Exercise — 400 discussions

Homework Statement I have the matrix form of the Hamiltonian: H = ( 1 2-i 2+i 3) If in the t=0, system is in the state a = (1 0)T, what is Ψ(x,t)? Homework Equations Eigenvalue equation The Attempt at a Solution So, I have diagonalized given matrix and got...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with Exercise 5.1, Part (iii) ... ...Exercise 5.1 reads as follows: Can someone please help me to get a start on this exercise...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with Exercise 5.1, Part (ii) ... ...Exercise 5.1 reads as follows: Can someone please help me to get a start on this exercise...

Hello everyone, could you help me with this exercise? I am stuck, and I can't find anything on the internet that solves this. Your help is very much appreciated :) 1. Homework Statement Circular steel bar, clamped at extremities. Two parts: A(ab)=800mm² A(bc)=400mm² L(ab)=...

Homework Statement We describe particle's movement with the Hamiltonian: H=- \frac{\Delta E}{2} |0\rangle \langle0| + \frac{\Delta E}{2} |1\rangle \langle1|, where |0\rangle and |1\rangle are the ortonormal basis. Let: |a\rangle = \frac{1}{\sqrt{2}}|0\rangle +\frac{i}{\sqrt{2}}...

Homework Statement I would really appreciate it if you could give me a hand with this exercise, not sure on what I've done. Data: Moody: L=55*10-3m D=10-1m k=0.0002m Homework Equations ##Re=\frac{D*u*ρ} {μ}## ##Re=\frac{4*m} {pi*D*μ}## Relative roughness ##ξ=\frac k D## where k=rougness...

Homework Statement Would really appreciate if you could lend me a hand with this tube and shell exercise.[/B] m=0.24kg/s ##D=2.5*10-2m## ρ=850 kg/m^3 cp=2000 J/kg*K μ=2*10-4 kg/m*s λ=0.3W/m*k Homework Equations Dittus-Boelter:Nu=0.023*Re0.8*Prn where n=0.4 heating and n=0.3 for cooling, so in...

Homework Statement I would really appreciate if you could give me some hints regarding what exactly to do at iv)[/B] iv) Given formulas: Homework Equations f(y)=(ro*R^5/E*t^2) The Attempt at a Solution we know that f(y)=0.75 1ton TNT=4.184*10^9 J ro=1.003kg/m^3 We have the above...

Homework Statement I would really appreciate if you could give me some hints regarding what exactly to iii) Homework Equations we know they are in parallel so Q=Q1+Q2+...+Qn delta hloss=delta hloss1+deltahloss2+... delta P=delta P1=delta P2=...The Attempt at a Solution We know flow is...

Have there been any studies looking at the ergonomics of using an exercise ball as your work desk chair? I have a close friend with lower back and leg pain who is looking for ergonomics options. There are lots of studies about keyboard positions, etc. EDIT -- She is also talking to her doctor...

Homework Statement I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter...

Homework Statement Hello! Here is my second post on the subject partial fraction decomposition. The subject looks pretty easy to learn, but when I try exercises, I do not get to the correct answer. Please, take a look at the exercise below and help me to see my mistakes. Homework Equations...

Homework Statement "Design a Synchronous Counter Mod-12 Up/Down, using only Flip-Flop Type D. A binary input ##U## that determines if the counter has to increase (##U = 1##) or decrease (##U = 0##). Homework Equations Flip-Flop Type D equation is ##Q_{t + 1} = D## The Attempt at a Solution I...

Homework Statement [/B] Consider an ideal rope where there is a wave moving at velocity ##v=20 m/s##. The displacement of one end of the rope is given by $$s(t)=0.1 \mathrm{sin}(6 t)$$ a) Find the wavefunction ##\xi(x,t)##, knowing that it is progressive b) Find the distance ##\delta## (in...

Homework Statement Charged pion with average life time $$\tau=10^{-8} sec$$, and mean free path in the water$$\ell=100m$$ falls prependicular to a lake (depth of lake is at $$\ell_0 =30m$$ with velocity $$V=0.9999c$$ What of the next is correct? 1). The particle isn't gona touch the bottom of...

Hey there community, I have a question on an exercise. Actually it is a general question based on it. Here is the exercise: We throw 3 dice. If we know that the sum of these 3 is 10, then what is the probability of at least one of them being 3? Well now, this exercise is very simple. I mean I...

My professor did this exercise that I didn't quite get how she went through all of it. We have a ##U = {(x, y, z, t) : x+y+z+t = 0}## and ##B_{Im(f)} = \left[ \begin{pmatrix} 7 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 5 \\ 0 \\ 1 \\ -5...

Homework Statement A point charge ##q = 30 mC## is located in the center of a conductor spherical shell with an internal radius of ##a = 10 cm## and an external radius of ##b = 20 cm## and total charge null. Find the surface density charge of both the internal surface and external surface of...

Homework Statement Calculate the acceleration of a 1400kg car if it can stop from 35km/h (9.72m/s) on a dime (diameter= 1.7cm) (0.017m). What is the force felt by the 68kg occupant of the car? Homework Equations v^2=v0^2+2a(x-x0) F=ma The Attempt at a Solution ok after solving for a in that...

Homework Statement Hello! I would be grateful for your help on finding my mistake - somehow my answers are wrong compared to the answer from the book. Here is the exercise from a paragraph on gases (cumulative gas law, basics): Consider the reaction for the synthesis of nitric acid: 3NO2 + H2O...

I am doing a Weather Data Log exercise, and I am looking for the program to run continuously. However, every time I run it, the program would always direct me to store the data in a file for every run I do. Please look at the following pic. Btw, I am running this on a Mac, using parallel's...

Homework Statement Three capacitors ##C_a = C, C_b = 2C, C_c = 3C## are positioned like in the figure. The A capacitor's electrode has a ##V_a = 20 V##, while the B capacitor's electrode has a ##V_b = 80 V##. What is the electric potential ##V_3## of the C capacitor's electrode? Homework...

Homework Statement You received many steel balls of the same diameter d and container of known volume V. All dimensions of the container are much greater than balls diameter. How many balls can be placed in a container? Homework Equations (\frac{4}{3}\pi)(\frac{d^3}{8})\approx0,52d^3 The...

At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.

Homework Statement The question as follows: Calculate the energy that is required to accelerate a particle of rest mass ##m\ne 0## from speed ##v## to speed ##v+\delta v## (##\delta v \ll v##). Show that it would take an infinite amount of energy to accelerate the particle to the speed of...

If I have a number n and I want to know all the unique ways in which I can use u addends to get that number... How do I do it? For example: If the number is 6 and I want to see how many unique ways I can add up to it (order matters: $$1 + 1 + 2 + 2\ne 2 + 2 + 1 + 1$$) by using 4 addends...

Homework Statement A mass ##m_1 = 5.0 kg## is hanging from the end of a thread, of negligible mass, that slides on a pulley, of negligible mass too and without friction. At the other end of the thread, at the same height of ##m_1##, there is another hanging mass ##m_2 = 3.5 kg##. Using the Law...

" Solve the equation: 2e^(-x) = 3e^(0.1x) " I've been fiddling around with this and I have no idea what I'm supposed to do. I know the final answer should be something like: x = [(2/3)log e] / 1,1 The only step I've managed to do was: (2/3) x e^(-x) = e^(0.1x) But after that, I don't know...

Homework Statement Being ##f : \mathbb R^4\rightarrow\mathbb R^4## the endomorphism defined by: $$f((x,y,z,t)) = (13x + y - 2z + 3t, 10y, 9z + 6t, 6z + 4t)$$ 1) Determine the basis and dimension of ##Ker(f)## and ##Im(f)##. Complete the base chosen in ##Ker(f)## into a base of ##\mathbb R^4##...

Hi everybody I'm currently looking for an introductory quantum mechanics book which emphasizes the mathematical aspects of it. I especially need exercises in order to pass a written exam, but I'd like to have even lots of examples. I've already gone through the whole "Picasso" (it's an italian...

Homework Statement Hello! Here is the quote of the exercise: Excessive exposure to sunlight increases the risk of skin cancer because some of the photons have enough energy to break chemical bonds in biological molecules. These bonds require approximately 250–800 kJ / mol of energy to break...

Homework Statement The acceleration of a particle moving only on a horizontal xy plane is given by a = 3ti + 4tj, where a is in meters per second squared and t is in seconds. At t = 0, the position vector r = (20.0 m)i + (40.0 m)j locates the particle, which then has the velocity vector v =...

I am reading Bruce Cooperstein's book: Advanced Linear Algebra ... ... I am focused on Section 1.3 Vector Spaces over an Arbitrary Field ... I need help with Exercise 2 of Section 1.3 ... Exercise 2 reads as follows:Hope someone can help with this exercise ... Peter*** EDIT *** To give...

I am reading Bruce Cooperstein's book: Advanced Linear Algebra ... ... I am focused on Section 1.3 Vector Spaces over an Arbitrary Field ... I need help with Exercise 1 of Section 1.3 ... Exercise 1 reads as follows:Although apparently simple, I cannot solve this one and would appreciate...

Homework Statement Hello! Please, take a look at this exercise. A parabolic arch is constructed which is 6 feet wide at the base and 9 feet tall in the middle. Find the height of the arch exactly 1 foot in from the base of the arch. I have trouble solving it. Please, guide towards a correct...

I am reading Bruce Cooperstein's book: Advanced Linear Algebra ... ... I am focused on Section 1.2 The Space $$\mathbb{F}^n$$ ... I need help with Exercise 12 ... since I do not get the same answer as the author ... Exercise 12 reads as follows: My attempt at a solution to this apparently...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.2.12 ... Exercise 1.2.12 reads as follows: https://www.physicsforums.com/attachments/5102 Can someone please help me to get started on this problem ...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.2.8 (c) ... Exercise 1.2.8 (c) reads as follows:Now ... from this exercise we have that $$M \equiv \mathbb{C}^3$$ ... and ... $$A = \begin{pmatrix}...

Homework Statement In this circuit, find i(t), knowing that v_s= 2 \cos \left(w x+\frac{\pi }{2}\right), and that, at the source's frequency, X_C= -1 Ω and X_L = 1 Ω. Homework Equations Basic phasors and dividers equations. Z_C = jX_C Z_L = jX_L The Attempt at a Solution I used dividers...

Homework Statement "Find all the points on the curve with equation 6y = 2x^3 + 3x^2 + 6x + 5 where the tangent is parallel to the line with equation 3x − y + 2 = 0 Homework Equations No idea The Attempt at a Solution There are no exercises in the book even similar to this example which is...

I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges ... and am currently focused on Chapter 3: Propositional Logic ... I need help with Exercise 3.2.5 which reads as follows:Can someone please help me with reconstructing the formula of the Gödel number that is given...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help to get started on Exercise 3, Section 2.2...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help to get started on Exercise 3, Section 2.2...

Hi! I can't find the method of the solution to this question, it was an exercise on an exam.. There are two grounding electrodes buried in the ground. We make three measurments. First, we measure the first electrode's grounding resistance, which is: 6 ohms. Then, the second's: 7 ohms. Then the...

Hello. I have the following exercise, and I would like you to say to me if I have it right and how to proceed: "A particle P moves with constant speed v along the X axis of a reference system O, being x0 = 0 the position in t = 0. Describe the movement on another system O' with the same...

EDIT: I've just realized this is the 'Calculus and beyond' subforum - I saw 'beyond' and thought, "Well I've done all my calculus, and now I'm doing group theory, so this thread must go here!". But now I realize it surely belongs somewhere else. Sorry about that. Mods feel free to shift it to...

1. Homework Statement (Uploaded photo from Zettili Quantum Mechanics - Chapter 3 - Solved problems 3.4 and 3.5) Check at problem 3.4 the relation that he gives between operator A and state φn. Now check the relation that he uses in problem 3.5 between A and φn again. They are different while on...