Unit Definition and 1000 Threads

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...

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...

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.

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 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...

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 .