Expression Definition and 999 Threads

Homework Statement Verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=∅(x) in each case.Homework Equations \frac{dX}{dt}=(X-1)(1-2X); ln(\frac{2X-1}{X-1})=t The Attempt at a Solution I know I need...

Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...

Hi all! I'm studying electrical generators, and while I was trying to come up to the expression of EMF induced in a conductor I got two different results following two different ways, and I can't find the error. With sinusoidal B, with e=bvl I get an RMS value E=2K_{f}f\phi, while with...

Homework Statement <Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr or the second example in the "Substitution" section here: http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf Homework Equations nada. The Attempt at a Solution Nothing to really attempt, I just...

Find expression for event "exactly one of A,B,C occurs" Homework Statement Let A,B,C \in F be three arbitrary events. F is a σ-algebra. Find an expression for the event "exactly one of A,B,C occurs". The Attempt at a Solution Define i,j,k s.t. i,j,k \in \{1,2,3\} \wedge i \not= j \not=k...

Homework Statement I am trying to solve the following two systems of equations and at every attempt I get completely stuck. x2 + y2 = 1 -x + √3y = 0Homework Equations not applicableThe Attempt at a Solution the answers have already been given to me but I have no idea how to get the answers...

Homework Statement I am trying to find when the square root of the expression 25+8a^2 is rational, where the number a also needs to be rational. \sqrt{25+8a^2}=b, where a and b are both rational numbers. I am trying to get an expression for a in terms of some other number m, which would always...

Good Day, I need some help with the following problem. I do not know how to generate a linear equation connecting y and x from the expression below as the 4 seems to complicate things \(3^y = 4(3^{x-2}) - 1\) Could some one please care to give me some advice? Thanks in advance.

Can anyone help me simplify the expression \frac{\delta g_{\mu\nu}}{\delta g^{\kappa\lambda}}? I haven't seen a term like this before and I don't know how to proceed. It seems like it might be the product of some kronecker delta's but I'm not sure.

1. The problem statement. AC voltage is expressed as 240 cos(2765t - 45°). Im trying to find the: Peak Voltage: RMS Voltage: Average Voltage: Peak-to-Peak Voltage: The Attempt at a Solution Peak Voltage: 240v RMS Voltage: 170v Average Voltage: 0v Peak-to-Peak Voltage: 480v...

\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \\ \frac{1}{(\frac{x - 3}{x -...

Homework Statement ~AB+AB~c+ABC Homework Equations AB+A~B=A [b]3. The attempt at solution ~AB+A A+B

Homework Statement Given successive terms of numbers starting from the 1st term: 11, 21, 35, 53, 75, 101,... What is the general expression of the nth term? where n is positive integer Homework Equations /The Attempt at a Solution Can't find a good attempt.

I have to simplify (or get it in terms of tan I guess?) \cot (\frac{2\pi }{3} - x) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this?

Simplify (x+3)1/2 - (x+3)3/2 i honestly am so lost on this one how i approached it was (x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)] but again, i have no idea what I'm doing.

Hii Every one, In one paper I read that, {\displaystyle \sum_{j\geq1}\left(\frac{c*m*logm}{2^{\left(\frac{j-1}{2}\right)}}\right)}^{j}<=m^{o(logm)} with the explanation "Since the sum is of the same order as its largest term". c>0, m>=2. m is an integer. Can anyone pls...

Hii Everyone, Plz tell me a tight upperbound for \frac{x}{1-x\left(1-y\right)} where o<=x,y<=1 regards, Bincy

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...

I have an expression with piecewise functions. the code looks like: function a() %some constants here f = 0:0.001:20; r1 = 0.05; p = something-f.*(something/something); for i=1:100 r1= R(p); end for i=1:100 r1 = R(P); y1(k,:) = r1...

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 Hello! I'm stuck and confused. I've been browsing the web, and reading books but can't seem to get it right. I've been looking for the mathematical expression for product of Inertia. I've managed to understand the 50% of it. But I'm stuck on the first part...

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.