System Definition and 1000 Threads

Find all triples $(x,\,y,\,z)$ of real numbers that satisfy the system of equations $x^3=3x-12y+50\\y^3=12y+3z-2\\z^3=27z+27x$

hi given such system of equations ## \begin{cases} \rho^2 = 2 \rho \\ 2\theta= -\theta+2k\pi , k\in \mathbb Z \\ \end{cases} ## in the solution of the professor the system is solved is solved as follows. ## \begin{cases} \rho=0 , \rho=2 \\ \theta= -\frac 2 3 k\pi , k = 0,1,2 \\...

Summary:: Suggest a geometry Hello! I have difficulties with this question. It is translated from Swedish so if something's weird tell me. The speakers in headphones often work with the help of magnetism, when a varying voltage is applied across a coil attached to the speaker membrane. The...

Hello, everyone, I am currently working on the following (real) problem, where I am not getting anywhere. It would be super nice if you could have a look at this. Thank you very much :-). I have a pipe system (Black Box) of which I only know the following things: At a set flow rate with a...

Since there are initial conditions stated, I would have to craft the s equation in mind, in order to find the impulse by laplace inverse; which is this: ##(s^2Y(s)-sy(0)-y'(0))+8(sY(s)-y(0))+16Y(s)=x(s)## ##(s^2Y(s)+\frac{1}{2}s-1)+8(sY(s)-1)+16Y(s)=x(s)##...

Spring has more potential energy when it is compressed or stretched from its initially balanced state. As external work is done, it stores energy in the form of potential energy. Here, we know energy is stored in spring but For the Earth-ball system, where the energy stored?

I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws.

I'm trying to understand the precise reason we claim that a value being conserved means that the system in question is invariant under the corresponding symmetry transformation. Take parity for example. If the parity operator satisfies the commutation relation ##[P, H] = 0## for a given...

For a system of two or more particles, it is customary to define potential energy functions ##V_{ij}## between pairs of particles, so that the total conservative force (not necessarily total) on any given particle is $$\mathbf{F}_i = \sum_{j\neq i} -\nabla_i V_{ij}$$as a sum over all other...

I am confused about conservation of momentum for this question. I take the system as two objects, each having mass m. For first object (the one performing simple harmonic motion), there is net external force acting on it in horizontal direction (restoring force of spring). For second object...

Suppose that $x$ and $y$ are positive real numbers. Find all real solutions of the equation $\dfrac{2xy}{x+y}+\sqrt{\dfrac{x^2+y^2}{2}}=\sqrt{xy}+\dfrac{x+y}{2}$.

If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system? I think I have a small misunderstanding of the...

The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...

Suppose the system of equations (coming from invariance of the wave equation) : $$B=-vE\\A^2-B^2/c^2=1\\E^2-c^2D^2=1\\AD=EB/c^2\\B=vA\\AE-BD=1$$ If one adds a lightspeed movement like $$A=a+f\\B=b-cf\\D=d+h\\E=e-ch$$ Then solving equ 1 for f gives $$f=(b+ve-vch)/c$$ Equ 4 for h implies...

Show that the nonlinear system $\dot{X_1}=2\cos X_2, X_1(0)=a$ $\dot{X_2}=3\sin X_1, X_2(0)=b$ has a unique solution for the arbitrary constants $a$ and $b$. how to solve this system? Thanks.

I have a doubt. It is said that antigens detected by macrophages and and Dendritic cells (by way of PAMPs and DAMPs) can initiate and mount an immune response, why antibodies need to be produced. Ok, antibodies opsonize the intruders. But then even without antibodies, the innate immune system...

I've marked correct answers above. Have a look at the solutions: How is the first equation justified? Shouldn't v2 and ωR be of opposite signs? What is v1? And how is it equal to v2? My biggest problem is the source of v1 since the ring is not having vertical displacement, then what is v1?

Good night! How do I find the values of a (real) so that the solution of this system is? (i) just an ordered pair? (ii) exactly two pairs. (iii) exactly 3? (iv) is there a place where you have more than 3 pairs as an answer?So... I thought like this: I developed the first part. I solved the...

1. How will the motion of M be? I assume wire S is inelastic so will M move downwards but not in straight line? (I mean M moves downwards but because the left side of pulley is connected to S, it will be static and the right side of pulley can go down along the extension of the spring so its...

Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...

I know that it will probably execute something similar to circular motion. I thought of conserving momentum but I think there is an external force being applied due to the impulse which will prevent me from doing so. I know that once I find the tension it would become very easy to find the...

I am writing a space opera, that is meant to be hard, except some alien magic. So far, i have the following points : asteroid belt is the most valuable for rare material mining, there they live in O Neil cylinders. Travel is done by fusion ships, that can maintain miliG-s of constant...

I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...

can i solve this problem i didnt go university due to Covid-19

Suppose we have a system of particles being acted upon by a single external force ##\mathbf{F}^{e}##. Each individual particle feels a force of ##\mathbf{f}_i = \mathbf{f}_{i}^{int} + \mathbf{f}_{i}^{e}## such that ##\sum_i \mathbf{f}_{i}^{e} = \mathbf{F}^{e}##, and ##\mathbf{f}_{i}^{int}## are...

I understand how they might have got to these answers but I'm still kind of shaky on how the mass of the rope plays a role in the tension at point B, and how to mathematically represent the tension at any point along the rope; I know the tension varies because the rope has mass. If I was to...

My best guess right now is use Newton's version of Kepler's 3rd Law to maybe find a combined mass, as I'm under the impression that the smaller star's mass would still be too large to ignore, but I'm not confident. And I wouldn't be sure as where t go from their, either. Any guidance would be...

This is my attempt the system The 1 is the initial configuration where the 3 electron is at infinity. The 2 is the final configuration where the 3 electron is midway.U1 is the potential energy between e1 and e2 U1 = (q1*q2)/(4*π*ε0 * (0.02)^2); // q1, q2 charge of electrons K1 =...

Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.

Hello, The question I have pertains to conservation of Angular momentum on a motorcycle. I know that the dynamic friction is less than the static friction, so when you are braking on a (say a motorcycle) and the wheels lock up, the bike is bound to fall over. This is the reason ABS (Anti-lock...

This is the problem's picture: My problem is that what I got for one acceleration (m3's) via Newton's equations is not the same as via D'Alembert's principle (I've checked on my PC if they are the same expression). I can't find the mistake. Any suggestion is welcome. I attach pictures of what...

I know that from the given problem, I need to find the expression for Kinetic energy, KE = 1/2 m [r(dot)]^2 and Potential energy, PE = 1/2 k r^2 So L = 1/2 m [r(dot)]^2 - 1/2 k r^2 Hence H = 1/2 m [r(dot)]^2 + 1/2 k r^2 I assume that the fixed length r0 is provided to find the value of end...

So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N. Now I think that I will take...

I use the following script and function in MatLab, but get three errors. I shall first write down the code and after that the errors that I get. function yprime = lorenz_de(t,y) %LORENZ_DE Lorenz equations. % yprime = lorenz_de(t,y). yprime = [10*(y(2)-y(1))...

Equal masses of ice at –10ºC and water at 80ºC are placed in an insulated container and allowed to reach thermal equilibrium. Calculate the equilibrium temperature Data: Water(ice): 37,65 J/mol.K Agua (l): 75,29 J/mol.K ## Lf = 6011 J/mol ## I solved it this way: ## -Q_{l} = Q_{ice} ## ##...

Hi, I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a. I need to try find dispersive relation...

Let a mass m charged with q, attached to a spring with constant factor k = mω ^2 in an electric field E(t) = E0(t/τ) x since t=0. (Equilibrium position is x0 and the deformation obeys ξ = x - x0) What would the hamiltonian and motion equations be in t ≥ 0, in terms of m and ω?? Despise magnetic...

(I hope this is not a double posting) I want to solve this system of equations, containing logarithmic terms: ##7\ln(a/b)+A = 7\ln(d/e)+D = 7\ln(g/h)+G## ##7\ln(a/c)+B = 7\ln(d/f)+E = 7\ln(g/i)+H## ##7\ln(b/c)+C = 7\ln(e/f)+F = 7\ln(h/i)+I## ##a\phi_1+d\phi_2+g\phi_3=X##...

I was solving a Physics problem, and for it to be consistent there should exist a function f(t) in real numbers and a time T, such that: $$\int_{0}^{T} f(t) dt=0 $$ $$\int_{0}^{T} \int_{0}^{t} f(t') dt' dt=0$$ $$\int_{0}^{T} f(t) (\int_{0}^{t} f(t') dt') dt>0$$ i.e. the integral is zero, the...

I don't know how to calclute error in derivative for daming ratio of 0.5

Hey! :o We have the matrix $A=\begin{pmatrix}1 & -1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1\end{pmatrix}$ and the vectors $b_1=\begin{pmatrix}1 \\ 0 \\1\end{pmatrix}$ and $b_2=\begin{pmatrix}-1 \\ 1 \\2\end{pmatrix}$. Check if the system $Ax=b_i$ for $i\in \{1,2\}$ has a solution. If the system is...

See the picture I am stuck at 12(1+2k)=0 So k=-1/2 for stability k must have value greater the - 1/2 which means there will no sign changes in rooth array and equation represents a stable system

I want to solve the following system of equations ##M_{1} = f_1+f_2+m_1+m_2\ \ ;\ \ M_{7} = f_1+f_2+s_1+s_2\ \ ;\ \ M_{13} = m_1+m_2+s_1+s_2## ##M_{2} = f_1+f_3+m_1+m_3\ \ ;\ \ M_{8} = f_1+f_3+s_1+s_3\ \ ;\ \ M_{14} = m_1+m_3+s_1+s_3## ##M_{3} = f_1+f_4+m_1+m_4\ \ ;\ \ M_{9} = f_1+f_4+s_1+s_4\...

If 1kg make a displacement of 1unit upward then A make a 1/2unit down because 1/sin 30.after that i have no idea what do I will really need help. Thanks!

Hi, So the question is to: derive the equations of motion for the following in terms of x1 and x2? The bar is assumed to be light and rigid. (NB. I know I posted another vibrations problem earlier in which I tried to use an energy approach to get to the equations of motion. However, we haven't...

I would like to design a system that is capable of generating frictional heat through its servo motor to heat up an enclosed chamber to 500 'Celsius . The challenge is that external heating source such as heating element, heat chamber etc. shall not be included in the design setup. Assuming that...

The first part is actually fine. You just note that since r=r1+r2 that means r1=r+r2 and r2=r1-r and you substitute that into the center of mass, R, and simplify to get r1=R+(μ/m1)r, and r2=R-(μ/m2)r But the next part is where I'm very confused. The general idea is that you want to prove ∇1 =...

<work done a system> a) w=5N*(0.4m)=2J I think this is right, but b) center of mass initial = ((0.5kg)(0.05m)+0.5kg(0.65m))/1kg = 0.35m center of mass final = ((0.5kg)(0.45m)+0.5kg(0.4+0.1+0.3+0.25))/1kg = 0.75m I'm not sure for this one... How can I calculate the displacement of the...