Expression Definition and 999 Threads

Hi I was wondering if there is any way to simplify this expression or if it's already in its simplest form. Thank you in advance: (a^n+b^n)/(a+b)

Well, I am now trying to figure out a single variable expression for Sin. I have a couple ideas using some pieces of geometric formulas I have played with recently but this is still new to me. I'm not talking about sin x, but an algebraic expression for the sin wave. Any thoughts?

Homework Statement Two students threw a paper plane towards the bin, hitting a desk at time t=10. The trajectory can be modeled as follows: x=t-2sin(t), y=4-3cos(t) Then there were a few simple questions before: The students are curious about what would have happened to the paper...

Hi guys I'm thinking on this problem for long time :) Let be one function defined only on POSITIVE INTEGERS I) f(1) = 1 II) f(2n) = 2 . f(n) + 1, if n ≥ 1 III) f(f(n)) = 4n + 1, if n ≥ 2 Find f(1993) ______________ First I got this, I got to this milestone f(2n) = 2 . f(n) +...

the questions are together with this file and my solutions are also attached. hope someone can comment on my solutions. thanks a lot and i hope i won't get any warning any more.

i am really really confused . I know what Drift velocity is but the problem is I have three Sources which tell absolutely different expression for drift velocity and I cat relate . please tell which is right . This website and MIT Profs. Walter Lewin In his Lectures says Vd = eE/m x (Tau)...

Hello. I just wonder why the energy expression of Hartree Fock method is symmetric. I tried to find out the reason on the Internet but I could only find that: since the Hartree Fock energy expression is symmetric, it is variational. In Hartree Fock method, the repulsive energy between...

How do I put down an expression that means the maximum value of a set of numbers?

Hello. I just wonder why the energy expression of Hartree Fock method is symmetric. I tried to find out the reason on the Internet but I could only find that: since the Hartree Fock energy expression is symmetric, it is variational. In Hartree Fock method, the repulsive energy between...

Homework Statement Hello! My problem is with a variational expression. I have a quantity, say L, which could be determined by the ratio: K = \displaystyle \frac{\left[\int_a^b E(x)e_n(x)dx\right]^2}{\left[\int_a^b E(x)e_1(x)dx\right]^2} Where e_1(x), e_n(x) are known functions and n...

Homework Statement If I have a expression like 5lx+2l, can I multiply the 5 with x+2? Homework Equations The Attempt at a Solution I'm guessing that I can only do this if the number in front of the absolute expression is a positive number. Because if -5lx+2l=-10 then multiplying...

A straight wire clamped vertically at its lower end stands vertically if it is short, but bends under its own weight if it is long. It can be shown that the greatest length for vertical equilibrium is l, where kl(3/2) is the first zero of J-1/3 and k=4/3r2*√(ρg/∏Y) where r is the radius, ρ is...

Homework Statement Use fundamental identities to simplify the expression: (sinx)^2 - (cosx)^2 ____________________ (sinx)^2 - (sinx cosx)*note: it's a numerator and denominator. The underscore line is the fraction line. *note: The answer in the back of the book is "1 + cotx" but I would...

I'm trying to prove by induction the expression: \sum_{i=1}^{n-1}(n-i)=\frac{n(n-1)}{2} For the base case, n=2, S(2)=\frac{2(2-1)}{2}=1 For S(n+1)=\frac{(n+1)((n+1)-1)}{2} I have: S(n+1) = \frac{n(n-1)}{2} + (n+1) <--- Is this correct? I don't know what is the term for n+1. Any help?

In the Turing Machine, the machine accepts a word if the computation terminates in the accepting state. The language accepted by the machine, L(M), has associated an alphabet Δ and is defined by L(M) = {w \in \Delta} This means that the machine understands the word w if w belongs to the...

Hey, I'm going over series expansions and was wondering if someone could check my work and tell me if my work is correct. If not, could you explain it to me? I couldn't find any example like this problem in my book so I'm posting it online. Here it is, The closed form series expansion for...

Homework Statement http://www.physics.ox.ac.uk/users/yassin/mechanics/problems/probs6_2011.pdf Q 2b. Homework Equations The Attempt at a Solution T is torque and J is angular momentum. T=dJ/dt=I dω/dt I tried solving dω/dt=ωk to get dω/dt=ce^kt, but this may not help.

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...

y(4C) ≈ 7.3 + C + \frac{C}{3^{10C}} + \frac{C}{3^{20C}} + \frac{C}{3^{30C}} Would: y(nC) ≈ 7.3 + C\sum_{n = 0}^{\infty}{\frac{1}{3^{10Cn}}} Be an acceptable answer? If not, what am I doing wrong here?

Homework Statement Prove |\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}| = 1 Homework Equations The Attempt at a Solution I feel like this should be fairly simple, anyone have any hints? Also this is just one step in an attempt to solve a much larger problem, so don't...

Say we have NA blue balls and NB red balls mixed together in an urn. When we pick a ball it leaves the urn. I want to find the probability of picking n red balls in a row. The probability of picking a red ball is: NA/(NA+NB) But each time a red ball leaves the urn the probability of picking...

determine a closed expression for b(n), given b(0) = 3 b(n+1) = 2+\prod (k=0 to n) * b(k) , n >= 0 , without using recursion og or the product given by \prod. I want to start out by b(n+1) -1 = (b(n)-1)^2 for n >= 0 , but I am not sure. kind regards Maxmilian

I have managed to solve (i), so I'll just post the answer as it comes into play for (ii). I'm struggling with the differentiation of this expression. Can anyone help? Many thanks. Homework Statement Q. A tank, with a base, is made from a thin uniform metal. The tank, standing on...

Hi all How does one calculate the recoil velocity of a hydrogen atom when the electron in it jumps from a higher orbit to a lower orbit (say from 3rd to 1st) ?

Difficulty : College Homework Statement The Attempt at a Solution I am unsure how to approach this question. I think it involves a process where you add an expression & and subtract it (or multiply & divide) in order to manipulate the equation and rearrange it or reorder it. I've...

let be N(x)= \sum_{n} H(x-E_{n}) the eingenvalue 'staircase' function and let be a system so V(x)=V(-x) and V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) then would it be true that the two function \sum_{n}exp(-tE_{n})=Z(t)= \int_{0}^{\infty}dN(x)exp(-tx) and [tex]...

Basically I am trying to find an expression that can add exponents. Here is an example, let's say we start with n=5, I need something that will calculate 5^2+4^2+3^2+2^2+1^1 by putting in whatever value for n that I choose. So far I have n^3+n^2(n-1)+n(n-1) The end, n(n-1) isn't working...

Homework Statement a) Two observables A and B are represented by operators A(hat) and B(hat), which obey the following commutation relation: [A(hat), B(hat)] = iC, where C is the real number. Obtain an expression for the product of the uncertainties ΔAΔB. b) Hadrons, such as protons...

After doing A LOT of simplification on a complicated expression I am now at a point where my own skills can't take me any further. My problem is that I have an expression, which I am almost certain must be real, but it contains the imaginary units here and there. I have tried using Maple and...

Homework Statement This isn't really a specific question, I just need clarification on multiplying a radical expression If I were to do... x multiplied by 4√6, which number would receive the variable x when multiplied? Homework Equations The Attempt at a Solution

Homework Statement Express the following as A2+B2: 3[√3+√5+√7]2 Homework Equations The Attempt at a Solution I expanded it to 45 + 6√15 + 6√21 + 6√35 Should I collect like terms (the multiples of 6)? I don't know how to proceed from here. Thanks in advance for any help.

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

Homework Statement Express the repeating decimal as a series, and find the rational number that it represents 1) 3.2\overline{394} Homework Equations Geometric Series (a/1-r) The Attempt at a Solution I tried putting the value into a series by having n=1 as it goes to infinity Ʃ3.2...

Homework Statement find the magnitude and angle of the moment moment=-2.8i-1.53j+2.24k force tension=2.4 kNHomework Equations rxf=rfsin(theta)The Attempt at a Solution i used the cross product to get i j and k tried sin and cos of vectors but didnt work. inverse tan of vectors won't give...

Homework Statement A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b much greater than a and resistance R1. A Resistance dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by...

Homework Statement Not long ago I had a similar problem, which I was able to solve after reading this thread, but for this question I'm stuck and I could use a small hint. Homework Equations The Attempt at a Solution Thanks

A bar of length l, breadth b, and depth d when loaded at the centre by a load W sags by an amount given by δ = W l^3/(4bd^3Y). Here Y is the young's modulus of the wire. My textbook says that we have to use little calculus to derive this expression. Can you please derive this?

"Waves" of sine expression So, I have been working with a lot of Math today(sorry if I am asking so many questions), and I found and expression. All sine functions use radians. sin(y) + sin(y) / sin(y) Now, assuming you start with 1, if you were to plot y on a graph with variable x...

I know that in an AC circuit at the steady state a capacitor behaves like a short and inductor behaves like an open. Since the inductor is open wouldn't that just mean the answer is 0?

what does it mean.

Homework Statement ℝ(3-7i)^4 Is this asking for just the real part of this complex expression? I suppose I could go about expanding the whole thing out, but is there a more convenient method? We've learned a few methods, such as expressing it in polar form and such. But here the angle...

Homework Statement A 300-foot-long cable, originally of diameter 5 inches, is submerged in seawater. Because of corrosion, the surface area of the cable diminishes at the rate of 1250 in 2 /year. Express the diameter d of the cable as a function of time t (in years). Homework Equations...

1. Homework Statement (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5) 2. Homework Equations Find an expression for the sum of the series. Give your answer as a product of linear factors in n. 3. The Attempt at a Solution I haven't tried it since I don't know what to do.

Homework Statement (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5) Homework Equations Find an expression for the sum of the series. Give your answer as a product of linear factors in n. The Attempt at a Solution I haven't tried it since I don't know what to do.

How do you come up with this approximation? [1+H(t-t_0)- \frac{1}{2}qH^2(t- t_0)^2]^{-1}\approx1+ H(t_0-t)+ \frac{1}{2}qH^2(t-t_0)^2+ H^2(t-t_0)^2 Is there a rule that leads to this approximation?

How is it possible...that the integral performs an infinite amount of calculations to give the area under a curve. The integral expression has to find an infinite amount of areas of the (dx by f(x)) rectangles. I'm guessing there is a simple answer to this, I'm just not quite piecing it...

In the lab you place a beaker that is half full of water (density pw) on a scale. You now use a light string to suspend a piece of metal of volume V in the water. The metal is completely submerged, and none of the water spills out of the beaker. Give a symbolic expression for the change in...

Homework Statement The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero. Homework Equations Electric Field...

Hello everyone, I have a bit of an issue regarding scaling of an expression. So, the scenario is as follows. I have a confidence value that can be associated with the solution given by an optimization routine and it is as follows: C = exp(-A)/(exp(-A) + exp(-B)) where A, B and C are...

Homework Statement Given vectors {\bf r}=\left[r_1,r_2,r_3\ldots{}r_n\right]^T {\bf e}=\left[e_1,e_2,e_3\ldots{}e_n\right]^T I need to write the sum \sum_{i=1}^{n}r_ie_i^2 in terms of {\bf r} and {\bf e} Homework Equations Nil. The Attempt at a Solution Without...