Expression Definition and 999 Threads

See the photo of the question+ mark scheme! I don't understand a question on finding an expression for the variance of something... Attempt at solution: also I worked out c as (3/2) previously, which is correct Var(U) = (3/2)^2 x Var(Xbar) = 9/4n^2 x a^2/18 I'll attach a photo of this too if...

Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}$.

Homework Statement https://www.dropbox.com/s/d3qdr96n27j8wa7/circuit.png?dl=0 The questions is as follows: For each circuit write the equivalent logic expression. Homework Equations (B' + C) * A (?) My Attempt at circuit 2 (A* (A' * C') * B') + (A * C * B) My Attempt at Circuit 1 The Attempt...

Homework Statement A positive charge +q is located at the point x= 0, y = -a and a negative charge -q is located at the point x=0, y=a (a) Derive an expression for the potential at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the...

How can you derive an expression from the given direction defined by dx=2dy=-2dz. This is just a part of a problem that I'am solving. I have no idea how to get a vector expression using the given info. please help. Thanks! by the way I'm trying to find the directional derivative of a certain...

Homework Statement Find ## \sum_1^{23} tan^{-1}(\frac{1}{n^2+n+1}) ## Homework Equations ## tan^{-1}x + tan^{-1}y = tan^{-1}(\frac{x+y}{1-xy} )##The Attempt at a Solution I think we have to split the question in a form of relevant equation given above. First thing what should I do?

Homework Statement http://www.inter-ped.no/skei/MAT1013%20Matematikk%201T%20%20bokmal.pdf Page 10 task 4 for a picture. The window above consists of a rectangle and a semicircle. The windows perimeter is 8.0m. What does the radius in the semicircle have to be for the area of the window to be...

1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...

Homework Statement A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk. Find an expression for the bullet's speed vbullet. Express your answer in terms...

Hi there. I'm reading Jackson's Classical Electrodynamics. 1. Homework Statement In chapter 6, the equation for the electric field of a moving point charge is derived. I could follow the mathematics to get the electric field for the moving charge, which is given in equation 6.57 in Jackson...

Taken from Hobson's book: How did they get this form? \dot u^{\mu} = - \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u^{\mu} g_{\mu \beta} \delta_\mu ^\beta = - g_{\mu \beta} \delta_\mu ^\beta \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u_{\mu} = - \frac{1}{2} g_{\mu \beta} \delta_\mu ^\beta...

Homework Statement For the circuit in (Figure 1) , suppose va=10cos16,000tV vb=20cos4000tV. Suppose that R = 700Ω . Write the steady-state expression for io(t) as io=I′ocos(ω′t+ϕ′)+I′′ocos(ω′′t+ϕ′′), where −180∘<ϕ′≤180∘, −180∘<ϕ′′≤180∘, and ω′>ω′′. Find the numerical value of I′o. Find the...

Simplify the expression below: $\dfrac{w^2(z-x)(z-y)}{(w-x)(w-y)}+\dfrac{x^2(z-y)(z-w)}{(x-y)(x-w)}+\dfrac{y^2(z-w)(z-x)}{(y-w)(y-x)}$

Homework Statement Identify and fix all hazards in ##f = (ab + \bar{a}c)(c + \bar{b}) + ab##. Re-check if the final expression obtained is hazard free. Homework EquationsThe Attempt at a Solution So I used a binary tree and found a static 1 hazard present for ##bc = 11##. The hazard was ##a...

Hey! :o How can we find the regular expression of a language given by an automaton M?? Could you give some hints?? (Wondering) Which are the steps that we have to follow so that we convert an automaton into a regular expression?? (Wondering)

Hey! :o I have to convert the following regular expressions to a NFA: $$(0 \cup 1)^{\star} 000 (0 \cup 1)^{\star}$$ $$(((00)^{\star} (11)) \cup 01)^{\star}$$ $$\emptyset^{\star}$$ $$a(abb)^{\star} \cup b$$ $$a^+ \cup (ab)^{\star}$$ $$(a \cup b^+)a^+b^+$$ For the regular...

How did they arrive at this expression? I understand the ##Q^2## term in the nominator and the ##r = r_0 (A)^{\frac{1}{3}}## term in the denominator. Where did the ##\frac{\alpha}{2}## term come from? Putting in Z=40, A=100 gives ##3.3 \times 10^{14} J##, not ##65 MeV##. The energy term...

Simplify $\left(\sqrt{3}\sec \dfrac{\pi}{5}+\tan\dfrac{2\pi}{5}\right)\tan \dfrac{2\pi}{15}$.

Homework Statement I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x) I want to simplify this expression.Homework Equations None The Attempt at a Solution I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it...

Find a closed form expression for \sum_{k=1}^{n^2}\dfrac{n-\lfloor\sqrt{k-1}\rfloor}{\sqrt{k}+\sqrt{k+1}}.

This is from from Sakurai and Napolitano HW Prob #2.6. I've done the HW problem and can fit all the pieces together with the mathematical formalism, but even afterwards I'm still scratching my head wondering what I'm looking at. I start with the commutator [[H,x],x]. If I take...

Homework Statement According to my textbook, the electric flux through a disk of radius R situated at a height d from the xy plane is given by: ##2 \pi k_0 Q [1- \frac{d}{\sqrt{R^2+d^2}}]## Where ##k_0 = \frac{1}{4\pi \epsilon_0}## I'm having some difficulty obtaining this answer. Homework...

What is this asking for? Is it asking for the trig expression in the form of x and y? Or is it asking for something else?

Hi, this is my online homework exercise. I think I did it right, but the system gives me wrong answer... Can someone please check what I did y=$\sqrt{x+\sqrt{x+\sqrt{x}}}$...

Hi Folks, I have a symbolic A=18*1*18 array containing symbols/expressions. I want to populate certain entries of this array into another matrix. For example K(1,1)=A(1,1,1) I get the following ? The following error occurred converting from sym to double: Error using ==> mupadmex Error in...

If A is an additive subgroup of a ring R, A is said to be an ideal if Ra is contained in A for all a in A; that is, if every multiple of an element of A is again in A. Is it true that A is an ideal of R if Ar is contained in A for all r in R? To me it seems like they are equivalent statements...

My working: S3 = A S2 = B S1 = C' S0 = D' F = Sum-Minterm(0, 1, 2, 4, 5, 8) (Basically i find when is X smaller then Y) Used Kmap to arrive at A'C' + B'C'D' + A'B'D' Am i correct?

Hello! (Wave) I am writing a text in LATEX and I wrote this: \begin{align*} \epsilon_p(a+b)&=((a+b)\pmod p, (a+b)\pmod{p^2}, (a+b)\pmod{p^3}, \dots )\\ &=(a\pmod p+b\pmod p, a\pmod{p^2}+b\pmod{p^2}, a\pmod{p^3}+ b \pmod{p^3}, \dots) \\ &=(a\pmod p, a\pmod{p^2},a\pmod{p^3}, \dots)+(b\pmod...

May there exist an integral domain R, with fraction field K, that fulfills the following condition: there exists x\in K, x\not \in R and a maximal ideal \frak m of R{[}x{]}, such that \frak m does not contain x-a for any a\in R ? Motivation : I am trying to prove a difficult result. A way to...

Homework Statement A particle with charge q moves with velocity v near a long, straight wire which has a current I flowing through it which generates magnetic field B. Give an expression for the magnitude of the force on this particle in terms of q, v = | v | and the magnitude of the magnetic...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > (A+B)&(C+D) + (A+B)&(C+D)' + C (A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans (A+B)&[(C+D)+(C'&D')] + C by Distributive I'm just wondering if I did anything wrong in this simplification or if it...

Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...

How can one compute and/or tell if a given expression is a traveling wave? I thought of using the characteristic wave equation δ^(2)ψ/δt^(2)=v^(2)δ^(2)ψ/δx^(2). An example of an expression would be ψ(x,t)=A(x-t). Should I partially derive this expression twice with respect to x and then to t...

I just wanted to post a solution for anyone interested. Any notes on how to solve would be nice for others. 1. Homework Statement Mastering Physics (3rd edition) Problem 26.40 The figure (Figure 1) shows a thin rod of length L with total charge Q. Part A) Find an expression for the...

This comes from one of the research papers that I'm reading. The authors decompose Eq. 1 and obtain Eq. 2. After several attempts, I have been fairly unsuccessful at obtaining Eq. 2 from Eq. 1. I have tried using partial fractions decomposition without much success. Any help would be greatly...

ds2=guvdxudxv Why is the invariance of ds2 as shown above? Why can't it be something like ds2=guudxudxu or ds2=dxudxu ? Isnt it based on Pythagoras theorem? Why must it have 1 u and 1 v instead of just 2 u or 2 v? Forgive me for such dumb question as I just started.

If $x,\,y,\,z>0$ and $x+y+z=1$, find the minimum of $\left(x+\dfrac{1}{x}\right)^{10}+\left(y+\dfrac{1}{y}\right)^{10}+\left(z+\dfrac{1}{z}\right)^{10}$.

(tg 570* sin 1469) / (ctg 495 * cos 781) = Its in degrees

Evaluate the expression $(2^{2^{2014}}+1)(2^{2^{2013}}+1)\cdots(2^{2^2}+1)(2^{2^1}+1)(2^{2^0}+1)+1$

I encountered this expression while trying o express $f(x)=\ln\left({\frac{1+x}{1-x}}\right)$ in terms of a power series: $$\int \left[ \sum_{n=0}^{\infty}(-1)^n x^n + \sum_{n=0}^{\infty}x^n\right] \,dx$$ The book simplifies this expression as $\int \sum_{n=0}^{\infty}2x^{2n} \,dx$ by expanding...

Take for example a fetus of 2 weeks old and a baby of 2 years old. The fetus doesn't show any limbs, skull. How do I know that is a human fetus ? :nb)

Homework Statement A voltage source given by ##v_s(t)=25cos(2\pi\times10^3t-30^\circ)## is connected to a series RC load. If R = 1MOhm and C = 200pF, obtain an expression for ##v_c(t)##, the voltage across the capacitor. Answer known to be: ##v_c(t)=15.57cos(2\pi\times10^3t-81.5^\circ)##...

i couldn't find the definition of Minterms and maxterms of boolean's expression on the internet nor my book. Can someone explain it? I was given only this in my book, without any explanation.

Hello I'm working through the see-saw mechanism. This is currently from the one-generation section. (I haven't got to the three generation workings yet... although I'm guessing I'll come across something very similar in the three generation model) Could someone please tell me if it is correct...

Hi guys i need your help! How can i reduce this equation: (Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)] into this: (B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)? I'm totally depressed, I'm always stocked in sqrt part of the equation: if there's a techniques in dealing this kind...

Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to...

If $k^{101}=1$ and $k\ne1$, evaluate $\dfrac{k^2}{k-1}+\dfrac{k^4}{k^2-1}+\dfrac{k^6}{k^3-1}+\cdots+\dfrac{k^{200}}{k^{100}-1}$.

Evaluation of range of real values of $t$ for which $\displaystyle 2\sin t = \frac{1-2x+5x^2}{3x^2-2x-1}\;,$ Where $\displaystyle t\in \left[-\frac{\pi}{2}\;,\frac{\pi}{2}\right]$

Homework Statement Find a closed form expression for the function f(x) which the power series Σn=0..∞ n(-1)nxn+1 converges to and determine the values of x for which f(x) equals the given power series. Homework Equations N/A The Attempt at a Solution I'm actually not sure how to start. First...

Homework Statement [/B] I need to differentiate the exponential function i = 12.5 (1-e^-t/CR) and I need to plot a table so that I can do a graph of i against t but I'm not sure how. (CR is the equivelant of Capacitance 20 Micro Fards and Resistance 300 Kilo Ohms)Homework Equations [/B] How do...