Mistake Definition and 296 Threads

Integration in the order of dy then dx: $$\int_{-1}^{1} \int_{0}^{1-x^2} x^2 \sqrt{1-y} ~dy~dx$$ $$=\int_{-1}^{1} -x^2 \left[\frac{2}{3} (1-y)^{\frac{3}{2}}\right]_{0}^{1-x^2}dx$$ $$=\int_{-1}^{1}\left(-\frac{2}{3}x^5 + \frac{2}{3} x^2\right)dx$$ $$=\left. -\frac{1}{9} x^6 + \frac{2}{9}...

Ha. Half-assed is usually an adjective or adverb. From now on I'm skipping past the half-assed efforts of Oxford Languages. They must be paying someone to uprate their stuff.

This is from Feynman's lectures: https://www.feynmanlectures.caltech.edu/II_26.html Should the (b) say F1=q1E2 and F2=q2E1?

Sorry if there are mistakes regarding the post itself, this is my first time posting. This an easy problem to solve, but this isn't what I'm looking for, but first of all, you can plug in the values and solve for ##\omega##, and it equals ##\frac{170 V}{0.87 T(0.0300 m^2)}## = 6513 Hz, my...

The question My Working:

My answer is (D) but the correct answer is (B). I thought the intensity will be 4 times since the slit width is doubled and amplitude becomes twice. What is my mistake? Thanks

Here's the problem: ##\int_0^{2\pi} \cos^{-1}(\sin(x)) \mathrm{d}x## If I do the substitution ##u = \sin(x)##, both the limits of integration become 0 and the integral would result in 0. But the graph of the function tells me the area isn't 0. Where am I going wrong?

$$K'_{ij}A'_{jk}=B'_{ik}=a_{ip}a_{kq}B_{pq}=a_{ip}a_{kq}K_{pr}A_{rq}=a_{ip}a_{kq}K_{pr}a_{jr}a_{kq}A'_{jk}$$$$K'_{ij}=a_{ip}a_{kq}a_{kq}a_{jr}K_{pr}$$ Can someone point out my mistake? What I've found shows that K is not a tensor. It is different from my book and I cannot find my mistake...

##P^5_0=\frac{5!}{(5-0)!}=1## But when I use ##P^n_r=n(n-1)...(n-r+1)##, I get ##P^5_0=5(4)...(6)## Where is the mistake? Thanks

The answer is (D), but I don't understand why. Option (A) is wrong because the work done = 0. Then, I divide the motion into 3 parts: 1) motion on snowy surface Since the sledge is being pulled horizontally (let assume to the right), there will be tension force T to the right and friction...

TL;DR Summary: I want to mainly figure out where in the problem solving I went wrong. I understand the correct answer (since I looked it up), but to me, it does not make any sense. I am honestly stumped at this point. Online solutions say that my equation y = 0.5774x-0.003354x^2 should...

I divide the question into three cases: 1) P (Y = 1 and X = 5 or 7) = 1/5 + 1/5 = 2/5 2) P(Y = 2 and 1st spin = even and 2nd spin = 7) = 2/5 x 1/5 = 2/25 3) P(Y = 3 and 1st and 2nd spin = even and 3rd spin = 7) = 2/5 x 2/5 x 1/5 = 2/125 Total probability = 2/5 + 2/25 + 2/125 = 62/125 But...

[FONT=times new roman]Problem Statement : Solve the inequality : ##\left( \dfrac{1}{3} \right)^x<9##. Attempts: I copy and paste my attempt below using Autodesk Sketchbook##^{\circledR}##. The two attempts are shown in colours black and blue. Issue : On checking, the first attempt in black...

What can I do so as to never make a mistake regarding the object of a verb, that is whether the verb will take an object or not (transitive/intransitive) and if it takes then how many are allowed? Learning all the verbs in each category doesn’t seem to be a very good idea. General knowledge...

Hi everyone To solve the below problem, I assumed the affected area was 2x2 minus the definite integral of the given function between 2 and 4. I then equated the answer for that with the given function to solve for a, b and c. I don't know why the solutions give b as 2ln5. Have I made a...

Long story short, my career goals are to work as a researcher/research scientist in machine learning or to develop models/algorithms for forecasting such as in financial markets or otherwise. Fundamentally, I find think this is quite similar to physics as a science, but that is for another...

Recently I saw this YouTube video from Veritassium about CPT -Symmetry: In this video an experiment of Prof. Chien-Shiung Wu is presented, which has proven that parity is not symmetric, by observing the emmition of electrons from Co60 atoms with synchronised spin. After thinking about this...

it was a situation that would have led to me getting some of the money back (i.e., I paid too much that year)? I know if you paid too little, the IRS would want you to correct it obviously, so they can rake in that $. But, what if you made an error and should have paid less that year? Would...

Hello everyone, Once I got through the VDW state equation I came to the expression of the thermal expansion coefficient. When I place the values I get an illogical answer. Is there a problem with the units? (Please ignore the values) Thanks. This is the unit equation I get to and get stuck:

In the last step of the derivation of escape velocity, the two sides of the equation seem to have opposite signs. $$-1/2mv_0^2=-mgR_e^2\,\lim_{r\to\infty}(1/r-1/R_e)$$ $$-1/2mv_0^2=mgR_e^2 \frac{1}{R_e}$$ Since the mass and the square of the velocity are positive, the left side of the equation...

Find the acceleration of block A and B, given that the mass of pulleys and strings are negligible.. I could see that the block B has gravity acting on it, therefore the gravitational force on the block ##B## is ##F_B = 5 g## and hence the acceleration is ##g##. From the pulley to which...

This is my sketch: I think the only possible way to get emergent beam perpendicular to AB is when the incoming ray is refracted towards side AC then total internal reflection occurs as shown in my sketch. Angle QAR = 60o and angle ARQ = 90o so angle AQR = 30o It means angle CQP is also 30o...

I literally don't know what's going wrong today, I can't seem to get anything right :oldconfused:. The velocity in S' is easy enough $$v' = \frac{dx'}{dt'} = \frac{\partial f}{\partial t} \frac{\partial t}{\partial t'} + \frac{\partial f}{\partial x}\frac{\partial x}{\partial t}\frac{\partial...

Is it just me, or is the statement simply untrue? I have created a simple counterexample that is consistent with the hypotheses, but results in a contradiction of the result. It is included in pictorial form as the second attachment. Any insights?

I tried to substitution n = infinity so I got (infinity)*sin (1/infinity). I thought 1/infinity is approaching zero. So, sin (1/infinity) is same with sin (0). With these idea, my solution is lim n--> infinity n sin(1/n) = 0. But, the answer book say that the answer is 1. I tried another...

The steps are as follows (apologies for my awful formatting, I'm not sure which Chemistry latex package there is!), $$(CH_3)_2CO \xrightarrow{HCN} (CH_3)_2C(OH)CN \xrightarrow{H_2SO_4} (CH_3)_2C(OH)COOH \xrightarrow{PCl_5} (CH_3)_2C(OH)COCl \xrightarrow{NH_3} (CH_3)_2C(OH)CONH_2$$ As far as I...

"Mad Mike" Hughes wanted to see for himself if the Earth was a sphere or flat. Went up in a rocket, when it failed, he ejected without his parachute and died in the fall. https://www.polygraph.info/a/flat-earth-believer-mad-mike-hughes-dies-in-diy-rocket-crash/30454704.html Just think how...

They write the following on page 646: Now, equation (17.17) reads: ##\alpha_s(Q) = \frac{2\pi}{b_0 \log(Q/\Lambda)}##, so if I plug ##\alpha_s(Q^2) = \frac{2\pi}{b_0 \log(Q^2/\Lambda)}## into Eq. (18.204) I get: ##\frac{a^f_n}{4b_0}\frac{1}{\log(Q^2/\Lambda)}M^-_{fn}##. Perhaps the...

I've been reading this interesting thesis recently posted. But I think I spotted a mistake. On page 52 of "Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity": https://arxiv.org/pdf/2001.04651.pdf It says "In general, removing ##k## vertices from ##[v_0, v_1, ...

Hello, so there's a graph provided in the task which I'm trying to solve for a quite a while and I am really confused where the 5 to 8 line came from, because (5x+8y<5) doesn't create that sort of line. Is it possible that there's a misstake done by my teacher or am I understanding something wrong?

I've tried to carry out the solution to this as a normal 2nd order Differential Equation ##\psi ##'' - ##-k^2 \psi ## = 0 Assume solution has form ##e^{\gamma x}## sub this in form ##\psi## and get ##\gamma ^2## ##e^{\gamma x} ## + ##k^2 e^{\gamma x}## = 0 Solution is ##\gamma## = 0 or ##k^2##...

I have a pendulum and an object with radius "R" and mass "m". There are forces: constant gravitational acceleration and tension on the rope. I can write: $$x=R sin(\theta) \ \ y=R cos(\theta)$$ $$\dot{x}=R\dot{\theta}cos(\theta) \ \ \dot{y}=-R\dot{\theta}sin(\theta)$$...

That's what I found. But the answer is arctan(sinθ*sqrt(1-v^2/c^2)/(cosθ+v/c))

In "The Theoretical Minimum" (the one on classical mechanics), on page 218, the authors write a Lagrangian $$L=\frac m 2 (\dot r^2 +r^2\dot \theta ^2)+\frac {GMm} r$$ They then apply the Euler-Lagrange equation ##\frac d {dt}\frac {dL} {d\dot r}=\frac {dL} {dr}## (I know there should be...

Schaum's Outline of Group Theory, Section 3.6e defines {{\rm{L}}_n}\left( {V,F} \right) as the set of all one to one linear transformations of V, the vector space of dimension n over field F. It then says "{{\rm{L}}_n}\left( {V,F} \right) \subseteq {S_V}, clearly". ({S_V} here means the set...

Solving using Linear Momentum: M vb2/2 = M g 2L vb = 2√(g L) m v = m v/2 + M (2√(g L) ) v = 4 M √(g L) / m Note: I see from the answers - that this is correct. -------------- Next, I tried to solve it via Energy conservation point of view. M vb2/2 = M g 2L vb = 2√(g L) m v2/2 = m v2/8 + k...

Homework Statement This is the problem from the book "physics for scientists and engineers..." by Serway, Jewett / Chapter 5, problem 98 Initially, the system of objects shown in Figure P5.93 - is held motionless. The pulley and all surfaces and wheels are frictionless. Let the force F be...

Hey there! I was recently pointed to this thought experiment, claiming an apparent 'contradiction' involving the various predictions of the observers. Now, this has been discussed on PF quite recently, but I found the discussion rather hard to follow. I've read the paper, the PF discussion...

Homework Statement A cylinder with a mass of M and radius R is attached to a spring with a constant of k. The attachment always stays the same as described in the picture. The cylinder is moved to the right and the released, and it rolls without slipping (pure rolling). What will be the...

Homework Statement Suppose ##R## and ##S## are relations on a set ##A##. If ##R## and ##S## are transitive, is ##R \cup S## transitive? Why? Homework EquationsThe Attempt at a Solution Suppose that ##a## is an arbitrarily but particularly picked element of ##R \cup S##, then $$a \in R \...

The question provides the vector field (xy, 2yz, 3zx) and asks me to confirm Stokes' theorem (the vector calc version) but I am trying to use the generalized differential forms version. So, I am trying to integrate \omega = xy\,dx + 2yz\,dy + 3zx\,dz along the following triangular boundary...

Homework Statement This graph was given, which describes the current through a resistor, as a function of the voltage. Then, we were supposed to find the resistance of the resistor when 3V<V<5V. But it changes throughout this range, doesn't it? Because in the answers (Mind you, this is the...

I am sure I am overlooking something elementary, but playing around with exponentiation (this is not an assignment), I seem to be making a mistake somewhere. Please don't send me a link for a more compact way of getting the correct result; I wish to know what my particular mistake is. Suppose...

The patent in Russia being operated on for ovarian cysts had a formalin (37% formaldehyde solution) mistakenly introduced into her abdomen. It was washed out when the mistake was recognized, but ultimately, too late. Formaldehyde is used for many things, in biology it is often used to fix...

Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...

The image is below. My question is, why he considers ##p' = p## on the RHS of ##(2.5.14)## but not on the LHS, i.e., the sub index on the left ##\Psi## remains ##p'##. Is it a mistake? And he continues on the derivation (not shown here) even considering ##|N(p)|^2## instead of ##N(p')^*N(p)## so...

Rule: Suppose a>0, then |x|>a if and only if x>a OR x<-a So |x|>|x-1| becomes: x>x-1 which is false (edit: or more accurately doesn't give the whole picture, it implies true for all x) OR x<-x+1 2x<1 x<1/2 which is false

The following is kind of a semiclassical reasoning which goes along the style of the discussions between Bohr and Einstein in Solvay Conference. Suppose we have a single slit from which a particle may be emitted and, on a very large distance from it, a thin cloud chamber CC, which we use as a...

I was thinking and came up with this. I know it's wrong but can't find the mistake :( dy/dx sin(x) = cos(x) dy/dx sin(kx) = kcos(kx) So dy/dx sin(3x) = 3cos(3x) Now let Y = 3x dy/dx sin(Y) = cos(Y) = cos(3x) 3cos(3x) = cos(3x) 3 = 1 Where is the mistake?

Homework Statement The residents of a small planet have bored a hole straight through its center as part of a communications system. The hole has been filled with a tube and the air has been pumped out of the tube to virtually eliminate friction. Messages are passed back and forth by dropping...