Value Definition and 1000 Threads

Homework Statement We know: In a measurement of quantum mechanics (basic) the average value is the cosine of the angle between the orthonormal basis of the measurement apparatus and the qubit (vector) entering it. Question: How do we prove this?Homework EquationsThe Attempt at a Solution Can...

Homework Statement In an oscillating series RLC circuit, with resistance R and inductance L, find the time required for the maximum energy in the capacitor during an oscillation to fall to 1/5 its initial value. Assume q = Q at t = 0 Homework Equations ## U(t) =...

A sequence as follows : $0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$ please find :$a_{2008}=?$

A trapezoid ABCD given : (1)$\overline{AB} // \overline{CD}$ (2)$\overline{BC}\ \perp \overline{AC}$ and $\overline{BC}=\overline{AC}$ (3)$\overline{AB}=\overline{BD}$ find the value of $\angle BAD$

Homework Statement Find the exact value of sin 345.5o Homework Equations Trigonometry Identities The Attempt at a Solution Don't know where to start. Tried sin 345.5o = - sin 14.5o but stuck. Also tried multiply 345.5 with positive integer to get sin 2θ or sin 3θ or sin 4θ but also stuck Thanks

Homework Statement Consider the boundary value problem \begin{equation} u''(t)=-4u+3sin(t),u(0)=1,u(2)=2sin(4)+sin(2)+cos(4) \end{equation} Homework Equations Derive the linear system that arise when discretizating this problem using \begin{equation} u''(t)=\frac{u(t-h)-2u(t)+u(t+h)}{h^2}...

I'm a psychologist and I'm currently studying physics but, because this is not my field of study, I'm having great difficulties. I am currently studying biological motion and I have to calculate the jerk of my 2D motion data and I don't even know where to start. My data is basically a bunch of...

Homework Statement Find the exact value of sin 65o Homework Equations Trigonometry Identities The Attempt at a Solution I tried using sin 3x = 3 sin x - 4 sin3x but ended with nasty algebra. sin (3 . 65o) = 3 sin 65 - 4 sin3 65o sin (195o) = 3 sin 65 - 4 sin3 65o sin (180o+15o) = 3 sin 65 -...

According to Wolfram it is approx. -1.895 How do I find the exact value of the root though?

Hello! Simple as it sounds, I would greatly appreciate help on finding the exact value of Cos(\frac{-\pi}{3} If I need to find a negative value of Cos, does it become the inverse? So, since if I draw on unit circle, I get (\frac{\sqrt{3}}{2}, \frac{-1}{2}), would the value of Cos(-pi/3) = the...

Homework Statement Consider the bipartite observable O_AB = (sigma_A · n) ⊗ (sigma_B · m) Where n and m are three vectors and sigma_i = (sigma_1_i, sigma_2_i, sigma_3_i) with i = [A,B] are the Pauli vectors. Compute using abstract and matrix representation the expectation value of O_AB...

Hello, I'm struggling with a simple problem here. It asks me to solve the following initial value problem: So far I've calculated the integration factor μ(x) = ex-x2 and I multiplied both sides of the equation by it and got this...

Homework Statement A sinusoidal supply defined by ## v(t)= 325.27 sin(314.16t+\frac{\pi}{6}) ## is connected across a coil of resistance 25Ω and inductance of 0.5 H. The instantaneous value of the current at 2.968ms is 13.13 mA 21.6 mA 87.8mA 13.8mA Homework Equations ## i(t) = \frac{v(t)}{Z}...

Find the greatest value of $a$ for which the inequality $x^4+y^4+z^4+xyz(x+y+z)≥ a(xy+yz+zx)^2$ holds for all values ​​of $x ,\,y$ and $z$.

For my final year project at uni, I am designing a new racquet grip. Past of investigating current products, I am going to test the friction properties of current grips. My plan is to rub a number of grips for a set time and then, using a heat sensor gun, measure the grips heat. My question...

Going from the Newtonian to relativistic version of Friedmann's equation we use the substitution kc^{2} = -\frac{2U}{x^{2}} The derivation considers the equation of motion of a particle with classic Newtonian dynamics. I can sought of see that if space is flat the radius of curvature will be...

Homework Statement Use laplace transforms to find following initial value problem -- there is no credit for partial fractions. (i assume my teach is against using it..) y'' - 4y' + 3y = 0 ; y(0)=2 y'(0) = 8 Homework Equations Lf'' = ((s^2)*F) - s*f(0) - f'(0) Lf' = sF -...

Homework Statement Let p: x and y satisfy inequality x2 + y2 + 4x - 8y + c < 0 where c is real number q: x and y satisfy x - y + 8 > 0 ; 4x + 3y - 24 < 0 ; y < 0 Find the range of c so that: a. p is sufficient condition for q b. p is necessary condition for q Homework Equations Circle...

Homework Statement Let u = (2,k,1,-4) and v = (3,-1,6,-3) For which values of k is the distance d(u,v) = 6? Homework EquationsThe Attempt at a Solution 6 = √((3-2)2 + (-1-k)2 + (6-1)2 + (-3-4)2) 6 = √(1 + 1 + k2 + 25 + 21) 6 = √(k2 + 48) 36 = k2 + 48 k = √-12 The answers seem to be 6k, -16k...

If x values are: 10, 20, 30, 40, 50 corresponding y values are:20, 65, 180, 390, 505 then what is y value at x=25. I was having an argument with maths sir. I was saying to take x0 as 10 to get the answer as 107.14, which is correct application of formula, but our maths sir said that we should...

Solve the following inequality. Represent your answer graphically: ## |z-1| + |z-5| < 4 ## Homework Equations ## z = a + bi \\ |x+y| \leq |x| + |y| ## Triangle inequality The Attempt at a Solution ## |z-1| + |z-5| < 4 \\ \\ x = z-1 \ \ , \ \ y = z-5 \\ \\ |z-1+z-5| \leq |z-1| + |z-5| \\...

Homework Statement Solve: ##\displaystyle \lim_{x\rightarrow 2} \frac{\left | x^2 + 3x + 2 \right |}{x^2 - 4}##. Homework EquationsThe Attempt at a Solution I am trying to solve the following limit: ##\displaystyle \lim_{x\rightarrow 2} \frac{\left | x^2 + 3x + 2 \right |}{x^2 - 4} =...

Homework Statement Determine the value of b and c such that the function is continuous on the entire real number line Homework Equations f(x) = { x+1 , 1<x<3 x^2+bx+c, |x-2| >=1 The Attempt at a Solution What is the best way to get the b and c value?[/B]

Example 3 shows the derivation of one of the kinematics equations. I am quite familiar with it. At the part where it says dx/dt = gt + constant, how does one determine if constant = x_0 or v_0? Thank you.

\sum^{\infty}_{n=1}\frac{1}{n^{\alpha}}=\zeta(\alpha) For ##\alpha=-1## ##\zeta(-1)=-\frac{1}{12}## I do not see any difference between sum ##1+2+3+4+5+...## and ##\zeta(-1)##. How the second one is finite and how we get negative result when all numbers which we add are positive. Thanks for...

Hello! (Wave) I want to find the value of $a$ for which the system $\begin{pmatrix} a & 1 & 1\\ 1 & a & 1\\ 1 & 1 & a \end{pmatrix}\begin{pmatrix} x_1\\ x_2\\ x_3 \end{pmatrix}=\begin{pmatrix} 1\\ 1\\ 1\end{pmatrix}$ has a unique solution has infinite solutions has no solution The...

Hello! (Wave)Consider the boundary value problem $\left\{\begin{matrix} - \epsilon u''+u'=1 &, x \in [0,1] \\ u(0)=u(1)=0 & \end{matrix}\right.$ where $\epsilon$ is a positive given constant. I have to express a finite difference method for its numerical solution. How can we know whether it...

Homework Statement If X1 has mean -3 and variance 2 while X2 has mean 5 and variance 4 and the two are independent find a) E(X1 - X2) b) Var(X1 - X2)The Attempt at a Solution I am not very clear on what I am supposed to be doing for this problem. I don't fully understand this expectation value...

If R = [−3, 1] × [−2, 0], Use a Riemann sum with m = 4, n = 2 to estimate the value of ∫∫R(y2 − 2x2) dA. Take the sample points to be the upper left corners of the squares. So far, I found the indefinite integral of the function to be y3/3 - 2x3/3 Not sure where to go from here

So, I know that P ⊃ Q is a true statement even if P is false as long as Q is true. However, I don't understand why that is, or how that is logically sound. Is it because I'm stuck in thinking of these types of statements as "If P, then Q," and they are not supposed to be thought of that way? How...

1. Homework Equations Solving Polynomial Inequalities The Attempt at a Solution Then I used the property of absolute value inequality to get rid of it. But I really don't know if I'm doing the right step. Is this correct? So that I could separate them in two cases and find the...

Homework Statement Solve the initial value problem and determine at least approximately where the solution is valid (2x-y) + (2y-x)y' = 0 y(1) = 3 Homework EquationsThe Attempt at a Solution I know how to solve it, and I got the correct answer, which was: 7 = x^2 - yx + y^2 and then applying...

Hello, I am willing to know if the value of pressurized fluid along a rectangular path placed normal to ground (let's say 2 stories high) would show any change in pressure along the lines normal to ground. I am not worried where fluid would move horizontal to ground but what would happen when it...

Here is the problem: If -1 is a range value for the function f(x) = -6x + 11, find the domain value. thank you for your help

Homework Statement My teacher made up this question, but I think there's something wrong. Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx. Homework Equations Fourier trick and...

In conjunction with diving, a mixture of helium and oxygen called heliox. It will form the background to the following model invoice. Suppose that 1 mole of He and 1 mole of O2 is compressed as fast at half the volume that no heat exchange with the environment have time to take place...

Homework Statement Under what condition on the constant ##c## and ##c'## are the boundary conditions ##f(b) = cf(a)## and ##f'(b)=c'f'(a)## self-adjoint for the operator ##L(f) = (rf')'+pf## on ##[a,b]##? (Assume that ##r,p## are real.) Homework Equations The boundary conditions are...

Homework Statement Hello everyone, I need to find K for the following differential equation to be exact. (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 Homework EquationsThe Attempt at a Solution (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 dM/dy = d/dy(y3+kxy4-2*x) = 4*k*y3*x+3*y2 dN/dx =d/dx(3xy2 +20x2y3) =...

Hi folks, I'm a new graduate student in biology. I'm interested in doing theory (either simulations of biomolecules, physical models of the brain/consciousness, or models of cellular dynamics). I have had very intriguing discussions with fellow students along the following lines: 1. There are...

Homework Statement Homework Equations Newton's 2nd Law The Attempt at a Solution I was wondering if anyone could verify that I have all the correct vectors or if I am missing any. I just wanted to check before I started trying to derive the equations. [/B]

1. Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of nHomework EquationsThe Attempt at a Solution the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9...

I'm given an operator $\mathcal{L}$ is Hermitian, and asked to show $<\mathcal{L}^2>$ is $\ge 0$ I believe $<\mathcal{L}>$ is the expectation value, $=\int_{}^{}\Psi^* \mathcal{L} \Psi \,d\tau $ (Side issue: I am not sure what $d\tau $ is, perhaps a small region of space? And the interval?) I...

Homework Statement http://imgur.com/RlIdmFh http://imgur.com/3dnLK3m Homework Equations |x| = -x? The Attempt at a Solution I'm trying to make sense of this definition in my book because they are trying to prove the triangle inequality(second link), yet it keeps saying that the absolute value...

Specifically when doing integration problems. I know the indef integral of cosx/sinx+1 is ln(sinx+1) + C, but absvalue is not required here. I think it's because the sine fn must be >= 0 or it's undefined? What about in other cases, is there a general rule to know when to use absvalue? Thanks

If ##\sqrt{x^2} = |x|##, why ##\sqrt{16} ≠ |4|## instead of 4 (please see below image)?

Homework Statement The dimension h is to be determined to that a worker can comfortably slides boxes weighing up to 106 lb up and down a frictionless incline. If the worker can apply a 50 lb horizontal force to the box, what is the largest value h should have? Hint given: Before taking any...

How does one solve an equation with two absolute value functions as below My algebra book does not show how to solve with two abs functions. 2|4x-1| = 3|4x+2| I thought this might work.. |4x-1|/|4x+2| = 3/2 then |(4x-1)/(4x+2)| = 3/2 and solve the normal way..

Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. 3x1+6x2 = −6 3x1+9x2−6x3 = −12...

Homework Statement The displacement of a machine is given by the simple harmonic motion as x(t) = 5cos(30t)+4sin(30t). Find the amplitude of motion, and the amplitude of the velocity. Homework Equations x''(t) = -4500cos(30t)-3600sin(30t) The Attempt at a Solution [/B] I should note that...

Homework Statement Derive ##\sum_{n=1}^\infty \frac{1}{n^2+b^2} = \frac{\pi}{2b}\coth b\pi - \frac{1}{2b^2}## from either ##e^{b\theta} = \frac{e^{2\pi b}-1}{2\pi} \sum_{-\infty}^\infty \frac{e^{in\theta}}{b-in}## for ##0 < \theta < 2\pi##. or ##e^{b\theta} = \frac{\sinh...