Addition Definition and 641 Threads

The additional law with two elements can be expressed $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$, while the law with three elements can be $$P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)$$ Now I wonder if there is the more general form of addition law, which applies...

i know its pretty basic but please give some insight for triangle law of vector addition and pythgoras theorem. becuase ofcourse if you use traingle law to find resultant it will be different from what is pythagoras theorem

im trying to complete mips program code about a calculator program that can calculate integer addition / subtraction written using the MIPS assembler. im having hard times to debug this. The input is given to the array of Formula char (base address $ s0) in the form of a formula. The null...

Any ideas?

I am 100% reading too much into this, but I am curious which of the properties provided by Spivak allow one to justify a specific argument. For reference/context, the properties are: P1: If a, b, and c are any numbers, then $$a +(b + c) = (a + b) +c$$ P2: If a is any number, then $$a + 0 = 0 +...

##\sum F_{X} = F - F_k## (The net force, ##\sum F_{X}## is always equal to m.a) ##ma = F - \mu_{k}.F_n## ##ma = F - \mu_{k}.(mg)## [Here ##F_n = mg## when body is on flat surface] ##20(a) = 150 - 0.25(20)(10)## ##\large a = \frac {150 - 0.25(20)(10)}{20}## ##\large a = 5\frac{m}{sec^2}##...

How can you prove that ##f(x)=g(x) \Leftrightarrow f(x)+C=g(x)+C##

How Dihalogens Catalyze Michael Addition Reactions. - NCBI What Michael Addition is about: https://en.wikipedia.org/wiki/Michael_reaction I do not know what the definition of 'piectron' is. In the abstract of the paper, I assume it is a misspell. Which makes me wonder? I learned about...

This post is meant to be a fun one. It is at the beginner level, because I think most people at the intermediate level would know what the solution is, but they might also find it entertaining as well. ## \\ ## A hypothetical situation: An algebra teacher observed that ## 3^2+4^2=5^2 ## and...

Can somebody please explain below ##F_{4k+4} = F_{4k+3} + F_{4k+2}## I thought it would be ##F_{4k+4} = F_{4k+3} +F_{4k+1}## Thanks!

tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y)tan(y-z)tan(z-x) I have redone this problem two or three times and all the steps just make my head spin. I've tried looking up tutorials online but they introduce things into the problem that we haven't been taught yet and that just confuses me more. Help!

Homework Statement Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that |u|=√2, |v|=√3, u is perpendicular to v, w=u×v. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ The Attempt at a Solution [/B] Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...

OK from the text bk I did not see any example of this the circle red is mine ... why is this here so not sure how these questions are to be answered. Much Mahalo

Homework Statement Shown is two binary numbers adding with the answer The Attempt at a Solution Looking at the end side 1.1+1.1, shouldn't that be 11.00... instead of 10.00...

Please see the attached page to see what I'm talking about. In the top right paragraph, it states to use "the positive direction of the x-axis". It is given that ##θ_2=30°## and it shown visually at the bottom of the page. In the problem it's using -60° and I'm not sure how they're getting that.

If given two variable of the form p=x±δx and q=y±δy where δx and δy are the error obtained while measuring p and q and x and y are it's absolute value obtained. We define R=p+q,p-q,p/q,pq In each of this case I want to know what will be the error in R.(e.g δR) Thank you

Suppose a spaceship is flying past me, an observer on earth, at .86c. A traveler on the ship has a ball which is attached to a string which is 100 feet long in the ship frame. The traveler grabs the string and throws the ball out of the front window of the ship at a speed of 100 feet per second...

Homework Statement I am reading through Griffiths' Electrodynamics, and I have come to the scenario in the Relativity chapter where in an inertial reference frame ##S##, we have a wire, with positive charges (linear density ##\lambda##) moving to the right at speed ##v##, and negative charges...

I was reading an old thread about multiplying successive prime numbers adding 1 to obtain another prime number. I have worked with prime numbers for several years now and have developed what I best call a bi-linear advancement. It is an open-ended sieve of Eratosthenes. After many, many hours...

Homework Statement Determine whether there exist ##A## and ##B## such that: $$\frac{1}{3x^2-5x-2} = \frac{A}{3x+1} + \frac{B}{x-2}$$Homework Equations None The Attempt at a Solution [/B] First I divided the polynomial ##3x^2-5x-2## by ##3x+1## and got ##x-2## as a result without a...

Homework Statement Give an example of the associative property of vector addition using vectors in Cartesion form. Homework Equations (u+v)+w=u+(v+w) The Attempt at a Solution I can't figure out how to get the arrow on top of my work so I wrote it without it. I'm somewhat confused on why I...

Dear Everyone, I have some feeling some uncertainty proving one of the axioms for a group. Here is the proof to show this is a group: Let the set T be defined as a set of 2x2 square matrices with coefficients of integral values and all the entries are the same. We want to show that T is an...

Homework Statement "A bird flew 40 m to the west, then 100 m in a direction 36.9 degrees to the north of east. Use the algebraic addition of vectors to fins the magnitude of the bird's net displacement" Use sin (36.9) =0.6 and cos (36.9) = 0.8 Homework Equations Vector addition? A =...

Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? Homework EquationsThe Attempt at a Solution I tried using the dot product and solving for the angle but i...

Hello, Could someone help me find a general derivation of the formula for addition of capacitance of conductors? I'm hoping to find something that could be applied to a general assortment of conductors, not just parallel plate capacitors. I look forward to your response, Pete

aa3.2 Let Q be the group of rational numbers under addition and let $Q^∗$ be the group of nonzero rational numbers under multiplication. In $Q$, list the elements in $\langle\frac{1}{2} \rangle$, In ${Q^∗}$ list elements in $\langle\frac{1}{2}\rangle $ ok just had time to post and clueless

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis. When I find their Components trigonometrically, I get 70N each; as Fx = 100xCos(45) = 70N Fy = 100xSin(45) = 70N Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N. Why is there discrepancy or where am I...

I know that n-body problem can be complicated, but that's for the dynamics. What about a static case: e.g. if I have the distances of several bodies A, B and C etc. and their distance to a reference mass m, can I just use the vector addition of the Newton's gravitational force to add up all of...

To whom it may concern, I am having issues with a given assignment in my quantum mechanics class. The instructions listed below are all I have to go on since the prof. is not available for discussion and I have searched through at least 15 articles regarding plane waves and a dozen textbooks...

Homework Statement Hello, I am currently studying mathematics and physics on my own, and I ran into a type of problem in physics that is a bit unclear to me. Say we have pulley at the top of an inclined plane with a base angle of alpha and the top angle is alpha. Homework Equations I assume...

Observer A measures B moving east at .8c and measures C moving west at .8c . Then wouldn't the impact of the two will be a result of relative motion greater than c in frame A. I understand B and C frame will not see any object speed greater than c. So the impact in frame A and frame B will not...

Homework Statement ##f(x)=\sum_{n=0}^\infty x^n## ##g(x)=\sum_{n=253}^\infty x^n## The radius of convergence of both is 1. ## \lim_{N \rightarrow +\infty} \sum_{n=0}^N x^n - \sum_{n=253}^N x^n## 2. The attempt at a solution I got: ## \frac {x^{253}} {x-1}+\frac 1 {1-x}## for ##|x| \lt 1##...

Homework Statement Two spaceships pass each other. Spaceship A moves relative to nearby planet at velocity v1 , while spaceship B moves at velocity v2 relative to the planet . How fast does spaceship A moves relative to spaceship B. Homework Equations Velocity Transformation : v* =...

Homework Statement Given the following diagram, use vector addition to sketch the resultants: a) u→−2v→ b) 3v→−u→ Homework EquationsThe Attempt at a Solution For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some...

Homework Statement Can you partition the positive integers in such a way that if x, y are member of A, then x+y is not a member of A. x and y have to be distinct. That is, {1, 2, 3} cannot be in the same set, since 1+2 = 3, but 1 and 2 can be, since 1+1=2, but 1 and 1 are not distinct...

Homework Statement I have an exam on vectors and 2 dimensional motion today. I NEED to know if it is possible to solve any GRAPHICAL VECTOR PROBLEM using only INTEGRATION AND MATH WITHOUT ADDING VECTORS TOGETHER GRAPHICALLY. So given any word problem that is supposed to be solved using that...

Homework Statement Say you have a fn FoG = x+2/x+1 + x+1/x+2 if x = -1, the first one is undefined. But the second one would end up as 0, a real number I'm trying to understand, would x = -1 make the whole term FoG undefined? because only x+2/x+1 would be undefined, x+1/x+2 would be =...

Good evening, If a ship is moving at 0.5C east in a gravity free environment, and fires a bullet perpendicular at 0.5c, is it just the hypotenuse (a squared + b squared)/c squared that we use for the speed? Or is there more to it since we are at great speed?

Homework Statement Homework EquationsThe Attempt at a Solution I tried to rationalize the fractions by multiplied it by $$\sqrt{n + 1} - \sqrt{n} $$ it will be sum of $$ \frac {\sqrt{n + 1} - \sqrt{n}} {2n +1} $$ also tried to see the arithmetic structure $$ 1 + \frac{1}{\sqrt{2} +...

Hello everyone, For some time I'm a little bit confused about (at the first view) a very simple question, which is about the conversation of the energy of moving objects (in terms of special relativity). As an example let's talk about firearms. If the mass of the gun M1 is infinitely higher...

Homework Statement Given 3 spins, #1 and #3 are spin-1/2 and #2 is spin-1. The particles have spin operators ## \vec{S}_i, i=1,2,3 ##. The particles are fixed in space. Let ## \vec{S} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3 ## be the total spin operator for the particles. (ii) Find the eigenvalues...

Homework Statement Write a chemical equation for addition reactions to produce 3-methyl-3-hexanol. Condensed structural formulas should be used for each organic compound.Homework Equations none The Attempt at a Solution https://i.imgur.com/REIpKHK.jpg Is this correct? My friend tried...

If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c. The relevant formula is: u_y = u_y'/(gamma * [1+v u_x' / c^2]) Apologies for formatting. Details: gamma = 1/sqrt(1-v^2/c^2)...

Homework Statement Two snowcats in Antarctica are towing a housing unit north, (an example is shown in Figure 4-50 on page 102). Snowcat A pulls at an angle 49 o west of north, and snow cat B pulls at an angle 31 o east of north. The sum of the forces FA and FB exerted on the unit by the...

Homework Statement Express the following in the form x = Re{Aeiαeiωt} (a) x= cos(ωt) + sin(wt) (b) x= sin(ωt +π/4) + cos(ωt) (c) x= 2cos(ωt+π/3) + (√3)sin(ωt)-cos(ωt) Homework Equations cos x = 1/2 e^ix + 1/2 e^-ix sin x = − i/ 2e^ix + i/2 e^−ix The Attempt at a Solution To be honest, I have...

Do we have any proof to show that we can represent the addition of two vectors like this, i mean do we have proof for triangle law of vector addition(or its a law that is why we can't have its proof, then please give me a satisfying reason for this)

Just out of curiosity, what would a proof of ##a^m a^n = a^{m+n}## amount to? Of course obviously if you have n of one thing and m of another you get m+n, but I am wondering if this is rigorous enough, or if you need induction.

Homework Statement Find the coordinates for the center of mass in the picture above. Plate is uniform.Homework Equations Since it's uniform, the lengths can be converted to the mass. So: coord x =(M1X1 +M2X2 + M3X3 + ... +MiXi)/(M1 +M2 + M3 + ... +Mi) coord y =(M1Y1 +M2Y2 + M3Y3 + ...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.7 (1) ... Theorem 1.2.7 reads as follows: https://www.physicsforums.com/attachments/6976...

This is the problem I'm trying to understand: Consider two particles with spin 1 without orbital angular momentum. If they are distinguishable, from the rule of addition of angular momentum applied to spin, we'll have states of total spin j=0,1,2. If we have, however, identical particles which...