Terms Definition and 1000 Threads

Hello! I am stuck at the final step. How do I get x+iy from the equation? Help! I am so sorry for posting this question in a picture instead of writing it out, because I don't know how to write equations on here.

Hello! I am stuck at the final step. How do I get x+iy from the equation? Help! I am so sorry for posting this question in a picture instead of writing it out, because I don't know how to write equations on here.

if I am finding the surface area, and I am given the equation in term of x=g(y) about the x-axis, do i have to solve for y or can i just integrate in terms of y? would i just use dx/dy instead?

Homework Statement If f(x) = 3x+1 en assume δ > 0. Assume ε>0. Give a δ > 0 with the following property : |x-1|< δ => |f(x) - f(1)| < ε Homework Equations The Attempt at a Solution |f(x) - f(1)| < ε <=> |3x+1-(3*1+1)| < ε <=> |3x-3| < ε <=>...

Hi, Thank you for reading this. I understand the functioning of DC current. You create a potential difference and the electrons flow from the power source through the electrical appliance (thereby, powering it) and flows back, completing the circuit. But, in AC, the electrons...

Other laws in terms of circulation and flux Why others vector fields no are studied like the magnetic and electric fields? In other words, why others vector fields, like the gravitational and the hydrodynamic, haven't "supreme laws" based in the circulation/flux or curl/divergence?

I have an integrand with a handful of terms, and some of them have poles in the denominator of the form (x+c) (but not all). There are three poles in total, and I want to collect all the terms according to each pole individually (eg all the terms with (x-1) in the denominator, (x-5), etc.)...

Homework Statement If \frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}, prove that x^{b+c-a}.y^{c+a-b}.z^{a+b-c}=1Homework Equations The Attempt at a Solution I solved a question similar to it in a way. So I tried this in the same way. The only difference between the two questions is...

Browsing in the wiki, I found those formulas: http://en.wikipedia.org/wiki/Determinant#Relation_to_eigenvalues_and_trace So, my doubt is: if is possible to express the determinant in terms of the trace, thus is possible to express the trace in terms of the determinant too?

Given the following: $$\\ \begin{bmatrix} A & 0\\ 0 & B\\ \end{bmatrix}$$ the eigenvalues is exactaly A and B. So analogously, is possible to write a matrix with only two elements, T and D, such that the trace is T and the determinant is D? I tried something: $$\\ \text{tr} \left(...

Homework Statement Write ##sin(ax)## for ##a \in \mathbb{R}##. (Use generating function for appropriate ##z##) Homework Equations ##e^{2xz-z^2}=\sum _{n=0}^{\infty }\frac{H_n(x)}{n!}z^n## The Attempt at a Solution No idea what to do. My idea was that since...

Hi, Is there a better way to write this? 'terms of order O(R^{-Y}) where Y>1 are neglected' I feel like this is a bit clumsy. Thanks for the help!

Hi all, I can't seem to find any historic account of when those two theories got their (quite strange) names. Can someone point me to a source? One of the reasons I am interested in this is the persistent idea in popularizing texts, especially from the 1970's, that Special Relativity could...

I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...

So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...

Homework Statement for this question, i sub u=xy and try to eliminate y in my working.. but how should i proceed since the term ux cannot be separated Homework Equations The Attempt at a Solution

Is possible express the sine in terms of cosine and vice-versa: ##\sin(x) = \cos(x-\frac{\pi}{2})## ##\cos(x) = \sin(x+\frac{\pi}{2})## So, of some way, is possible express the sinh in terms of cosh too and vice-versa?

I am doing some analysis and I have come up with the following integral: \int \frac{e^{-ax}}{1+be^{-cx}}dx where a>0, b>0 and c>0. I have found out this integral has a solution in terms of the Gaussian hypergeometric function http://en.wikipedia.org/wiki/Hypergeometric_function but it...

Homework Statement Find the sum of the first n terms of the sequence U1, U2, U3... Ur Homework Equations The Attempt at a Solution $$ \sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n $$ But I don't this is right... any help?

Okay, so the job I need to do is derive an equation for the radius of an object in terms of its frequency. These are the equations that we are allowed to use: v(Linear velocity) = rω v=2πr/T ω (angular velocity)=2πf f (frequency)= 1/T (time period) T= 2πr/v a (centripetal...

Homework Statement Wn = 2 + 3(1/2)^n Homework Equations The Attempt at a Solution I am confused, all I tried so far is writing out the first 5 terms, but all that was helping me to do is basically find the Sum to infinity... so what should I do to find the Sum to n terms? I know...

Homework Statement Attached the question. Homework Equations (total) tension = mg The Attempt at a Solution I'm not sure how the tension gets divided here. I know the tension on the right hand side of the turnbuckle is the same tension on the left hand side since they are...

Homework Statement find the general formula to calculate the sum Homework Equations 1+11+111+1111+11111+....upto n terms The Attempt at a Solution 100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ... ==> (100+100+100+...upto n terms) + (101+101+101+...upto n-1 terms)...

Hey! :o $f(x)=\sum_{i=0}^{7}{a_ix^i}, g(x)=\sum_{i=0}^{5}{b_ix^i}$, $a_i, b_i$ are integer coefficients. The prime $p$ divides $a_0, a_1, a_2, a_3, a_4$ but it does not divide $a_5, a_6, a_7$. $p$ divides also $b_0, b_1, b_2$, but it does not divide $b_3, b_4, b_5$. $h(x)=f(x)g(x)$ Show that at...

Which the difference between diff equations of kind: \frac{dy}{dx} = \exp(x) \frac{dy}{dx} = 1/x and diff equations of kind: \frac{dy}{dx} = y \frac{dy}{dx} = \frac{1}{\exp(y)} ?

I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...

Two questions, based on the same situation: in http://physics.stackexchange.com/questions/34204/relativistic-acceleration-equation (question A) it is mentioned that, for an object with a constant acceleration g_{M}, and with \tau_{0} =1/g_{M} , after proper time \tau, the coordinates are...

Homework Statement Find the second derivative of sin y+cos y=x, giving your answer in terms of x. Homework Equations Implicit derivatives The Attempt at a Solution ##\sin y+\cos y=x## ##\cos y \frac{dy}{dx} -\sin y \frac{dy}{dx}=1## ##\frac{dy}{dx}=\frac{1}{\cos y-\sin y}##...

How to solve this question. Please explain step by step.

The stress energy momentum tensor of the Einstein field equations contains multiple density terms such as the energy density and the momentum density. I know how to calculate relativistic energy and momentum, but none of the websites or videos that I have watched make mention of any division of...

Hi all! Let me use an example to make this clear. There is a car traveling directly toward a man at 10m/s. The car is pressing down its horn, producing a frequency of 100hz. The speed of sound is 330 m/s. What frequency does the man hear? Ok, so we can use the equation: f_observer=(...

In Hamiltonian formulation there is an expression df / dt = { f , H } + ∂f / ∂t where f is function of q, p and t. While expressing Hamiltons equations of motion in terms of Poisson Bracket, i.e if the function f = q of p then its partial time derivative ∂f / ∂t becomes zero.. Please explain why?

I'm giving a presentation to a group next week made up of mathematicians, physicists and mechanical engineers. My talk is going to be related to my work so it's going to be very biology based. I want to start the talk pointing out that life science and the physical sciences are very different in...

Does anyone have a link to a version of the EFE fully expanded in terms of the metric?

I'm a bit confused with limits of big-O terms. What should be the answer for following:- 1) limit of O(1/x) as x->0. O(1) maybe but I'm not sure. 2) limit of O(x) as x-> 0. O(1) or 0?

Homework Statement Let k be a constant. If α and β are the roots of the equation 3x^2 + 2x - k = 0, find the value of 3α^2 - 2β in terms of k. Homework Equations The Attempt at a Solution Obviously, the usual αβ = -k/3 α + β = -2/3 has been written but I couldn't put them...

if ψ(o)=(1 0)^{T} at time t=0. According to some Hamiltonian, it was found that the corresponding eigenstates are |ø_{1}> = 1/√2(1 i)^{T} and |ø_{2}> = 1/√2(1 -i)^{T} so then we wanted to expand ψ(0) in terms of |ø_{1}> and |ø_{2}>: the author got: 1/√2|ø_{1}> + 1/√2 |ø_{2}> My question is...

I am trying to write the Einstein field equations $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu} R=\frac{8\pi G}{c^4}T_{\mu\nu}$$ in such a way that the Ricci curvature tensor $$R_{\mu\nu}$$ and scalar curvature $$R$$ are replaced with an explicit expression involving the metric tensor $$g_{\mu\nu}$$...

Homework Statement Hey. I need help simplifying and factoring a differential equation in terms of v and p (velocity(xdot) and position(x) respectively). I need the final answer to be in this form: a = ( )v + ( )p. This is so i can put the governing equation in a state-space and eventually use...

All analitic function can be express how: f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ... that is the taylor series of the function...

Homework Statement This isn't exactly a homework question, but I figured this would be the best subforum for this sort of thing. For the sake of a concrete example, let's just say my question is: Express the position operator's eigenstates in terms of the number operator's eigenstates...

Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...

Homework Statement ∫(a= -3 , b= 0) (1 + √9 - x^2) dx Homework Equations ∫(a,b) f(x) dx = lim as n → \infty \sum f(xi) delta x The Attempt at a Solution I tried plugging in my a and b value into the function just as I would with any other function to find the area and i get a number...

Hello! Well, I guess it's all in the title, really. I was reading about k-essence, and it was described as a scalar field having a non-canonical kinetic term. I did a bit of browsing and couldn't find a clear explanation of what, exactly, a non-canonical kinetic term is. Any help would be...

We can represent π, in terms of primes by using Euler's product form of Riemann Zeta. For example ζ(2)=(π^2)/6= ∏ p^2/(p^2-1). Likewise, is there a representation of e that is obtained by using only prime numbers?

find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z

This is how one poster tried to explain it to me but for people who have only taken a basic physics course in college it leaves a lot wanting. "If a system is in a pure state, and you know what the pure state is, then your knowledge of the system is complete, and all uncertainty is quantum...

A limit of a sequence is definitely convergent if: If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N My only question is what exactly are K, N, an and n? What values are they? How would...

How do you find the inverse of metric tensor when there are off-diagonals? More specifivally, given the (Kerr) metric, $$ d \tau^2 = g_{tt} dt^2 + 2g_{t \phi} dt d\phi +g_{rr} dr^2 + g_{\theta \theta} d \theta^2 + g_{\phi \phi} d \phi^2 + $$ we have the metric tensor; $$ g_{\mu \nu} =...

I wonder what parts of statistics have specific terms existing for them - I see a relevant notion which would be relevant, but not sure if there is a term for it. If variable values can be ordered then it possesses a median. If the values can also be added then they also possesses an average. A...