Addition Definition and 641 Threads

Relevant Rules: N5: -(a+b) = - a - b N4: a = -(-a) N2: a + (-a) = 0 and -a + a = 0 I tried just manipulating -(a - b) with the rules to get the answer: -(a - b) = -(a + (-b)) With N5: = - a + (-(-b)) With N4: = - a + b Commutativity: b - a The provided solution in the book used N2 to prove it...

Can mathematics rest on new foundations? See the attachment. a little explanation about the form of addition adding or joining , as performed R a+b=c same as now, combined numbers 222+33=2253, when they are the same along (gap) they are joined, here 2 and 3, we get 5 R2 here there is an...

I can show that ##f(x) \ge 0## but I can not show ##f(x) \ne 0## ##x=y=t/2## then ##f(t) =f^2(t/2)\ge 0##

Is angle Vag 180 since the vector is a straight line pointing left? Also you can add 30 degrees with 150 which will be 180?

I am going through https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf, here I don't understand how we wrote eq. 1.5.3 with the help of three-vectors to get eq. 1.5.4.

This is a really basic stupid question but has me beat. I am almost certainly missing something but for the life of me cat see what. If A and B are are the lower sets of two Dedekind cuts addition is defined as the sum of the elements (r+s) with r in A and s in B. Is that correct or have I...

For every instance of addition or multiplication there is an inverse, closed on the naturals. Not every instance of subtraction and division is defined, so not closed on the naturals. This looks like two kinds of inverse. Instance inverse - the inverse of instances of addition and...

(a) $$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$ Unit Vector Formula $$\hat a_A=\frac{26\hat a_x+10\hat a_y+4\hat a_z}{\sqrt {26^2+10^2+4^2}}$$ $$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$ The book gives ##0.92\hat a_x+0.36\hat a_y+0.4\hat a_z## Not sure how the book get 0.4 for...

The screw eye is subjected to two forces, F1 and F2. Determine the magnitude and direction of the resultant force.

The solution (green arrow) states that for example : 0xD + 0x9 = 0x16 Details : 0xD = 13, 0x9 = 9, 13 + 9 = 22, 22 = 0x16 Where does the 0x16 come from? I do get to add D + 9 = 13 + 19 = 22 so how come 22 is equal to 16 (assuming D + 9 = 16 is correct) How am I suppose this solution?

I was watching this video by Brian Green about relativistic velocity addition when he said something at the end that I wondered about. https://www.britannica.com/video/222286/Your-Daily-Equation-07-Relativistic-Velocity-Combination It was along the lines of the formula will always result in...

https://www.networkdls.com//Articles/AESbyExample.pdf I'm confused because there are lots of XOR in this case. And I am not very technically aware when we'd XOR vs when we'd add. I just follow the guidelines given in standards. But here I got confused in page 9 of that pdf. When we do B7+4B...

Hello friends. Excuse my ignorance. Why is addition linear and not multiplication?

We had a thread a while ago where a poster was particularly interested in the SR rule of velocity addition. And in that thread, I suggested a better foundation was the k-calculus approach, with a reference to Bondi's treatment in "Relativity and Common Sense". Here I would like to show how to...

From the top of my head, I would say that yes, the very moment our clocks are aligned, and the two bullets are launched it is perfectly ok to use the relativistic velocity addition formula to determine the speed of the bullets from my reference frame. But the more the disk keeps rotating, the...

If we imagine launching an electron wave in a reference frame S with speed v, should someone viewing the electron from frame S1, which is in inertial motion referring to S, use the relativistic velocity addition to calculate the speed of the electron?

I kind of just made up the questions. I realize this is a basic question but my knowledge of physics is very limited.q1 answer v_left_ball = v_left_ball - v_train v_right_ball = v_right_ball + v_train q2 answer To get the speed from Bob's frame I would use v_Bob = v_Bob + v_Alice To get the...

Hi, I have a question regarding these 2 possibilities: Why does the addition of RMgX on an ester always form a ketone? We could very well have that tetrahedral intermediate without eliminating the alcoolate group no? Since your reaction pretty much always tend towards the formation of a weaker...

Adopt the speed of light equals one. Calls ##cos = c##, ##sin = s## $$ux' = \frac{v-uc}{1-uvc}$$ $$uy' = \frac{us}{\gamma(1-uvc)}$$ $$tan \theta' = uy' / ux' = \frac{us}{\gamma(v-uc)}$$ So that's basically my solution. The problem is: The answer is ##\frac{us}{\gamma(v+uc)}##. Now, i can't...

The definitions of them seem like arbitrary choices or an abuse of notation. I wonder what the reasons behind the definitions are. Thanks. PS. My instructor said such defs simplify the process of solving modular equations.

Hello, guys. Interesting riddle here. I have no idea how to solve it. Tried different methods, but point is answer is always wrong, exact answer Downriver, at an angle of 53.13(degree) to the bank. That exercise is from "Pohl’s Introduction to Physics"

I am following along with an example in my book regarding force from an electric charge. I understand the process but I believe I am getting something wrong when it comes to adding the vectors. Essentially, F13 is equal to -1.35*10^-3 j and when I add that to the j component of F23 which is...

edit: I had a sign error that is now corrected, no further help needed. Consider in the laboratory frame one second passing. Let ##(t,x)## be the coordinates of various events in a spacetime diagram. Both particles are released at ##(0,0)## Then after one second the left moving particle is at...

Something seems wrong with my use of velocity addition: A fly of rest mass ## m_{0} ## in your reference frame (say a platform) is posed in a train passing with a velocity ## v ## relative to the platform. The fly mass is now for you ## m_{1} = m_{0} \gamma(v) ##. Now in the train the fly is...

So for the formula, u'=u/(δ(1-(uv)/c^2) u=2.06E8 and v=0. I am only looking at the y components here. Since v=0 it really becomes u'=u/δ or u'= u*sqrt(1-(u^2)/c^2)). Anyways when I plug this in I am getting 1.49E8 when the answer should be 0.951E8. Am I not using the correct formula here?

A new meteorite into my collection from Roberto Vargas (USA) - The Indonesian Punggur, first fall for 2021 (Jan 28) 1.2g of awesomeness, high iron breccia Thanks so much buddy, much appreciated

The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...

Velocity addition paradox: In observer A's frame, observers B and C move away from him at the speed of light c, B to the left and C to the right. In B's, frame A and C are both moving away from him at c, i.e. at the same speed. In both A's and C's frames they are moving at different speeds...

The Doppler effect of light corresponds to the classical Doppler effect corrected by time dilation, but the first one is obtained with classical velocity additions (c+v at the front of the source and c-v at the back) whereas velocity addition of special relativity gives c at the front and c at...

What if any is the experimental confirmation for length contraction and the velocity addition formula?

I want it to be able to add vectors of different length with a 'shift' of c, and where elements do not align to assume a zero in the place of that, My function is: %c is the parameter shift function[sum]=vecadd(y,b,c) p=length(input) q=length(a) if p > q for i= 1+delay:p+delay...

Doing a review for my SAT Physics test and I'm practicing vectors. However, I am lost on this problem I know I need to use trigonometry to get the lengths then use c^2=a^2+b^2. But I need help going about this.

Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...

Hello all : i am asking if there is a class of respiratory protective equipment , that can be installed inside the human body to support the normal PPE and reduce the possibility to getting infected buy some biological agent : as virus size is between 50 to 160 nm , and the first area of...

Hi To calculate the moment of inertia of a large sphere , I can calculate I for a smaller sphere and then add to it , I for the spherical shell that added to the smaller sphere makes the larger sphere. Does this general process apply to all shapes ? If so , does this process have a name ie. is...

So I have figured out two equations model a Ferris wheel ride(two different ferris wheels). F1 = Ferris wheel one F2= Ferris wheel two F1, $$h=-12\cos\frac{\pi}{10}t+12.5$$ F2, $$h=-12\cos\frac{\pi}{30}t+15$$ Now from these two equations, I want to know when F2+F1= 27.5m i.e I want to find...

The expansion equation of the universe be ##\dot{R} = f(R)##. There shall be a photon at distance ##x## from us moving directly towards us along the line of sight. Are the velocities to be simply added, so the photon has speed ##f(x) -1## relative to us (local velocity of light set unity)? This...

Now following is my attempt for the very first one. Let ##\arctan(x) = \alpha## and ## \arctan(y) = \beta ##. So, I have ## x = \tan(\alpha)## and ##y = \tan(\beta)##. Since the domain is restricted to define inverse function, I have that ##\alpha \in (-\pi/2, \pi/2) ## and ##\beta \in (-\pi/2...

I keep getting into these discussions and finding out they are not as simple as I thought. Or at least, my math is rusty. Scenario A: Two ships are each receding from Earth at .9c in opposite directions. Since these are velocities, they should have opposite signs. That can't be right, since...

I was looking at some websites that show the proof of addition of limits for a finite output value, but I don't see one for the case of infinite output value, which has a different condition that needs to be met - i.e., | f( x ) | > M instead of | f( x ) - L | < ε...

First of all, sorry for the units. This is a problem I found on the internet and am confused about the solution. I calculated the two components of the moment (torque) to be ##T_x = 18\times Fcos(30)## and ##T_y=5\times Fsin(30)## The problem is, I got the proper answer (the two options...

Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...

Determine the value of $$\frac13+\frac16+\frac1{10}+\frac1{15}+\frac1{21}+...+\frac1{231}$$ I know that it means $$\frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\frac1{1+2+3+4+5}+\frac1{1+2+3+4+5+6}+...+\frac1{231}$$, but how do I answer? It's from a student worksheet for 7th graders, so they...

Hi gentlemen. My model is simple. Imagine, I watch a body which approaches me with velocity of w which value I can measure . I know that this a body has velocity v in a some reference system which aproaches me with same velocity of v. This velocity needs to be calculated (I can not mesure it)...

In basic optics, we are given the general solution of the wave equation (massless string of length L) as a linear combination of normal modes, that need to have some of the permitted frequencies due to boundary conditions. In laboratory, we observed that phenomenon. We generated a wave in a...

I used the two equations above to solve for u_x and u_y and got u = 0.987c, where u_parallel = u_x and u_perpen = u_y. I wonder if I can use velocity four-vectors to solve this problem. Modify η'μ = Λμνην so we can use it for velocity addition?

Trying to solve it