Unit Definition and 1000 Threads

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

Homework Statement Given ## d \vec r = dr \hat r + r d \theta \hat {\theta} + r \sin \theta d \phi \hat {\phi}.## Find ## d \hat r , d \hat {\theta} , d \hat {\phi}. ## Homework Equations I know that ## d \hat {e_j} = \omega^i_j \hat {e_i} ## and that ## \omega_{ij}=- \omega_{ji} ## and ## 0 =...

Can anyone explain to me how it comes that US not have accepted the use of SI ? Do you not understand the benefits ? Would it not be more effective if the new generation of students could concentrate on understanding fundamental physics relations rather than struggle whith old-fashioned and...

Homework Statement The problem is described in the picture I've attached. It is problem number 6. Homework Equations Tangent line of a curve Length of a curve The Attempt at a Solution I don't know why I'm so confused on what seems like it should be a relatively straightforward problem, but I...

Homework Statement An arrangement of four wires, in cross section, with θ=30° and u=5cm. Wire 2 and wire 4 carry the same magnitude of current (I2=I4=10mA) directed out of the page. Wire 3 carries current I3=25mA directed into the page. If the resultant force per unit length on wire 1 is zero...

1. Homework Statement An air coaxial transmission line has a solid inner conductor of radius a and a very thin outer conductor of inner radius b. Determine the inductance per unit length of the line. Homework Equations the book states the methodology to find the inductance as follows: 1)...

Homework Statement Homework Equations The Attempt at a Solution So I began by subtracting. (205-160)=55 i (495+128)=623 j Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and...

I am trying to find out how to reverse the unit step function. The closest I could find is this sentence, which is more like a definition? "if we want to reverse the unit step function, we can flip it around the y-axis as such: u(-t). With a little bit of manipulation, we can come to an...

Hi all, I want to buy an air conditioning unit while they're cheap and I know you're not meant to have any windows open. I have strange windows so cannot use the fishnet attachment, long story short, if I hang the hose out of the window and just try to close the window as much as possible, will...

If trying to find a branch of ##(z^2-1)^{1/2}##, it can be shown that one acceptable answer is: ## i e^{0.5 Log(1-z^2)}## But I just want to clarify, is not the following an acceptable answer, too: ## iz e^{0.5 Log (\frac{1}{z^2} -1)}## It appears the argument of Log in both cases is always...

$\tiny{s6.12.3.35}\\$ 35. Find the unit vectors that are parallel to the tangent line to the parabola $y = x^2$ at the point $(2,4)$. \begin{align} \displaystyle y'&=2x \end{align} the book answer to this is $\pm\left(i+4j)/\sqrt{17}\right)$ but don't see how they got this?

As most know and rest can find out, radians are a dimensionless unit. Actually, it's even worse: angle in general is a dimensionless quantity. That stems from it being defined as a ratio of the arc versus the radius. I now present my opinion of disagreement to this concept. In the strict...

Homework Statement the point (log a, log b) exists on the unit circle. find the value of axb. round to the nearest thousandths. Homework Equations x2 + y2 = 1 The Attempt at a Solution x2+y2 = 1 loga2+logb2 =1 2loga+2logb = 1 2(loga+logb) = 1 loga + log b = 0.5 logb = 0.5−loga now i try...

The volume form on the unit sphere ##S^{n}## in ##\mathbb{R}^{n+1}## is given by $$i_{{\bf r}}\ dx^{1}\wedge \dots \wedge dx^{n+1}=\sum (-1)^{i-1}x^{i}dx^{1}\wedge\dots \widehat{dx^{i}} \dots \wedge dx^{n+1}.$$ Why must the volume form ##dx^{1}\wedge \dots \wedge dx^{n+1}## act on the vector...

I am in a study of sizing air compressor for a new manufacturing plant ,I googled for some calculation and i got the problem shown in the attachment .i have one doubt how they got the unit bar in the final answer ...?

I'm given the code: #include <iostream> using namespace std; class InventoryTag { public: InventoryTag(); int getQuantityRemaining() const; void addInventory(int numItems); private: int quantityRemaining; }; InventoryTag::InventoryTag() { quantityRemaining = 0; } int...

Homework Statement Find power of signal A u(t) A is constant like 5, 6 some value.[/B]Homework Equations Power is integration over -T/2 to +T/2 of [x(t)]2 dt The whole divide by T The Attempt at a Solution Power is integration over -T/2 to +T/2 of [A u(t)]2dt[/B] The whole divide by T So...

Homework Statement find the vector in R3 that is a unit vector that is normal to the plane with the general equation x − y + √2z=5 [/B]Homework EquationsThe Attempt at a Solution so the orthogonal vector, I just took the coefficients of the general equation, giving (1, -1, √2)[/B] then...

Why trigonometric functions are defined for unit circle, here "why" refers to what made them to define it this way, they may have defined it for right triangle only , can you give me a application where sin(120°) or sin, cos , tan of more than 90° is used to find some values like in physics or...

Okay so I understand that in order to represent a vector which is in cartesian coordinates in spherical coordinates.. we use the transformation which is obtained by dotting the unit vectors. So my question goes like this: when we dot for example the unit vector ar^ with x^ we obtain sin(theta)...

Experimentalists usually provide chemical unit cell information including full symmetry (space group) information of the crystal together with coordinates of independent atoms. But this cannot be directly used by ab initio packages, which requires either primitive cell or unit cell information...

Homework Statement How does the unit vector have no units I know that the unit vector has a length of 1 and zero units. A representation would be I-hat j-hat k-hat(depending on the coordinate system). But the unit vector is the vector/magnitude. If the unit vector is its vector/magnitude then...

The standard unit of mass is defined to be "equal to the mass" of a cyliner of platinum and iridium in france. I have always wondered what this means? Why are all sources saying mass is defined in terms of mass? What were the steps taken to decide this unit? I know that base quantities have to...

Homework Statement Find the unit tangent vector T(t) for vector valued function r(t) = (e^t)(cos t ) i + (e^t)(sin t ) j + (e^t) k Homework EquationsThe Attempt at a Solution i gt stucked here ... , the ans is [1/ sqrt (3) ] [ (cos t -sin t ) i + (sin t + cos t ) j +k) [/B]

Hi all, I have long had this unsolved question about arclength parameterization in my head and I just can't bend my head around it. I seem not to be able to understand why velocity with arclength as the parameter is automatically a unit tangent vector. My professor proved in class that s(s) =...

Homework Statement I'm fully convinced that the zero values make sense, yet they are wrong, can somebody please explain why is that the case Homework Equations N/A The Attempt at a Solution Attempt in the image above

Homework Statement A patient is treated for cancer using radiation from a cobalt-60 unit. Exactly 1.5 years later another patient is treated for the same cancer using the same co-60unit previously used. How much longer would treatment be for the second patient? Homework Equations Decay...

Hi folks, It is an elementary question for people expert in superconductivity. I know there is a theory, the BCS theory, and the GIzburg Landau theory too that apparently explains superconductivity. My question is, if I give you a unit cell would you be able to tell me the temperature at...

Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...

I read that states are positive operators of unit trace - not elements of a vector space. Is it referring to quantum states or all classical states? I know operators are like minus, plus, square root and vectors are like rays in Hilbert space.. but why can't quantum states be vectors when in...

Hi everyone Does anyone help about unit of below MCNP line for neutron? Is it "neutron*barn/cm^2" right ? fm14 (1 108 102) And also what's the unit difference between "fm14 (1 108 -6 -8)" and "fm14 (1 108 -6 )" ? Many thanks

Despite being a constant, It has both dimensions and a unit, can someone kindly explain why ?

Homework Statement frequency, Tension, mass, mode of vibration Homework Equations v = sqrt(T/μ) The Attempt at a Solution length of string is 2.14m weight .00247kg mass per unit length (μ) .00089 However, I need to confirm this graphically. I solved for mass per unit length μ = T/V^2 or...

I would like to prove that if $\|f\|_p = 1$ then $f$ is extreme point of unit closed ball in $L^p[0,1]$. [here $1<p<\infty$] I suppose we should try to prove it by contradiction. That is, if $f \in L^p$, with $\|f\|_p=1$, is not extreme, then exists $g,h \in L^p$ with $\|g\|_p,\|h\|_p \leq 1$...

this may be a stupid question, but does anyone know the conversation from millgauss to hertz. Let me explain because I feel it's made up. Someone posted this on another forum I frequent. http://www.monsterfishkeepers.com/forums/threads/emf-radiation-aquarium-pumps.674555/ I didn't know what a...

my question is why physical quantities need a unit?

what does "Gg" represent ?

I am studying physics, and I see the equation ##\hat{A} = \frac{\vec{A}}{A}##. What makes this relation obvious? It's quite obvious when one of the components of vector A is zero, but if both components are not zero, then what leads me to believe that this relation works every time?

Homework Statement Let be ##f : V \rightarrow \mathbb{R}## a ##C^{1}## function define on a neighbourhood V of the unit sphere ##S = S_{n-1}##(in ##\mathbb{R}^{n}## with its euclidian structure.). By compacity it exists u in S with ##f(u) = max_{x \in S}f(x) = m##. My goal is to show that ##u##...

Hi Specific Speed is defined as: Ns=N(Q^0.5)/(H^.75) How Dimensional Analysis of it can be done? Unit of N is 1/sec and Ns is unitless. Then Dimension of Q^0.5 must be equal to dimension of H^0.75. It seems no to be equal. Please explain it.

Problem: CO2 is contained in a vertical cylinder at a pressure of 30 atm by a piston with a mass of 57 lbm. If g is 32.4 ft/sec2 and the barometric pressure is 29.7 in. Hg what is the area of the piston? Relevant equations F = Ma/gc W = Mg/gc P= F/A gc = 32.174 lbm ft / (lbf sec2) 1 atm = 29.9...

I would like some help in working out the correct unit of concentration in the question below please. I added a substance which has a density of 1.020 kg/m3 to a sample at a rate of 800 uL/ L of sample The substance is also 60% w/w. Will the final concentration in the sample be in 490 ug/L or...

Homework Statement http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Vector-Valued_Functions_and_Motion_in_Space/The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I can't understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone...

Hi, I read in some papers which say the unit of atom scattering factor is e/atom. what is the meaning of that? thank you!

Why are some inertia units lb-in-s^2 and others lb-in^2. what the difference? The first one is from a gear box spec and the second is from a motor rotor.

So I'm reading the Schaum's outlines while trying to prepare for a big test I have in September. And I'm trying to understand something here that maybe someone can offer some clarification and guidance. So, using Coulomb's Law, we can find the electric field as follows: \begin{equation} dE...

The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time. The average energy density ##d\psi## is obtained by dividing the radiant energy ##dE## received by the surface ##dB## in 1 second by the...

what is Ring Main Unit design in electrical panels ?

Hi I have a value that is 10.7 mJy, that I need to convert to SI units. I thought it would be 1.7*10^(-2)*10^(-26) but that might be wrong? Then I have a flux value, kappa, of 2 cm^2.g^(-1) that needs to be converted to meters and kilogram. I thought it was 2*10^(-7) m2/kg, but that might be...