Addition Definition and 651 Threads

A plane, traveling with a velocity relative to the air of 320km/h [28 S of W], passes over Winnipeg. The wind velocity is 72km/h [s]. Determine the displacement of the plane from Winnipeg 2.0 h later. Cosine Law -> c^2 = b^2 + a^2 - 2*b*a*Cos<C Sine Law- (Sin<A)/a = (Sin<B)/b = (Sin<C)/c...

The problem I'm trying to solve involves the effect that two charges has on a third and I need to find the magnitude of the resulting force. In this particular problem it's the effect of A and B on C. The work I've done so far is attached so please take a look. I've been trying to add...

[SOLVED] Addition of Spin 1/2 Homework Statement A system is composed of two spin 1/2. The system's hamiltonian is H=w_1 S_1z + w_2 S_2z. The initial state of the system is, at t=0, | \psi (0) > = \frac{1}{\sqrt(2)}[|+ -> + |-+>] . a) At time t, we measure S^2 = (S1+S2)^2 What...

Homework Statement Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4? 1. The two pairs of expressions give the same length and direction for C_vec. 2. The two pairs of...

Homework Statement Two positive charges = = 2.0 are located at = 0, = 0.30 and = 0, = -0.30 , respectively. Third point charge = 4.0 is located at = 0.40 , = 0.What is the net force ((a)magnitude and (b)direction) on charge exerted by the other two charges? Homework Equations Columbs...

To jump from a single celled organism to a multicellular one, we need beneficial addition mutations in DNA sequences. My question is this: has this phenomena ever been observed? By beneficial I mean a mutation in the genotype that serves to cause some phenotype that can be used by an organism...

We all know BEDMAS from grade school: brackets, exponents, division, multiplication, addition, subtraction. My question is, why does multiplication precede addition, and likewise their inverse operations?

[SOLVED] pH of solution Homework Statement What is the pH of a solution in which 30.0mL of 0.010 M NaOH are added to 10.0mL of .010 M H2SO4? Homework Equations The Attempt at a Solution So first thing I did was write the equation. 2NaOH + H2SO4 ----> Na2SO4 + 2H2O I never...

For two phasors a and b, with magnitudes of A,B respectively and phase angles of \phi_{a) and \phi_{b}, the angle of the sum of the phasors (call it p) has a magnitude of: P^{2} = A^{2} + B^{2} , and a phase angle of: \phi_{p} = -tan^{-1}(\frac{B}{A}) The magnitude identity makes...

a. 2cm N + cm W b. 5m S+ 8cm N c. 30m/s W+ 50m/s S d. 5cm N + 7cm W +9cm S My answers: a.7.2 b.9.43 c.58 d.? I want to know if a,b, and c are right; I don't know d.

Homework Statement A 5.0 Kg block at rest on a frictionless surface is acted on by forces F1= 5.5N and F2= 3.5N, as illustrated in the figure. A) What additional force (in unit vector notation) is required to keep the block at rest? B) What additional force (in unit vector notation) is...

Homework Statement 27 drops of salt water with same radius, are each charged to a potential of V volts. They are made to coalesce into a single drop. How is the potential of a new drop compared to the potential of the original drops. Homework Equations V ( potential ) = k* q/r...

I don't understand this, can someone help?: What is an example of a subset of R^2 which is closed under vector addition and taking additive inverses which is not a subspace of R^2? R, in this question, is the real numbers. Thanks!

Homework Statement Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication Homework Equations The book says this holds for addition but fails for scalar multiplication. The Attempt at a Solution Im a little confused. You can...

rather than use the standard definitons of addition and scalar multiplication in R^2, suppose these two operations are defined as follows. (x1,y1)+(x2,y2)=(x1,0) c(x,y)=(cx,y) what would the zero vector be? can it be (0,-y1)? why or why not? I think it should fail this axiom u+0=u.

Homework Statement Given: \vec{A}=(6.0\hat{i} - 8.0\hat{j}) \vec{B}=(-8.0\hat{i} + 3.0\hat{j}) \vec{C}=(26.0\hat{i} + 19.0\hat{j}) If aA+bB+C=0, what are the magnitudes of a and b? Homework Equations The Attempt at a Solution a(6.0\hat{i} - 8.0\hat{j}) + b(-8.0\hat{i} +...

Homework Statement I am not sure where I am having trouble here. A car id driven 125km west and then 95km southwest. What is the mag and direction of displacement?Homework Equations Triangle method says that if I draw the vectors from tip to tail, the displacement vector is the vector that...

[SOLVED] Vector addition ]Homework Statement (a) Express the vectors A, B, and C in the figure below in terms of unit vectors. (b) Use unit vector notation to find the vectors R = A + B + C and S = C – A – B. (c) What are the magnitude and directions of vectors R and S? Homework...

vector A= (2,-1,1) vec. B = ( 3, 0, 5) vec. C = (1,4,-2) what is 2A + 3(B+C) this is what i did: 2A = 2(2,-1,1) = (4,-2, 2) (B+C) = (4,4,3) x 3 = (12,12, 9) 2A + 3(B+C) = (16,10,11) is this the correct way to think and do this problem?

If B is added to C = 2.5 i + 3.5 j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B? I have tried 0, which seems to make sense to me, but it is wrong. and I don't know if it means b+c=2.5i+3.5j or if b=? and...

[SOLVED] the addition of three simple harmonic motion Homework Statement A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. If the amplitudes are 0.25, 0.20 and 0.15 mm, respectively, and the phase difference between...

Homework Statement A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30* above the horizontal. It then travels 135 ft at an angel of 40* downward. What is its displacement from its starting point? Homework Equations Standard trig, I guess. The Attempt...

Question--Proper form for nuclear addition Homework Statement Say I am doing Binding Energy calculations, and I want to know the sum of mass for all the parts for, say, Carbon12 (C12). Which of the following is the correct form: Homework Equations 1.) 6p + 6n = total 2.) 6(H1) +...

Car 1 is traveling at 3/4c. Car 2 in behind Car 1 is traveling at 1/2c. Car2 fires a bullet that travels at 1/3 c. OK. In order to determine whether the bullet reaches Car 1 or not we need to use Einsteins velocity addition rule and determine whether the relative velocity of the bullet...

Homework Statement How do I find, sin\left(\alpha - \beta + \gamma\right) = ? Homework Equations sin\left(\alpha\pm\beta\right) = sin\alpha{\textcolor[rgb]{1.00,1.00,1.00}{.}}cos\beta \pm cos\alpha{\textcolor[rgb]{1.00,1.00,1.00}{.}}sin\beta and...

Hello, I have found that in some processing cases that additional elements are added to metals which result in increased potential for smaller grain size. Does anyone know why this is so? Am I signiificantly misunderstanding the issue? Thanks, -scott

Say a spacecraft is traveling just a few miles per hour under the speed of light. Now say a person on board this spacecraft starts running towards the front of the ship. If the craft is already moving just under light speed, and the person inside is running at a speed of say 8MPH, isn't the...

I just wanted to know if subspace A + subspace B is the same as the "union of A and B".

If I add the chemicals C3 H6 O (2-propanone) and C8 H18 O (2-ethylhexanol) will I wind up with the chemical formula C11 H24 O2 ? thanks

Homework Statement During a rodeo, a clown runs 8.0 m north, turns 55 degrees north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown's total displacement? The Attempt at a Solution I drew a...

I have a question on 'vector addition'. I know that resultant is the sum of two or more vectors. But this sum doesn't mean the sum of magnitudes of two or more vectors, right? So what does that 'sum' refer to? Combined effect? Hope you can answer my question, thanks.

Homework Statement Particle is at (9, 4) on coordinate plane. Initial velocity: 5.5 x - 7 y Acceleration: 1 x + 8.5 y Time: 1.5s 1: What is the x-component of velocity after that 1.5s? 2: Y-component? 3: Magnitude from origin of graph? Homework Equations sqrt(x^2 + y^2) for magnitude...

Homework Statement Particle has two displacements. 1 - 11m, 89 degrees 2 - ? 1+2 - 8.6m, 129 degrees So: 1 = (11, 89°) 2 = ? 1+2 = (8.6, 129°) Homework Equations X-component = M x cos(Θ) Y-component = M x sin(Θ) Total magnitude = sqrt((total x-component)² + (total y-component)²) Total...

This is just a general question that I hope someone can answer. Why do we add alkali before extraction rather than afterwards? This is in the experiment I recently did, which was the preparation of p-Toluidine? This was my main thought... that it helps to saturate the solution so that when...

Homework Statement hi, i have a lab for thermal physics in which the cooling of coffee is monitored. The variable change is the amount of milk that is added once the coffee is brewed. My question is whether there is an equation that relates heat exchange between 2 liquids in a solution? (an...

What simple operations, if any, precede or succeed the series ". . . exponentiation, multiplication, addition. . ."?

Homework Statement A K-meson at rest decays into two pi-mesons, and each pi meson has a speed of 0.85c. If a K-meson traveling at a speed of 0.9c decays, what is the greatest speed the one of the pi-mesons can have? Homework Equations u\prime = \frac{u-v}{1-\frac{v}{c^2}u} The...

Homework Statement So I have to prove that addition and multiplication in Zn are well defined. Homework Equations The Attempt at a Solution I have no idea where to start.

Hello I got some funny idears don't know if they are true, but I will share them with you. Homework Statement I would like to prove these formula (1)sin(z_1 + z_2) = sin(z_1) \cdot cos(z_2) + sin(z_2) \cdot cos(z_1) (2)cos(z_1 + z_2) = sin(z_1) \cdot sin(z_2) - cos(z_2) \cdot...

http://img117.imageshack.us/img117/1482/graph015tt6.png I know an alternative way of showing Sin C is cos 'theta'. Thanks

Fundamental frequencies Using the formula Would it be correct to say that to determine the necessary tension for the fundamental frequency at 60hz, substitute into the equation f, m, and L, then solve for T?

Please , can you help in finding the addition theorem of gegenbauer polynomials on the web? many thanks

does cos + sin = 0?

Consider a scenario which involves a stationary machine gun (MG) and a moving target T. MG emits successive bullets at constant time intervals t(e) which hit the moving target at constant time intervals t(r). The bullets move with velocity U and the target with velocity V. The first bullet...

I have studied N.David Mermin "Relativistic addition of velocities directly from the constancy of the velocity of light," Am.J.Phys. 51 1130 1983 and others with the same subject quoted by the Author. He describes a derivation of the addition law that dispenses not only with the LT but also...

Homework Statement A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 14.0 m, and C = 23.0 m. Using the component method, find the magnitude and direction of the resultant vector A + B + C...

Homework Statement A merry-go-round is a common piece of playground equipment. A 4 m diameter merry-go-round with a mass of 220 kg is spinning at 16 rpm. John runs tangent to the merry-go-round at 5.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is...

Hi! I'm currently reading Edmund Landau's book Foundation of Analysis. I kinda got stuck right at the beggining where the author tries to develop the natural numbers theory from axioms. Theorem 4 states the following: (where x' denotes the successor of x) The following proof is quite hard...

addition formulae - Trig help requested! I have a problem with this with regard to Sin 120 or Cos 120. Eg sin 165 sin (120 +45) sin120.cos45-cos120.sin45 How do I deal with sin 120 or cos 120? I know that cos 45 is 1/square root 2 and so is sin 45. But in the above problem, the...

Hi. Are there any addition theorems for inverse trigonometric functions? Like arccos(x+y)=? or something... I was wondering about this when I tried to find the derivative of f(x)=arccos(x) by setting f'(x)=\frac{\arccos(x+\Delta x)-\arccos(x)}{\Delta x}