Mistake Definition and 296 Threads

Homework Statement Homework Equations F = ma [/B]The Attempt at a Solution Why is the angle 60 degrees? Isn't it 30 degrees? [/B]

Homework Statement Suppose you have a mole of water at 25##^{\circ}## at atmospheric pressure. You then raise its temperature to 30##^{\circ}##. Determine the change in Gibbs free energy. To compensate for the change, once can raise the pressure on water, how much pressure you need to increase...

Most people don't get to cal 1 in high-school by the time they are seniors. People are excepted to get ready for cal 2 by the time they get to college. People don't get to cal 1 because they don't study at their home. However, in my personal opinion, is homework a mistake to give to students...

Homework Statement Homework Equations[/B] I have a circuit that consists on 3 components in parallel: a current source Ia, a resistor R and a capacitor C. Ia is directed upwards, while the currents through the capacitor and the resistor are both directed downwards. Select the correct option in...

Is there any mistake in Heisenberg's uncertainty principle?

In this paper (https://arxiv.org/abs/astro-ph/0603302) the authors derive the field equations for f(R) gravity considering a spherically symmetric and static metric. Now the Ricci scalar only depends on r so you could write f(R(r)) = g(r) for some g. However what it seems the authors have done...

Say, we have two particles of equal and opposite charge in an isolated system in which we neglect gravity. The energy of particle 1 is: E1 = U1 + T1 Where U1 is electrostatic potential energy and T1 is the kinetic energy of particle 1. The energy of particle 2 is: E2 = U2 + T2 Where U2 is...

Homework Statement Homework EquationsThe Attempt at a Solution My Solution: My Friend Solution: Are we both right? If not, who is right? and what is the mistake in other's solution! Thanks![/B]

I don't know if I'm losing my mind or not, but I am reading Artin's "Algebra", and in section 2.6 - isomorphisms, he writes "Corollary 2.5.9. gives us a way to verify that a homomorphism ##\varphi: G \rightarrow G'## is an isomorphism. To do so, we check that ##\mathrm{ker} \varphi = \{1\}##...

Was Charles II of Spain unlucky or inevitable mistake of biology? As you can see in the pictures, Charles II of Spain was born as a child of relatives. Due to inbreeding depression,he had a lots of abnormalities. But was it just a mere coincidence that the recessive deleterious genes ended up...

Homework Statement Use the method of variation of parameters to find a particular solution Homework Equations https://flic.kr/p/NqhtyQ The Attempt at a Solution https://flic.kr/p/NicCbN [/B] Can some find my mistake? The answer is just suplosed to be - 2/3te^-t[/B]

Hi, I've been unsuccesfully trying to derive the Schwartzschild solution, narrowing my mistake down to a single component of the Ricci tensor. The problem is the following(taken from Weinberg's book, with grr = A , gtt = -B and the angular part being the same as in spherical coordinates): I...

Homework Statement I'm actually a tutor, and a student of mine at uni has the following differential equation with initial conditions to solve imgur link: http://i.imgur.com/ptuymQv.gif From y(t) = c_1sin(3t) + c_2cos(3t), it is not possible to solve for the constants using the given...

Hi PF! I'm calculating the added mass of a sphere accelerating in a fluid, which I found here: http://web.mit.edu/2.016/www/handouts/Added_Mass_Derivation_050916.pdf My thought process was slightly different from theirs, but I am not getting the same answer. My thoughts are to take the surface...

Homework Statement I did some homework and wolfram alpha afterwards gave different result than what I have. Apparently I must have done some error, but I couldn't find error after I doublechecked about two times. So I decided to see if you guys can find an error. And what is the correct answer...

Hello I am in middle on solving problem 17 from Chapter 3 of Spivak's Calculus. We have a function f(x), which is a non-zero function and it obeys the following properties. \forall \, x \, y \, [f(x+y) = f(x) + f(y)] \forall \,x \, y \, \left[f(x \cdot y) = f(x)\cdot f(y)\right] We have to...

Hi everybody! I'm currently studying Noether's theorem, but I'm a bit stuck around a stupid line of calculation for the variation of the symmetry. The script of my teacher says (roughly translated from German, equations left as he wrote them): "V.2. Noether Theorem How does the action change...

Hi PF! When proving ##\left(AB\right)^T = B^T A^T## I was thinking of writing ##\left(AB\right)_{ij} = A_{ik} B_{kj} = D_{ij}##. Then ##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect. Can someone tell me where my mistake is made? Thanks!

I've pondered at this problem for a long time, and I don't know where I make a mistake, can anyone give me a hint? 1. Homework Statement find a ##\delta## such that ##|f(x)-L|<\epsilon## for all x satisfying ##0<|x-a|<\delta## Homework Equations [/B] ##f(x)=x^4##; ##l=a^4##The Attempt at a...

Does he make a mistake at 6:18? In case of associativity. When doing a+(b+c) he's just placing the tip of a to the tail of (b+c), but shouldn't he have added the tail of a to the tip of (b+c) ending in a different point? I understand vector addition is associative, but I think how he did it is...

The video:

I have tried like 5 times to do this problem ans still don't get the answer I'm supposed to (A). Anybody finds mistake in my work below?

On page 97, Wald is computing the component ##G_{ii}## where ##1 \leq i \leq 3## of the Einstein tensor, assuming that the metric is given by ##g = -d\tau^2 + a^2(\tau)\big(dx^2 + dy^2 + dz^2)## where ##a## is the time evolution function. He writes: ##G_{ii} = R_{ii} - \frac{1}{2}R##. But if...

Homework Statement Hi. My professor asked me if I know to solve this limit and I tried doing it, however I didn't get the same answer as him. Question: What is the limit of (cos(x)*cos(2x)*cos(3x)*...*cos(nx)-1)/x^2 as x approches 0 Homework Equations / The Attempt at a Solution [/B] So to...

In Einstein’s book Relativity – the special and the general Theory (authorized translation by Robert W. Lawson, University of Sheffield) in chapter XI (the Lorentz Transformation), he gives us these formulas as the transforms: x’ = (x-vt)/sqr(1-(v^2/c^2)) y’ = y z’ = z t’ = t-(v/c^2) ∙x /...

Here is the deal: I got accepted into a PhD program, fully funded, stipend, and tuition waived. The PhD would be in an area outside my expertise, but I am ok with this because the area is interesting and something I want to study. As I am communicating with my advisor I am getting potential red...

Hello, here is some reasoning how I got possibility to communicate faster than light. Likely somewhere are mistakes, but I can not find them by myself. Let's consider very simple setup with observers Alice, Bob and a source of entangled photons in-between of them like so...

Homework Statement Find the moment of inertia of a spherical shell Homework EquationsThe Attempt at a Solution So I've been mulling over this for about two hours now and haven't figured out where I've made a mistake. Here's what I've done: I know I can do the integral by doing ##\int ^{r}...

Homework Statement [/B] This circuit solves some differential equation, the question is asking for the equation based on the circuit diagram imgur link: http://i.imgur.com/b1npQSK.pngHomework EquationsThe Attempt at a Solution I refer to the input terminal for -f(t)...the signal from it...

Homework Statement the equation is E= k((xy)x[hat] +(2yz)y[hat] +(3xz)z[hat]) Homework Equations partial of x with respect to y on the x component partial of y with respect to x on the y component The Attempt at a Solution my professor said during class that the partial of x with respect to y...

Find the Fourier sin series expansion of dirac delta function $\delta(x-a)$ in the half-interval (0,L), (0 < a < L): Now $b_n = \frac{1}{L} \int_0^L f(x)sin \frac{n \pi x}{L}dx $ - but L should be $\frac{L}{2}$ for this exercise... So I would get $ \frac{2}{L} \int_0^L f(x)sin \frac{n \pi...

Hi - frustratingly I get some problems right 1st time, others just defy me (Headbang) $f(x) = -x, [-\pi,0]; = x, [0,\pi]$ I get $a_0 = \pi$ and $a_n = \frac{-4}{\pi \left(2n-1\right)^2}$ which agrees with the book - but I thought I'd check $b_n$ for practice, it should = 0 according to the...

The working out states that v = (m/r)sin(theta) but surely this should be (-m/r)sin(theta) ? I mean there is a negative in front of the ∂Ψ/dx ? Also, if v=0 then 0 = (m/r)sin(theta), therefore sin(theta) = 0? And from this we know cos(theta) = 1 or -1 which would mean u = Uinfinity + (m/r) or...

Homework Statement y'' + 3y' + 2y = r(t), r(t) = u(t - 1) - u(t - 2), y(0) = y'(0) = 0. I need to solve this by convolution, which I know is commutative. The problem is that my calculation gives (f * g) =/= (g * f). Could someone please tell me where my mistake is? Homework Equations...

Homework Statement Two objects with equal masses undergo an elastic collision in 2 dimensions. Object 1 has an initial velocity u1 and object 2 is initially at rest. After the collision, object 1 is observed to have a velocity equal to 3/5 of it's initial velocity. What is the velocity of...

The question asks to proof that the limit given in incorrect by contradiction. I tried working using the estimation method and the weird thing is that I completed the proof and found that the supposedly "incorrect" limit gave a correct answer although it was supposed to give me a contradiction...

I found a mistake in one paper. It is not only a lapse, but it changes and anihilates meaning of the paper. How to publish this? In the same journal as a addenda, (because it can remark in short.)? Or it should be published as pa article in this or in another journal?

This is an example at the beginning of the section on the Fundamental Theorem for Line Integrals. 1. Homework Statement Find the work done by the gravitational field \vec{F}(\vec{x}) = -\frac{mMG}{|\vec{x}|^3}\vec{x} in moving a particle from the point (3,4,12) to (2,2,0) along a piece wise...

This is a solved example in the book 'Applied numerical methods with MATLAB by Chapra' A bungee jumper jumps off a cliff 200 m high with an upward velocity of 20 m/s. Detemine when he hits the ground and plot dist vs time and velocity vs time. The problem is solved in the book using MATLAB as...

Hello! On p.145 of Shankar's Principles of Quantum Mechanics, the author derives the general propagator for the Schrodinger equation in the following manner. Shankar's working Expanding the state vector in the energy basis, |\psi(t)\rangle = \sum_{E} |E\rangle \langle E| \psi(t) \rangle...

Homework Statement Find the volume of the solid. Under the paraboloid z = x^2 + y^2 and above the region bounded by y = x^2 and x = y^2 Well, those curves only intersects in the xy-plane at (0,0) and (1,1), and in the first Quadrant, and in that first Quadrant y = sqrt(x), and over that...

This is a screenshot from my lecture notes provided by my lecturer. He says theta=-30 and then proceeds to use a value of theta=60? Surely this is wrong?

Hello, On all my REU applications besides two or three, I was asked to describe my previous research. I did so, but I realized I referred to the hydrogen atom as the hydrogen molecule. I showed in the case of H2+ that we develop the standard potential energy curve for the hydrogen atom. I...

$$\int \frac{3x-4}{x(1-x)}dx$$ $$=\int \frac{-4}{x}dx-\int \frac{1}{1-x}dx$$ $$=-4\int \frac{1}{x}dx-\int\frac{1}{1-x}dx$$ $$=-4\ln\left | x \right |-\ln \left | 1-x \right |+c$$ $$\ln \frac{x^4}{\left | 1-x \right |}+c$$ But the correct answer is $$\ln \frac{\left | 1-x \right |}{x^4}+c$$...

In the section on approximation methods, the formula for the period of a simple pendulum of length ##L## is given by: $$T_0 = 2\pi \sqrt{\frac{g}{L}}$$ I am no expert on simple harmonic motion, but it is clear that the equation is dimensionally incorrect. The problem is, the power series used is...

So, during my second year, I took a course known as Physics Problem Solving which was an elective for me. I did very well in the course initially, but my girlfriend broke up with me which led me to a downward spiral of depression. I realized that the emotional stress along with the coursework...

$$\int_{0}^{1}\frac{1}{x-2}dx$$ $$=\left [ \ln\left | x-2 \right | \right ]_{0}^{1}$$ $$=\ln1-\ln2$$ $$-\ln2$$ But the answer given is $$\ln\frac{1}{2}$$. Am I wrong?

I'm a European student currently applying to a few grad schools in America. This year I am taking a gap year to travel through Asia (where I am now). A professor I recently happened to speak to (unrelated to the schools I applied to!) said two weeks ago that it should consider flying to the USA...

Homework Statement We have the circuit in the figure.I have to find the average power consumed by all the elements and the source. Homework Equations P=0.5*(I^2)*R P=-VmImcosθ/2 The Attempt at a Solution The inductor consumes zero inductive power. I apply nodal analysis at node Vo We have...

I am actually quite sure I have it right but my book would then be wrong so I have posted my problem here to see if I didn't do a embarassing mistake in arithmetics. Homework Statement "Show that the energy equivalent of the length 10-18cm of a large extra dimension is roughly 20TeV" -Zwiebach...