Expression Definition and 999 Threads

Homework Statement (-3/x^(1/2)) / ((2/y^(1/2))-8) which, from my book, I see can be rewritten with radicals as: (-3/sqrt(x)) / ((2-8sqrt(y))/(sqrt(y)))The Attempt at a Solution Now, what I don't understand is how the denominator was rewritten. I understand that in the numerator, the 1/(...

My higher secondary book says that momentum[p] is equal to 'mv' where 'm' is mass and 'v' is velocity.Then it was also mentioned that the force[f] was dependent on the rate of change of momentum{[delta]p= m*[delta]v}. Though the book mentions various examples to support that momentum plays a...

lim as x -> 0, [(x+4)1/2-2]/x That's the limit I want to evaluate. I keep running into problems getting to the real limit (1/4). You don't have to give me the answer, but let me know if I'm missing something simple. Or you can just give me a hint.

I'm trying to find the general form for the nth derivative of f(x) = \frac{1}{x^m \log x} where m can be anything (set m = 1 for instance). For ease, you can take m to be integral. It sounds surprisingly simple, but the most I've been able to say is f^{(n)}(x) = (-1)^n x^{-(m+n)}...

Homework Statement hi i have been given the following electric field phasor E=(z(5)+x(10))e-jpi(y) mV/m Mr=100 er=3 Homework Equations The Attempt at a Solution i have been able to deduce from the results above that wave is traveling in positive y direction. intrinsic...

Homework Statement n(n+3)(n+6)(n+9)=x-81 Show that x is a squared expression Homework Equations These are some examples they give you: 0*3*6*9=92-81 1*4*7*10=192-81 2*5*8*11=312-81 The Attempt at a Solution To be honest, I have know idea where to start. So, I'd like a push in...

Homework Statement Show that the change in internal energy of a simple system between states (V1, T1) and (V2, T2) is given by ∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dVHomework Equations dU=dQ-pdVThe Attempt at a Solution As U is a function of...

Hi, I'm getting used to the anti-symmetric bracket notation used with indices and I can't seem to find the Weyl Tensor written fully out. So I want to make sure I get it. Here is my attempt in dimension 4...

My problem is this: I have an algebraic expression, and I want to express it in terms of one variable divided by another. It's a fairly large expression, and I'd like to do it in mathematica before attempting it by hand. I've tried Simplify, FullSimplify and Solve, but none of these have done...

Hi,i ve problem about C.i should write a program that read expression from standart input take derivative and print. For example: input: (X^2-1)*tan-ln^2/X output: (((X*2)*tan+(tan^2+1)*(X^2-1))-(1/X*ln*2*X-ln^2)/X^2) I converted expression to postfix form by shuting...

Homework Statement \frac{d}{dx} x+\sqrt{x} Using the definition of a derivative, no rules allowed. Homework EquationsThe Attempt at a Solution \frac{d}{dx} x+\sqrt{x} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0}...

Homework Statement Construct a circuit from the Boolean equation: Homework Equations P v (~P ^ ~Q) The Attempt at a Solution According to the textbook, I am supposed to go from right to left, working on the outermost part of the expression to the innermost part. I read this as...

I must construct a circuit from the following Boolean expression: P v (~P ^ ~Q) From my understanding I am supposed to go from right to left, working on the outermost part of the expression to the innermost part. I read this as saying even though the outermost part of the expression is on...

Homework Statement The plastic rod of length L shown in the figure has the nonuniform linear charge distribution λ =cx, where c is a positive constant. Find an expression for the electric potential at point P on the y-axis, a distance y from one end of the rod. V = ?Homework Equations V = 1/4πϵ

Is this expression (-5+12√3)/26 the same as (12-5√3)/26 ? Thanks

Homework Statement If n is an integer which leaves remainder one when divided by three, then (1+√3i)n + (1-√3i)n equals a) -2n+1 b) 2n+1 c) -(-2)n d) -2nThe Attempt at a Solution Multiply and divide each of the two expression inside bracket by 2. 2n(cosπ/3 + isinπ/3)n + 2n(cosπ/3-isinπ/3)n On...

Homework Statement For the following circuit, obtain an expression for the capacitor voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V. Homework Equations KVL Definite integrals, differentiation etc The Attempt at a Solution Right so I...

I need some help. I don't know how to make the intgral symbol, but here's the question. If somebody can get it started it'd be awesome. 1to e^10 1to e^6 1to e^2 1/xyz dxdydz

Homework Statement From Prussing and Conway (Q1.11): derive an expression for the eccentricity e in terms of the initial speed v, radius r, and flight path angle x (they use gamma). Homework Equations (1) h^2 = mu*a*(1-e^2) [a is semimajor axis, mu is gravitational parameter] (2) h =...

If a and b are real numbers, and we know that (2a-b-3)^{2} + (3a+b-7)^{2}=0, how much is 3a-7b Any ideas on this? I'm guessing the solution can go two ways: either i find a and b separately, or i calculate the expression above somehow and i'll be left with 3a-7b

Homework Statement x^2 + x + \frac{1}{4} Homework Equations This should be written in the form: (x+y)^2 Just to add a bit more info, the exercise is to "Write each of the following as the square of a binomial expression". So basically the book teachs to take the rook of x^2 and 1/2...

Hi guys, I am hoping you can either point me in the right direction here or show me how to do this a bit. the problem is as follows: "a particle with weight 86.8 N is positioned at r= (8.1t)i - (7.2t-9.4t2)j. t is in seconds. Find an expression for angular momentum, L and torque, T which act...

Homework Statement Find an expression for x(t) and plot on graph T < 0 < 3T v = 4 for t < 0 = 1 for t >= 0T is time const. Homework Equations Voltage across capacitor cannot change instantlyThe Attempt at a Solution Well the transfer equation is \frac{X}{Y}(jw) = \frac{2+jwC}{1+jwC}...

Homework Statement find the minimum value taken by the integral expression integral from 0 to pi/2 [(y')^2]-(y^2)+2xy dx y(0)=0 y(pi/2)=pi/2 The Attempt at a Solution using euler lagrange d/dx(2y')-(-2y+2x)=0 2y''+2y-2x=0 from here I'm stuck

Homework Statement The potential energy of a system of two particles is inversely proportional to their separation, d. Find an expression for the radial force that each particle exerts on the other. Homework Equations The Attempt at a Solution I'm really stuck on this one guys...

Homework Statement I'm trying to derive the \epsilon - NTU Expression for a double-pipe counter flow heat exchanger. I know what I need to do the only problem I am having is: I don't know how to algebraically go from ln( \frac{\Delta T2}{\Delta T1} ) = -UA ( \frac{1}{Ch} + \frac{1}{Cc} )...

I am working through a problem from a Fluid Dynamics course and I have gotten to a point on a problem where it says to "… expand the resulting expression for small values of a2/(bz) and for small z/b … " I am not so sure how to interpret this? The expression that I am supposed to expand is...

Hello, I have this expression: 2(x-3)(x+2) + (x-3)^2 It is simplified to: (x-3) (2x+4+x-3) I understand how the (x-3) has been separated to start the simplification process, but I cannot grasp how the rest was done. Can someone please tell me the rest was simplified ? Thanks...

very sorry, this does not belong in this forum.

hello everyone,:wink: okay. i am stuck here now. i was experimenting and though why can not i enter an expression at once. you understand what i am trying to achieve. i am newbie to programming so achieving this is beyond me so you tell me:smile: in the output "((7+7)*9)/9" is a string. is...

While this is not technically an assignment for any particular class (that I'm aware of, at least), I think the nature of this problem makes it suitable for this forum. Please, inform me if I should direct my question elsewhere. Find x>3 such that ln(x)<x^0.1 (hint: The number is "huge")...

I mean "equation", not "expression"..sorry. I think I have issues with squared unknowns at the denominator. My big question is whether I STARTED OUT solving this equation correctly, or did I overcomplicate things perhaps? Attached is the problem with my attempt. I'll be happy for some...

can someone please tell me what is the value of the following expression when x=\infty: -xe^{-x} my guess is it is either -1 or 0 or -infinity...

I am attempting to do a simple volume integral over a particular shape. However Mathematica will not simply return an answer. For my input Volume = Integrate[ Integrate[Integrate[1, {z, 0, c}], {y, 0, b}], {x, 0, a}] + Integrate[ Integrate[Integrate[1, {z, c, c + a}], {y, b/2, b...

When we are calculating the scattering amplitudes in QFT, we often encounter something like \int \frac{d^Dp}{(2\pi)^D} \frac{p^\mu p^\nu}{(p^2+\Delta)^n} and we often make the substitution for the numerator p^\mu p^\nu \rightarrow \frac{g^{\mu\nu}p^2}{D} It looks like...

How is this expression for angular frequency in an L.C.R. circuit derived- w = (1/LC - R2/4L2)1/2 (I came across this while solving a problem)

Homework Statement Use the Boltzmann expression where v is the vibrational quantum number to complete the following table. Vibrational State Populations Molecule D2 (v=3115) F2 (v=917) I2 (v=214.5) Find Nv/No for 389 K and 1899 K Assume gv = go = 1 Homework Equations Nv/No=(gv/go)*...

the expression to integrate is: \int x^{3}e^{x^{2}}dx and in the spirit of "LIATE" I set my u and dv as the following: dv=e^{x^{2}}dx u=x^{3} however, doing this that I integrate dv=e^{x^{2}}dx in order to get v...and unless I'm missing something, this does not seem like an easy...

Trying to help out a friend. I appolagise if yet again this is in the wrong part of the forum, i haven't an idea what it is categorised as, I am an apprentice engineer and simply that lol Can someone explain how the following is done: x^2 – x + 1 / (x - 2)(x^2 + 1) ≅ A / (x - 2) + Bx +...

Homework Statement Determine an expression for the electric potential at a point P a distance z away from the center of a thin uniformly charged rod on the line that bisects the rod. Homework Equations V=k\frac{q}{r}\hat{r} The Attempt at a Solution I've defined r to be the...

Jacob Bernoulli's expression for e: n-> LIM (1+1/n)^n converges much slower than n-> LIM (n-1/n+1)^(-2/n) is this a better expression for e? edit! n-> LIM (n-1/n+1)^(-n/2) sorry for the typo!

I'm really not sure how to approach simplifying something such as this. Could anyone offer any advice?

Homework Statement A sound source moves at a constant velocity. A listener is standing at a distance L away from it. Given that the source moves in a straight line at a right angle to the listener and starts closest to the listener (ie at t=0) deduce an expression for the frequency heard by the...

I'm unsure if this regular expression can be simplified, if it can, could you please explain how? Thank you! (a U b)*(a U e)b* U (a U b)*(b U e)a* The e is the empty string, and the U stands for union.

Homework Statement write down the Lagrange-Charpit eqs for \frac{ \partial u}{ \partial x} \frac{ \partial u}{ \partial y} - y \frac{ \partial u}{ \partial x} - x \frac{ \partial u}{ \partial y}= 0 and use them to show \frac{ d^2 p}{ d p^2} = P assuming that u = x^2 when y=0...

After doing various searching through the google, most of the circular error probability I found are expressed interm of \sigma_x and \sigma_y, which the CEP(circular error probability) usually looks like (assume normal distribution): P(r) = \int\int...

Homework Statement I'm trying to understand an example in the book. They're simplifying the following expression: S=z \oplus (x \oplus y) =z'(xy'+x'y)+z(xy'+x'y)' I don't get how they go to this from the above =z'(xy'+x'y)+z(xy+x'y') =xy'z'+x'yz'+xyz+x'y'z Homework Equations DeMorgan law...

Hey there, I got a problem with one recast of an expression which pops up by considering the completeness relation of common spherical harmonics: \sum_{l=0}^{\infty} \sum_{m=-l}^{+l} Y_{lm}(\theta,\phi)Y^{*}_{lm}(\theta^{\prime},\phi^{\prime}) = \frac{1}{sin(\theta)} \delta(\theta -...

Homework Statement Find the exact value of each expression: a) sec-1(\sqrt{}2) b) sin-1(1) Homework Equations sec\theta=\stackrel{}{}1/cos\theta The Attempt at a Solution I've never learned this, but I am really curious in how it is solved. Is there a formula for this? Thanks!

I'm trying to find the time derivative of the following function, where E is a constant, spatially uniform vector field, and B is as well, but B varies with time. \frac{d}{dt}\left(\frac{\vec{E}\times\vec{B}}{B^2}\right) Remembering that B is time dependent and E is not, I've calculated the...