statement The Hyperbolic coordinate system is given by: u=2xy and v=x^2 - y^2 a.) Find the unit vectors u and v in terms of u,v,x(hat),y(hat) b.)Find the time derivatives of u(hat) and v(hat), your answers will have du/dt and dv/dt in them Homework Equations None really...

Let be w=w(σ) a curve on a surface parametrized by the arc length (the natural parametrization). Consider the m surface normal along this curve as the function of the σ arc length of the curve. Prove that m'(σ) is parallel to the t(σ) tangent unit vector of the curve for all σ, IFF this curve is...

http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .

This is the final question on a static equilibrium quiz i had today (physics 12). when comparing answers (as you tend to do after the quiz "did you get x for question y?"), half of my friends (all of equal ability in the course) got a different answer from me, and the other half the same. I am...

One atomic mass unit = .001660565 x 10-24 grams One gram Hydrogen / .001660565 x10-24 grams = 6.02 x 10 26 ? This should be Avogadros number 6.02 x 1023 what is the mistake here ?

Homework Statement Let f(z) be a function that is analytic for all |z|≤1, with the exception of z_0, which lies on the circle |z|=1. f(z) has a first order pole at z_0. Letting Ʃ a_n z^n be the Maclaurin expansion of the function, prove that z_0 = lim_(n→∞) a_n/a_(n+1) Homework Equations...

dear PF.. what is the Bernoulli equation in terms of energy per unit volume the equation include the 1) static pressure 2) hydrostatic pressure 3) dynamic pressure 4) stagnation pressure

If I have a negative quantity pointing in the positive z direction, is that the same as a positive quantity pointing in the negative z direction? e.g. does -A\hat{z}=A\hat{-z}?

Hello, I am trying to find the angle between two unit vectors but I was wondering what I am supposed to do when the dot product is greater than 1 or less than -1. For example -0.0288067i + -0.989524j + -0.141463k 0.169194i + -0.0644865j + -0.983471k

This is an example from Bott and Tu 's book DFAT(page 125).The example is in the image.I don't understand why can we get the local degree of the section s by constructing an vector field by parallel translation and calculate the rotating number of it.And why the local degree is 2? Could...

can i get some help in how i can convert from cartesian to cylindrical and spherical unit vectors and vice versa ? thank you

Homework Statement Does anyone know what d(r-hat)/d(theta) in Cylindrical coordinates is? Homework Equations The Attempt at a Solution I'm pretty sure its -(theta-hat) but I'm not sure, any help? Thanks so much

Homework Statement In cylindrical coordinates: what is d(theta-hat)/d(theta)? Homework Equations The Attempt at a Solution I'm fairly certain it is -rho... without a direction? or is it -rho*theta-hat? Thanks in advance!

Homework Statement In the special theory of relativity the mass of a particle moving at speed v is given by the expression m/(1-(v2/c2)) where m is the mass at rest and c is the speed of light. At what rate is the mass of the particle changing when the speed of the particle is (1/2)c and is...

Hello all, I'm new to the forums and this seemed like the perfect place to discuss an issue that has been bugging me. I know MW refers to power (the rate of energy production basically in millions of Joules per second) and MWh refers to energy (essentially the total amount (in millions of...

Homework Statement We have to calculate the mass concentration for a particle size distribution. I'm just doing the first size range here, since once I get that the rest is just repetition. FYI, the particles are spherical. Size range (diameter) = 0.005-0.5 μm Average particle size...

Let us say there is a curved region of spacetime whose curvature is \kappa(s). How does one find the coordinates of the unit vector normal to a certain point on the region of spacetime? I tried searching Hamilton's principle and the general theory of relativity but I could not find any equation...

i am trying to find the total kw usage of a 10 ton rooftop unit. Its model # is TCD120C40AAB. Its EER value is 9.2. Nominal CFM is 4000. Gross Cooling Capacity is 125,000. System Power is 12.83 kw. I am trying to figure out how much kw i will be saving by getting a "cool roof" instead of a...

In my ODE course I learned that for a time invariant operator p(D), if p(D)x=q(t) then p(D)\dot{x}=\dot{q}(t). Then the professor "justified" that the derivative of the unit step response, v(t), is the unit impulse response, w(t), because the derivative of unit step function is the Dirac...

Homework Statement I am trying to do some revision for an upcoming exam and one question I am trying to figure out is Use the second shifting theorem to find the Laplace transfrom of the following function: f(t) = t2, t < 4 t, t ≥ 4 Homework Equations The Attempt at a...

Homework Statement What can you say about a. the sum of a complex number and its conjugate? b. the conjugate of anumber on the unit circle? c. the product of two numbers on the unit circle? d. the sum of two numbers on the unit circle? Homework Equations The Attempt at a...

B=Boexp[-(kz-ωt)2)] i(hat) Calculate the electric field associated with the above magnetic field pulse. Calculate the Poynting vector for the EM field and the total energy per unit area. Use Maxwell's equations in vacuum and assume electric potential is zero. Homework Equations...

Homework Statement A particle moving in xy plane has velocity components in x and y directions Dx/dt = b1+c1t and dy/dt = b2+c2t A) integrate above equations to give displacement components x and y as functions of time B) write the velocity (v) of the particle at time t in terms of...

I know power = Torque x angular velocity (rad/s) AND I am wondering if angular velocity can be calculated through strokes per minute? The product is a reciprocating saw (not orbital). In this case are RPM's the same as SPM'S? Thanks

Homework Statement Let p be a positive prime and let Up be the unit group of Z/Zp. Show that Up is cyclic and thus Up \cong Z/Z(p − 1). The Attempt at a Solution What do they mean by the unit group? Is that just the identity? Is it the group [p]? I'm lost without starting the question...

Homework Statement f(x) = \begin{cases} 0, & t < \pi \\ t - \pi , & \pi \leq t < 2 \pi \\ 0, & t \geq 2 \pi \end{cases} Homework Equations Unit step function: u_c(t) = \begin{cases} 0, & t < c \\ 1 , & t \geq c \\ \end{cases} The Attempt at a Solution u_{\pi}(t)(t-\pi) - u_{2...

Homework Statement Suppose f is a smooth function of x and y, and at the point (1,1), \partialf/\partialx = 1, \partialf/\partialy = -1. Find the unit vector u such that Duf(1,1) = 0 Homework Equations Duf(1,1) = \nablaf(1,1) * u = 0 The Attempt at a Solution My answer was...