Value Definition and 1000 Threads

If $\left| a \right| \le b$, then $-b\le a\le b$. Let $a,b \in\Bbb{R}$ The definition of the absolute value is $ \left| x \right|= x, x\ge 0$ and $\left| x \right|=-x, x< 0$, where x is some real number. Case I:$a\ge 0$, $\left| a \right|=a>b$ Case II: a<0, $\left| a \right|=-a<b$the solution...

Homework Statement https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202016-02-02%20kl.%2007.35.26.png I want to find variance matrix and expected variance vector of Y=(Y1,Y2). Y1 and Y2 are independant. Γ is the gamma function and ϒ is a known parameter. λ1>0 λ2>0 and ϒ>0...

Homework Statement ## H ## is the Hamiltonian of an electron and is a Hermitian operator. It satisfies the following equation: ##H |\phi_n\rangle = E_n |\phi_n\rangle ## Let ## U = e^{\frac {iHt}{\hbar}} ##. Find the expectation value of U in state ##|\phi_n\rangle## Homework Equations ##...

What is the basis for the believe that the value of field is fluctuated at micro-level?Does the existence of photons demontrate the need of express field in form of operators then deducing the fluctuation of quantum field through Heizenberg commutators?

I have am having trouble and I am a bit stumped on where to go. Looking to get help with calculating the neutralizing value 3 parts by weight of anhydrous potassium carbonate.

I am calculating a value and want to find the real value of sin(i). I can use series expansion and only take the terms without i (correct?) but is there any nicer way to express the result of taking the real value of sin(i)?

Homework Statement I and J are open subsets of the real line. The function f takes I to J, and the function g take J to R. The functions are in C1. Use the mean value theorem to prove the chain rule. Homework Equations (g o f)' (x) = g'(f (x)) f'(x) MVT The Attempt at a Solution [/B] I know...

Homework Statement why we need to make x as absolute value ? as we can see, the original is x , why we we need to make x as absolute value ? is the working wrong ? Homework EquationsThe Attempt at a Solution

I have studied about the formula of refractive index which is: . That means in the case of water which have μ =1 (approximate) and ε = 81, then n should be 9. But why we often use the value n = 1.33 for water ? Who can explain for me? I don't think the above formula is wrong, of course!

Homework Statement The mass of A is 5kg and the mass of B is 10kg. If the acceleration of A is 2m/s^2 which is smaller than acceleration of B, where A is placed on top of B, then the value of frictional force applied by B on A is: A) 50N. B) 20N. C) 10N. D) None of these Homework Equations...

Homework Statement Let f is differentiable function on [0,1] and f^{'}(0)=1,f^{'}(1)=0. Prove that \exists c\in(0,1) : f^{'}(c)=f(c). Homework Equations -Mean Value Theorem The Attempt at a Solution The given statement is not true. Counter-example is f(x)=\frac{2}{\pi}\sin\frac{\pi}{2}x+10...

Essentially, I have a function of two variables f(x, y), and I want to find the total value (sum) of that function for all values of (x, y) over an interval. How would I do that? The closest thing I can think of is the mean value theorem for integrals, but I want the total value, not the average...

I am following Griffiths' intro to quantum mechanics and struggling(already) on page 16. When a particle is in state ##\Psi##, $$\frac{d<x>}{dt} = \frac{i\hbar}{2m}\int_{-\infty}^{\infty} x\frac{\partial}{\partial t}\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial...

find the least possible value of a + b where a and b are positive integers and 11 divides $a+ 13b$ and 13 divides $a + 11 b$

It's my first post so big thanks in advance :) 1. Homework Statement So the question states "By interpreting <pxΨ|pxΨ> in terms of an integral over x, express <Ekin> in terms of an integral involving |∂Ψ/∂x|. Confirm explicitly that your answer cannot be negative in value." ##The 'px's should...

Homework Statement How do I find the EN value for a compound with more than two elements? Homework Equations C6H12O6 The Attempt at a Solution Do I just subtract all EN values? I don't think so bc then I get negative numbers so confused.

hey I was browsing the web a while ago and I found an equation for infinity to equal 1.5 when subjected to a equation. however I can no longer find this. I was wondering if anyone knew what it was and if they could explain how it works. many thanks Ewen

If I want to find the standard ΔG for a reaction in an electrochemical cell, I can use the equation ΔG° =-nFE° where n is the number of moles transferred, F is Faraday's constant, and E° is the standard emf of the cell. If I know the standard reduction potentials of the redox reactions happening...

Homework Statement It's been a little while since I did one of these. My question is: We have to use http://phet.colorado.edu/sims/mass-spring-lab/mass-spring-lab_en.html to find the measurement of k, the spring factor using two different methods. For the method I am looking at, is the static...

I found two definitions of wigner function on space time. the first uses a Fourier transform of ##\rho (q+ y/2,q-y/2)## the second uses the Weyl transformation and parity operator ## exp (i \pi \theta N)## where N is the occupation number operator. Could you give me a link which shows the...

Homework Statement In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x? Homework Equations I used the cosine rule here The Attempt at a Solution As we have 2 sides and an angle I used the cosine rule - Am I correct? (2) means squared b(2)...

I am not sure why a factor of (½) appears in front of the summation over orbitals, i, j to N, of the Coulomb and exchange integrals in the HF energy expectation value.

Homework Statement Hi, I was working on a homework problem and could not resolve it. The problem reads as follows: A ladder that weighs 240N rests against a frictionless wall at an angle of 60 degrees from the ground. A 600-N man stands on the ladder three-fourths of the distance from the...

Homework Statement I calculated theoretical value of resistance - I assumed that R4 and R5 are in series and parallel to R2 and R3 which are in series, because I've considered B as the starting point - this is the method I was taught, but I don't know any method of calculating the voltage...

$a>0,b>0,c>0 ,\,\, and \,\, a+b+c=1$ find $min(\sqrt {a^2+b^2}+\sqrt {b^2+c^2}+\sqrt {c^2+a^2} )$

Homework Statement ##\displaystyle (x+3)\frac{dy}{dx} = y - 2##, where x is not 3 and y is not 2. Homework EquationsThe Attempt at a Solution ##\displaystyle (x+3)\frac{dy}{dx} = y - 2## ##\displaystyle \frac{dy}{y-2} = \frac{dx}{x+3}## ##\displaystyle \int \frac{dy}{y-2} = \int...

Homework Statement Determine the tension cable A and B and the x , y , z reaction of the ball and socket joint at C . Homework EquationsThe Attempt at a Solution I let the reaction of ball and socket joint at C = Fx , Fy and Fz Sum of force in z direction : TA +TB +FZ= 400 Sum of force in...

https://qph.is.quoracdn.net/main-qimg-c22d8aa4be4fc2ed9b2f1c7060982e04?convert_to_webp=true How to find value of U on R2 long time after switch is being closed? Capacitors are charged so there is no current going through? Or? I used kirchof rule so i get Uo+Uc1-U=0 U=Uc1+Uo...

Hi guys, I have a very very simple and naive question, which I hope I shouldn't be ashamed to ask, but I would like to clarify an issue in my mind. We hear everywhere that the value of the ew vacuum is v ~ 246GeV, fixed by the Fermi Constant G_F, v = (\sqrt(2)*G_F)^(-1/2). Now this is also the...

Homework Statement A block of mass "m" is pulled across a rough table by a string at an angle "θ" above the horizontal at a constant velocity. What is an equation for the magnitude of the kinetic friction force, fk? The answer that I was given was μk(mg-T*cos(θ)) Homework Equations Fk=Fn*uk...

Homework Statement Solve \begin{equation*} 36x^2y''+(5-9x^2)y=0 \end{equation*} using the Frobenius method Homework Equations Assume a solution of the form \begin{equation*} y=\sum_{n=0}^{\infty}{a_nx^{n+s}} \end{equation*} then \begin{equation*}...

Consider a scenario where samples are randomly selected with replacement. Suppose that the population has a probability distribution with mean µ and variance σ 2 . Each sample Xi , i = 1, 2, . . . , n will then have the same probability distribution with mean µ and variance σ 2 . Now, let us...

Homework Statement This is a solution to a problem that was on a quiz, and I am confused about how to do it. Especially lines two (<0,1,1>=v(0)=<C1, 1+C2, C3> --> C1=0, C2=0, C3=1 and five (<1,0,0>=r(0)=<1+ K1, K2, K3> -->K1=0, K2=0, K3=0 How do you do these steps...

"Let X be a Bernoulli random variable. That is, P(X = 1) = p and P(X = 0) = 1 − p. Then E(X) = 1 × p + 0 × (1 − p) = p. Why does this definition make sense? By the law of large numbers, in n independent Bernoulli trials where n is very large, the fraction of 1’s is very close to p, and the...

Prove $\dfrac{3^{371}+5}{5^{247}+3}>\dfrac{2^{371}+3}{3^{247}+2}$.

I searched for, but could not find any name or published value for a constant (with units m-3 K-3) which when multiplied by temperature (in degrees Kelvin) cubed gave the corresponding photon density (in m-3). Does anyone know of such a constant with a published value? I calculated a value, but...

Homework Statement Find the extremizing (maximum) value of the function f(x) = sin x / x using Newton's 1D method. Homework Equations [/B]The Attempt at a Solution I know the maximum point in this equation is (0, 1). When I differentiated the equation twice and used the formula above, I...

can i know how much torque is required to move a 200kg weighed vehicle to 30kmph by using 24v, 250w dcmotor

I'm having a physics lab in which a report needs to be submitted after an experiment. The experiment includes many measurements: values with their errors. I need to round the error up to 2 significant digits, and then to round the value up to to the amount of digits that the error is presented...

I know the method and can solve other initial value problems. This is the question given: dy/dx + y(-2) Sin(3x) = 0 for t > 0, with y(0) = 2. I've brought the dy/dx and let it equal to the rest of the expression so it is now: dy/dx = -y-2 Sin(3x) , with y(0) = 2 (i.e. when x = 0, y = 2 ) The...

Does the function satisfy the hypothesis of the mean value theorm On the given interval, give reasons for your answer $$f\left(x\right)=\sqrt{x\left(5-x\right)},\ \ \left[0,5\right]$$ The graph of this is the top half of a circle My answer was It is continuous at all points on the...

Can anyone tell me what is the principal value of an integral? The integral in this case is a surface integral?

Need torque for single 24in wheel vehicle weighing 150lbs to reach top speed of 25 mph in 5 sec. So far I have got wheel rev of 350 per minute but not sure of torque in Ft lbs

Hello experts, I have attached the figure below kindly see it. And here is my calculation, Using law of sine, from figure we can say that α+β=120° and β=120°-α and sin(β)/sin(α)=PA/PB=3/40=0.075 so, sin(120°-α)=sin(120°)cos(α)-cos(120°)sin(α) since, sin(β)=sin(120°-α) so...

We begin with this definition of a hyperbola. \left(\overline{F_1 P}-\overline{F_2 P}=2 a\right)\land a>0 Perform a few basic algebraic manipulations. \sqrt{(c+x)^2+y^2}-\sqrt{(x-c)^2+y^2}=2 a \sqrt{(c+x)^2+y^2}=2 a+\sqrt{(x-c)^2+y^2} (c+x)^2+y^2=4 a^2+4 a \sqrt{(x-c)^2+y^2}+(x-c)^2+y^2...

Hello experts. I am attaching the image below. Kindly tell me how to calculate the values of A and B in the given figure? Now I must find A and B. How to get it? PS: P=-2.5+4.33i. But A is not at -2.5. Means PA is not making angle 90 with real axis. Thank you

Consider a set X with |X|=n≥1 elements. A family F of distinct subsets of X is sad to have property P if there exist A and B in F, such that A is a proper subset of B and |B\A|=1. Determine the least value m, so that any F with |F|>m has property P. This is a problem asked by our Discrete...

Suppose that $u$ is the solution of the Laplace equation $u_{xx}+u_{yy}=0$ in $\{(x,y)\in \mathbb{R}^2: x^2+y^2<1\}$ $u(x,y)=x$ for all $(x,y)\in \mathbb{R}^2$ such that $x^2+y^2=1.$ Find the value of $u$ in $(0,0).$ Use the property of median value.

Homework Statement Show that for a two spin 1/2 particle system, the expectation value is \langle S_{z1} S_{n2} \rangle = -\frac{\hbar^2}{4}\cos \theta when the system is prepared to be in the singlet state...

Let $\lim_{{k}\to{\infty}}d\left({x}_{m\left(k\right)},{x}_{m\left(k\right)-1}\right)=\varepsilon$ and $\lim_{{k}\to{\infty}}d\left({x}_{n\left(k\right)},{x}_{m\left(k\right)}\right)=\varepsilon$...Can we say that...