Form Definition and 1000 Threads

Homework Statement Reduce the Expression: 15sin(wt-45°) + 5cos(wt-30°) + 10cos(wt-120°) to the form Vmcos(wt+θ) Homework Equations The Attempt at a Solution My theta value at the end isn't coming out right. My first step was to put make sure each term was in terms...

Hello MHB, calculate $$\left(\frac{1}{2}+i\frac{\sqrt{3}}{2} \right)^{100}$$ in the form $$a+ib$$ progress: I start to calculate argument and get it to $$r=1$$ (argument) then $$\cos\theta=\frac{1}{2} \ sin\theta=\frac{\sqrt{3}}{2}$$ we se it's in first quadrant( where x and y is positive)...

I have a set of questions concerning the perennial sum \large \sum_{k=1}^{n}k^p and its properties. 1. For p \ge 0, the closed form of this is known (via Faulhaber's formula). I know little about divergent series, but I've read that in some sense there exists a value associated with these sums...

The Laguerre polynomials, L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right) have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] I am interested in a closed form expression of these roots...

Homework Statement The question is: Let C be a symmetric matrix of rank one. Prove that C must have the form C=aww^T, where a is a scalar and w is a vector of norm one. Homework Equations n/a The Attempt at a Solution I think we can easily prove that if C has the form...

The question is:Let $C$ be a symmetric matrix of rank one. Prove that $C$ must have the form $C=aww^T$, where $a$ is a scalar and $w$ is a vector of norm one.(I think we can easily prove that if $C$ has the form $C=aww^T$, then $C$ is symmetric and of rank one. But what about the opposite...

Hi, I'm trying to fill in the gaps in my notes - looking at a poroelastic model of tissue. We have the simple spherical model below. The centre sphere is where liquid is produced, then the two following spheres are brain tissue with different permeabilities, and the final sphere is an...

Homework Statement Suppose a,c>0 and b^2-4ac>0 . Explain how you could find x_1, x_2 ε ℝ such that a(x_1) ^2+bx_1x_2+c(x_2)^2<0 . Homework Equations q\begin{pmatrix}x_1\\x_2\end{pmatrix} = a(x_1)^2+bx_1x_2+c(x_2)^2 The Attempt at a Solution I'm not sure where to go with this...

Homework Statement 4{cos(13∏/6)+isin(13∏/6)} = 4((√3/2)+(i/2)) = 2√3+2i Homework Equations The Attempt at a Solution This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.

I assume people much more knowledgeable then me must have already thought this through, but the following line of thought has me very curious. I'm making a lot of intuitive leaps here though, so I am sure there is a lot of places I could have gone drastically wrong. Hawking radiation is...

Hello, If we look at a system of two two-level atoms interacting with light, most papers start with a Hamiltonian H_{int}=(\sigma_{1}^{+}+\sigma_{2}^{+})a_{\textbf{k},\lambda} + h.c. That is, we absorb a photon and lost one excitation in the atoms or vice versa. Why do we never...

Hi I've got a recurrence relation: x_n = a*x_(n-1) + b; I think I'm going mad trying to figure out a closed form, eg. x(n) = ? the nth iteration Is there a trick or something I'm missing? Thanks

Homework Statement The internal volume of the reducer is 0.2m^3 and its mass is 25 kg. The fluid being pumped is oil (specific gravity of 0.72). Evaluate the total force that must be provided to support the reducer. d1 = 0.4m d2 = 0.2m u1 = 3m/s p1 = 58.7 kPa p2 = 49kPa (gauge)...

Homework Statement See image Homework Equations KQ/r^2 The Attempt at a Solution I have seen several different ways of working this problem, but they have all failed on me. I tried this using the equation above from my book E = (8.99x10^9)(1036 C)/(4x10^-6m) E= 2.328x10^18 N/C I also...

The integral form of Ampere's law in vacuum is ∫B\cdotdl=μ_{0}I (a) Using the relation between I and J, obtain the differential form of Ampere's law. You may ignore any displacement current. (b)Define the displacement current density J_{d} in terms of the displacement field D and show...

For the vectors in the figure, with a = 1.1 and b = 2.6, what are (a) the z component of a x b, (b) the z component of a x c, and (c) the z component of b x c? Everything I've tried to look up involves vectors that are in unit notation, etc. I just don't understand how to do it when all you...

Homework Statement From a group of 5 women and 7 men, how many different committees con- sisting of 2 women and 3 men can be formed? What if 2 of the men are feuding and refuse to serve on the committee together? Part 1: my attempt: for men, we have 7 choose 3 for woman, we have 5 choose 2...

In my book it gives the relationship between voltage and electric field as Vb-Va= -\int _a^{b} E dl which for a positively charged conducting sphere Q simplifies to \frac{Q}{4\pi\epsilon_0} (\frac{1}{b}-\frac{1}{a}) my questions is that shouldn't it be \frac{Q}{4\pi\epsilon_0}...

$\displaystyle \int^{\infty}_0 \, \frac{\log (1+e^{ax})}{1+e^{bx}}\, dx $ I am not sure whether it can be solved :confused:

Homework Statement A hollow spherical shell carries charge density \rho=\frac{k}{r^2} in the region a<=r<=b, where a is the inner radius and b is the outer radius. Find the electric field in the region a<r<b. I'm not allowed to use integral form of Gauss's law, must use differential...

Homework Statement Suppose that F = ∇f for some scalar potential function f(x, y) = 1/2(x2 + y2) Let C denote the positively oriented unit circle, parametrized by r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏. Compute the flux integral of \ointF\bulletN ds, where N is the outward unit normal to C.Homework...

[b]1. The flux of a conserved quantity can be written q(x) = -x2 (du/dx)-u If the source term is f(x) = x, write the strong form of the conservation law. I know the form of the strong form is : d/dx(c du/dx)+f(x)=0 I have no idea where to begin for this problem. The examples my professor gave...

Hi Homework Statement Let f:\:\mathbb{Z}_{5}^{3}\rightarrow \mathbb{Z}_{5}^{3} be a linear operator and let [f]_{e_{3}}^{e_{3}}=A=\begin{pmatrix}3 & 1 & 4\\ 3 & 0 & 2\\ 4 & 4 & 3 \end{pmatrix} over \mathbb{Z}_{5}. Find a basis B of \mathbb{Z}_{5}^{3} such that...

http://www.scholarpedia.org/article/Celestial_mechanics#Newton.E2.80.99s_Celestial_Mechanics In this source, the gravitational potential energy is given as \frac{-MmG}{r}-\frac{mmG}{r}, seeming to imply that the \frac{MmG}{r} result only applies to a body, mass m, in a gravitational potential...

Homework Statement Determine a vector that is orthogonal to both (1,2,-1) and (3,1,0) Homework Equations As above. The Attempt at a Solution The solution, from the back of the book, is "any vector of the form (a, -3a, -5a), but I'm not sure how they got there. I get the...

HAI I am SYED , i am doing my project using strain gauges. Problem description: I have 4 strain gauges bonded to an octagonal ring. The strain gauge i am using is METAL FOIL TYPE , GF(gauge factor) -2 and 320ohm resistance. The strain gauge has two terminals ,my question is (1) Can anyone...

Homework Statement Use exponential notation to write (√3-i)(1+i√3) in the form a+ib. Homework Equations The Attempt at a Solution Let (√3-i) = z1 r1=|z1|=√((√3)2-i2) =√(3-1) =√2 Therefore, √3=√2cosθ and -1=√2sinθ cosθ = √3/√2 and sinθ = -1/√2 θ= arcsin(-1/√2) θ= -∏/4...

hi guys, this is literally my first post here on physicsforums so i apologize in advance that my latex formatting sucks. Homework Statement prove the alternative form of the 2nd translation theorem of the laplace transform: L[f(t)u(t-a)]=e^{-sa}L[f(t+a)] where u(t-a) is the unit step...

Hi

Is it possible to get either one to display the less factored form of an expression? what I am doing is multiplying matrices together for geometrical optics but my answers keep coming out really ugly. For example I have d-d\left(\frac{2d}{r}-1\right) I don't think a person would ever write...

For any integral where the integrand is of the form f(θ)^z, with z a complex number, and f(θ) = sin(θ), cos(θ), tan(θ), ... etc., θ being either real or complex. Is it possible to explicitly solve for an antiderivative? I'm not aware of any such way I could use residues/series representations...

Here is the question: Here is a link to the question: What is the limit of arctan( (x^2-4) / (3x^2-6x) ) as x approaches 2? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

If you are given a metric gαβ and you are asked to find if it describes a flat space, is there any way to answer it without calculating the Riemman Tensor Rλμνσ? and how can I find for that given metric the coordinate transformation which brings it in conformal form? For example I'll give you...

Homework Statement Find the polar form for zw by first putting z and w into polar form. z=2√3-2i, w= -1+i Homework Equations Tan-1(-√3/3)= 5∏/6 The Attempt at a Solution r= √[(2√3)2+(-2)2]=4 tanθ= -2/(2√3)=-1/√3=-√3/3=> acording to above... tan-1(-√3/3)= 5∏/6 so, in polar form z should be...

Hi everyone, I am trying to solve the following problem. Is there exist a transformation matrix T, different then the block diagonal, with all blocks the same, such that the form of the matrix A=[A1 A2 ; I 0], is preserved? All blocks of A are in R^{nxn}, I is identity and 0 is zero matrix. In...

Homework Statement I am in dif eq, but just need to know how to separate a power. separate e^(xi) into the form a-bi, where x is a constant (in my homework, x is 4pi/3, but that's not too relevant) i is the imaginary number sqrt(-1) Homework Equations I don't know if there is some simple...

Hi I have this integral that I want to express in terms of a gamma function. Unfortunately I am unable to bring it in this form. So can you give me a hint how wolframalpha does thishttp://m.wolframalpha.com/input/?i=∫e%5E%28ix%29%2F%28ix%29%5E%281%2F5%29dx+from+-+infinity+to+infinity&x=10&y=3

An electron is initially 2cm from a proton and is then give an initial velocity away from the proton. If v is 31m/s how far to the right does the electron move before it momentarily stops? is this right? http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0112_zps5361921d.jpg

Homework Statement Prove the collection of all finite order elements in an abelian group, G, is a subgroup of G. The Attempt at a Solution Let H={x\inG : x is finite} with a,b \inH. Then a^{n}=e and b^{m}=e for some n,m. And b^{-1}\inH. (Can I just say this?) Hence...

1 & 3 I have this differential form: ##\omega = F_1 dx + F_2 dy + F_3 dz## And I concluded that ##\omega## is closed because I calculated the partials and found out that ##\displaystyle \frac{\partial F_i}{\partial x_j} = \frac{\partial F_j}{\partial x_i}##. Also, ##F_1## contains only...

Hello, Does a star collapse directly to form a black hole without creating a supernova or whether a supernova forms some neutron stars which after crossing the TOV limit forms a black hole? Thanks.

1 - how does water rise to form clouds if oxygen is heavier than nitrogen? when it turns into a gas its hydrogen and oxygen---why does it rise (to form clouds) if oxygen is heavier than nitrogen, which makes up 78% of the Earth's atmosphere? *please note that I'm not confused as to the...

If this were the reduced row echelon form of an augmented matrix, 1 2 0 1 1 0 3 0 0 1 2 1 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0 0 What is the form of the following answer given, and how can I understand it? (x1; x2; x3; x4; x5; x6) = (3; 0; 1; 0; 0; 2)+ t(1; 0; 1; 0; 1; 0)+ s(1; 0; 2; 1; 0...

Conservation of relativistic momentum and energy, pion decays Homework Statement A small particle (pion), traveling at a velocity V, decays into two rays, γ1 and γ2. Find the Momentum and Energy of γ1 and γ2 if: a) γ1 is in line with V, and b) if γ1 is perpendicular to V. I drew out the...

Homework Statement How do I write 1-2i in polar form? Homework Equations The Attempt at a Solution I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.

So I've just started working with the index/einstein notation for matrices and vectors the other day. I've been doing a few exercises from a booklet I have, but I am still a bit confused. I am pretty sure my confusion is rather stupid though, so I apologize in advance. Homework Statement So...

Probability Question -- using the combinations counting form C(n,k) Homework Statement 4. A bowl contains 3 red chips, 4 green chips, and 5 blue chips. A batch of 3 chips is withdrawn at random. (a) What is the probability that the batch contains only red chips? (b) What is the probability...

Why is time constant form of transfer function in control system better than pole zero form ? If a closed Loop transfer function is given to me how should i find D.C gain ?

Homework Statement Let Ʃ 1\(n^2-1) from n=2 to k. It says find a closed for it and prove it using sum notation. Homework Equations The Attempt at a Solution I can easily prove it by induction but I don't know what a closed form means. I tried looking it up online but there really...

Homework Statement Starting from the sum: I=Ʃ mα*ρα2 and replacing it by the appropriate integral, find the moment of inertia of a uniform thin square with side length 2*b, lying in the x-y plane, rotated about the x-axis. Calculate its moment of inertia. Homework Equations The integral form...