Exercise Definition and 578 Threads

Iv'e got this proof from some claim: Any Pure maths doctors out there who can explain to me why since ##V\ne \emptyset## that ##1\notin \mathfrak{b}##? Thanks!

Good morning, I have an exercise with two points that gives a Matlab mat file in which are contained the samples of two measured signals and the variable fs indicating the sampling frequency A)Signal 1 consists of two sinusoidal signals of which you are asked to calculate: -the duration ⇒ I...

I can write $$\psi(x,t_0) =\frac{1}{\sqrt{2}}(e^{\frac{-iE_1}{\hbar}t_0}\psi_1(x) +e^{\frac{-iE_2}{\hbar}t_0}\psi_2(x))$$ for the second coefficient to be -1 i need ## -1=e^{-i\pi}=e^{\frac{-iE_2}{\hbar}t_0} ## so ##t_0=\frac{\pi\hbar}{E_2}## and the above equation becomes $$\psi(x,t_0)...

Hi there, I did an exercise and when we corrected it I realised that the oxidation number of Fe was (ll) but I don't know how can I find it. The common name is iron (ll) nitrate and the other name, that I don't know how is called because i study this in basque, is iron (2+) nitrate trioxide (2-)

My solution is different from the official solution and I don't understand what I did wrong. Here is my solution: The magnitude of the initial velocity is ##|v_0| = 12.0~\rm{m/s}##, so the vertical component of the initial velocity is ##v_{0-y} = (12.0 \sin{25^{\circ}})~\rm{m/s}##. Then I use...

Hello, I am attempting to work through problem 12.6 in MTW which involves formulating Newtonian Gravity using Curvature as opposed to the standard formulation. This is a precursor before standard GR. In it he states that the curvature tensor in this formulation is as follows...

I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...

I found a box of air core solenoids and was hoping someone could me think of a useful lab to use them for. They are about 700 turns each. They carry 7 to 10 amps. However I think I think I would only be able to provide 3 amps because of the power supplies I have. I would like to use them to do...

Hi, I'm calculating the work done by regular tetrahedron during taking from the water by crane (USING INTEGRALS). I don't know how bad is that solved so if anyone checks my work and gives me some advice or hints I would be very glad. Everything is written in the PDF file. There were given...

Figure: My attempt at a solution: a) ##\boxed{V_{TH}}## Current source equations ##\rightarrow \boxed{2=I_2-I_1}## Control variable equations ##\rightarrow V_1=4I_2\rightarrow \boxed{0=4I_2-V_1}## Super Mesh ##\rightarrow -0,5V_1+2I_1+I_2(4+8)-8I_3=0\rghtarrow...

I tried to solve it considering the canonical ensemble (since the system is at the equilibrium with temperature T) and started finding the partition function:The problem is I am not sure if I have done it correctly and need help because I don't really know where to check.

The official solution says ±25.4°, but I'm having trouble reproducing it. Here is my solution: 1) The components of the velocity of firework F with respect to the ground G in the moment of explosion are the following (Notice, I'm using sin, because the statement says 30.0° from vertical.)...

In the book it is mentioned that, in path c, the line integral would be: $$\int \vec{F}\cdot \vec{dr} = A \int_{1}^{0}xy dx = A\int_1^0 x dx = -\dfrac{A}{2}$$. but I think that dx is negative in that case, the result would be positive, right?

(a) Let be m a line and the only two semiplans determined by m. (i) Show that: If are points that do not belong to such , so and are in opposite sides of m. (ii) In the same conditions of the last item, show: and . (iii) Determine the union result , carefully justifying your answer...

Hello i am trying to solve a problem set about chemical equilibrium , the issue is that my results don't correspond to the correction . can someone tell me what is wrong with my answer , thanks here is the problem and his correction : here is my answer :

Hello , i am a little confused about this exercise because we talk about gases reaction and we are asked about the concentrations P.S : i have other questions that depends on your answer . Thanks .

My physics background is weak. My search found lots of ## E \times B ## and ## E^2 + B^2##, often associated with ## \mu_0 ## and ## \epsilon_0 ##, but never divided by ## 4 \pi ## and ## 8 \pi ##, respectively. Could someone provide a reference? Or a derivation? Thanks.

I am a beginner in GR, working my through Gravitation by the above authors. If there is a better place to ask this question, please let me know. I understand (from section 5.7) that the stress-energy tensor is symmetric, and from equation 5.23 (p. 141), it is explicitly symmetric. But...

Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help. A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...

I have doubts about the wording of the exercise: (1) energy density is ##u=\varepsilon_0 (cB)^2## but since the question asks for mean energy density should I perhaps average over ##cos^2 (\omega t)## (there due to the ##B^2##) and thus use ##<u>=\frac{1}{2}\varepsilon_0 (cB)^2##? (2) it seems...

So I understand the concept of lagrange multiplier but I fail at every single execise I encounter anyways. Because you always end up with unsolvable equations of x^3yzb3gh + 37y^38x^3 + k^5x = 0 Anways here's my stupid attempt: Instead of doing $$grad(f) + \lambda grad(g) = 0$$ I solve $$...

Hello all, I am trying to solve this one: John has n friends . He wants to invite in each evening (365 days a year) three of his friends for dinner. What should be the size of n, such that it will be possible not to invite the same triplet twice ? What I did was: \[\binom{n}{3}\leq 365\]...

Hello, everyone. I'm not sure if I did this problem right because there's no answer key. I got this question from a high school introductory Physics book. But it's jaded and I accidentally poured coffee on it, so I can't take a picture of the question. I copied it word for word though. This is...

Hello! I have two related exercises I need help with 1. Partition the space ##\mathbb{R}## into the interval ##[a,b]##, and singletons disjoint from this interval. The associated equivalence ##\sim## is defined by ##x\sim y## if and only if either##x=y## or ##x,y\in[a,b]##. Then...

I tried to solve it and I got the following, is it correct?

This is the image of the problem: I tried to solve it and I got the following is it correct? derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?

This is the image of the problem I tried to solve it and I got the following is it correct?

Hello PF, After thinking, googling, and reading many threads here, I decided that I'm going to start learning calculus using Stewart. The problem is that the book puts too many exercises after each section, in addition to those at the end of each chapter. What's the difference between these...

For a observer on Earth, a rocket takes Mike from Earth to Pluto with a speed of 0.82 c for 33.72 yr. Find the space-time interval for the two events such as Mike leaving the Earth and reaching Pluto considering Pluto is at rest relative to Earth for the observer on Earth. I confess that i am...

I'm trying to solve the Goldstein classical mechanics exercises 1.7. The problem is to prove: $$\frac{\partial \dot T}{\partial \dot q} - 2\frac{\partial T}{\partial q} = Q$$ Below is my progress, and I got stuck at one of the step. Now since we have langrange equation: $$\frac{d}{dt}...

Hi everyone! =) . I'm having some issues with this exercises, It's about functions. I remember the basic geometrics formulas and how to get the area and perimeter of a square or a circle but I don't get it. I need an explanation. 1. Express the area A of a square as a function of (a) the length...

Hi everyone, I'm an Italian High Schooler and I need a problem about maglev trains for the final exam. I apologize in advance if my english is bad or if I didn't follow some rules. I'm not native and new to this forum.

A math exam question asked for the ratio of two wheels given the required information about the number of revolutions made along a certain distance by the two wheels of a penny-farthing bike. Some students gave the ratio of the radii while others gave the ratio of the areas. What should an...

I'm trying to the following exercise: I've proven the first part and now I'm trying to do the same thing for fermions. The formulas for the mode expansions are: What I did was the following: $$\begin{align*} \sum_s \int d\tilde{q} \left(a_s(q) u(q,s) e^{-iq \cdot x}+ b_s^\dagger(q) v(q,s)...

Hello, I have this (I am solving scholarship exams)math problem and I don't quite know what to do with it , Could You please help? The exercise is about complex numbers and it says: Calculate in the algebraic form(a+bi) I thought on applying substitution since -1=i^2 and z is the real part but...

First, I think that I need to calculate the capacitance. It is ## C=\epsilon_0*\frac{l*w}{d}-x*\frac{w*\epsilon_0}{d}+\epsilon*\frac{x*w}{d} ##. After that I should calculate the potential energy. It is ##U=\frac{1}{2}*C*V^2 ##. After that I should take its gradient to get the force. So ##\vec F...

Summary:: Doubt in a spring exercise Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...

I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...

Let's imagine an ideal scenario where you're lifting your own weight in its entirety. Let's say a woman weighing 100 lbs. Suppose she's doing an idealized handstand and pushup from that position. So she's lifting 100 lbs. Let's say ideally all of the forces are on her arms only. Do these forces...

My attempt at solution: in tetrad formalism: $$ds^2=e^1e^1+e^2e^2+e^3e^3≡e^ae^a$$ so we can read vielbeins as following: $$ \begin{align} e^1 &=d \psi;\\ e^2 &= \sin \psi \, d\theta;\\ e^3 &= \sin⁡ \psi \,\sin⁡ \theta \, d\phi \end{align} $$ componets of spin connection could be written by using...

Hello, Can someone help me out with this one. I solved the exercise but didn't get the right answer so I went searching on internet for solutions. It seems something was wrong with my force-diagram. In my force diagram I had another force included excerted by the wire on the post, since the...

The doubt is about B and C. b) n = 4, $C = {I,e^{2\pi/4}} n = 5, $C = {I,e^{2\pi/5}} n = 6, $C = {I,e^{2\pi/6}} Is this right? c) I am not sure what does he wants...

Homework Statement:: 1) ##X## is number of success out of ##n## trials where ##p## is the probability of success. 1a) Show that ##\mathrm{E}\left[\hat{P}\right]-p=0##, where ##\hat{P}=X/n##. 1b) Find the standard error of ##\hat{P}##, then give calculate the estimated standard error if there...

1) Since I want at least ##6## flights to come within ##2## hours, then the time interval between each should be, at worse, ##2/6=1/3## hours, and the probability is ##P(X\leq1/3)=1-e^{-1/3}##. 2) The probability that at best 5 airplanes arrive at the airport is...

t is Torque I is the inertia moment P is the power c is the constant light speed r is the spot distance to the fiber p is the torsional constant theta is what we want In the equilibrium $$t = 0$$ $$ F\Delta T = \frac{E}{c} = \frac{P\Delta T}{c} => *F* = \frac{P}{c} (1) $$ This will be the...

Answer : Using Pascal's law, this is my answer : ##\color{blue}{\boxed{\vec F_a = \vec F_c < \vec F_b}}##. Reasoning : Forces ##F_a## and ##F_c## are equal because the pressures required at the two cylinders for case (c) is the same as that required in (a). It doesn't matter how many of those...

I am reading from Courant's book. He gave an example of the continuity of ##f(x)=5x+3## by finding ##\delta=\epsilon/5##. He then said that ##|x-x_0|## does not exceed ##|y-y_0|/5##, but I don't see how he came up with this inequality. I know that ##|x-x_0|<\epsilon/5##, and that...

Hi there, I have tried to do these questions but I don't understand. Any help would be appreciated!