Expression Definition and 999 Threads

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)

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 +...

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...

if you have a sequence of events {A_1, A_2, ...} then an expression for the event that "infinitely many A_i's occur" is: U(n = 1 to inf, U(m = n to inf, A_m) ) but wouldn't U(n = 1 to inf, A_n) also satisfy this?

1. Simplify ei6x(1+e-i10x)/(1+ei2x) 2. i have no idea how to simplify this its supposed to be in terms of cosines 3. i don't how i can simplify this such that i can use the 1/2(e^x +e^-x) = cosx formula

ok .lets say the expression we have is ex the taylor expansion becomes 1+x+x2/2+... integrating becomes x+x2/2+x3/6+...+c so how do we know that c = 1? for it to become back to ex becos it is said that integral of ex = ex do we just let x be 0 to find c = 1? does it work for all...

Homework Statement Hi I have an expression on the form \frac{\tau }{{\alpha - \varepsilon + i\eta }}\left( {1 + \frac{\tau }{{\alpha - \varepsilon + i\eta }}G} \right) where i denotes the complex i. I have to bring this into the form \frac{\tau }{{\alpha - \varepsilon +...

Given 2NO(g) + Br2(g) <--------_____> 2NOBr(g), Concentration (M) [NO] [Br2] [NOBr] Initial 2.5 5.0 1.0 Change P Q...

Homework Statement The expression {\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}} has a volume integral equal to 4\pi for arbitrary "a". Homework Equations The Attempt at a Solution \int_0^R {\int_0^{\pi /2} {\int_0^\pi {{\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}}...

Homework Statement I'm looking for a closed form expression for the partition function Z using the Canonical Ensemble Homework Equations epsilon_j - epsilon_j-1 = delta e Z = Sum notation(j=0...N) e^(-beta*j*delta e) beta = 1/(k_B*T) t = (k_B*T)/delta e N is the number of excited...

Homework Statement Rearranging an equation...can't quite see how it's done. Homework Equations r=\sqrt{2.5^{2}cos^{2}(t/2)+5^{2}sin^{2}(t/2)} r=2.5\sqrt{cos^{2}(t/2)+4sin^{2}(t/2)} r=2.5\sqrt{1+3sin^{2}(t/2)} The Attempt at a Solution I know that cos^{2}(x)+sin^{2}(x)=1 but...

Hi, I have a problem on how to convert the imaginary parts of expression into all real parts. For example: x1 = - (a + ib) x2 = (a + ib) x3 = - (a - ib) x4 = (a - ib) My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used...

[/tex]1. Homework Statement [/b] Given: \phi(x)=\phi^+(x)+\phi^-(x) Where: \phi^+(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a(\mathbf{k}) \mathrm{e}^{-\mathrm{i}kx} and \phi^-(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a^\dagger...

Books for self-teaching previously taken math courses, and other problems :) What I want to focus on: While I am a CS student, I am also interested in mathematics subjects as a whole and want to re-familiarize myself with some of the courses I took in the past. I received high grades, but to...

Hello everyone...can anyone tell me what is the modified expression for the gravitational potential in GR which takes into account the fact that the speed of gravity is finite (c, to be precise)...In fact, it may be a non-sense question as I haven't started to read GR yet...Is there any...

Factoring a very long expression! please help (x^6) - (4x^5) + (x^4) + (10x^3) - (4x^2) - (8x) then: x((x^5) - (4x^4) + (x^3) + (10x^2) - (4x) - 8) my teacher skipped many steps and ultimately found: x * [(x+1)^2] * [(x-2)^3] I guess he's assuming we know how to get through it. Can...

how to solve this hamilition? and Does this expression has an exact solution?

I must derive the 1/4th life expression for a first order rxn. ln(\frac{[A]_{\circ}}{[A]_{t}})=kt ln(\frac{[A]\circ}{\frac{1}{4}[A]_{\circ}})=kt_\frac{1}{4} ln(4)=kt_{\frac{1}{4}} do I set t=1/4 ? \frac{ln(4)*4}{k} \frac{5.545}{k} What am I doing wrong here? The answer is allegedly...

Homework Statement Sketch the graph of a function g(x) with a corresponding domain on (-5, infinity) whose first derivative is always positive and whose second derivative is always negative. Then come up with and algebraic expression to model your graph. Homework Equations The Attempt at a...

Homework Statement Convert the following expression into sum of products and products of sums (AB+C)(B+C'D) Homework Equations Distributive Property The Attempt at a Solution for product of sums it would be (AB+C)(B+C'D) since it is already in this form. When calculating sum of...

Homework Statement Show that the expression A, T(dP/dT)|V - P is equal to expression B, T^2 * [d(P/T)/dT]|V Also, show that expression C, -[d(P/T)/d(1/T)]|V is also equal to expression B Homework Equations A: temperature * (dPresure/dTemperature at constant volume) -...

Homework Statement Given z(t) as above, write out the expression for the vertical velocity Homework Equations z(t)=Asin(vt) where z(t) is the vertical position of a test particle, A is the amplitude of its motion, and t = 0 is the time when the particle is at the midplane The...

I need the following expression simplified. 36/[64.4*(0.5+(2+ x)*((1-(1/4)*x^2 )^0.5)) ]-x*((1-(1/4)*x^2 )^0.5)=0

Homework Statement Black body radiation inside a cavity at temperature T may be thought of as a gas of photons with an energy distribution given by the function n(E) given by n(E)dE = A [E^2 / (e^(E/kT) - 1) ] dE Where A is independent of E and T. (k is Boltzmann constant) The...

Homework Statement Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to...

The Attempt at a Solution I'm attempting to solve a question with a few unknowns, and I managed to get it to the following form: tanx(1-cosx)=0.25 I just can't seem to simplify it further and thus solve.. Any ideas?

Homework Statement Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.Homework Equations The Attempt at a Solution Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I...

Homework Statement The limit of \frac{8x^3+x^2-5x}{3x^4-5x^2+2} as x goes to 1Homework Equations Evaluate this limit algebraically.The Attempt at a Solution Tried using 1 instead of x. The denominator becomes 0. Divided denominator by (x-1) but couldn't continue.

Homework Statement Derive an expression for the temperature of an ideal blackbody so that its radiated light at the peak intensity wavelength has exactly enough energy to excite the ground state to fourth excited state. Homework Equations I = σ*T4 λm*T = 2.9 * 10-3 m * K E = hf = hc/λ...

Homework Statement f(x) = \frac{x}{x-1} + \frac{x+1}{3x} Homework Statement need to take the first derivative of this expression... I can do it but I am curious as too why i cannot take the derivative of \frac{x}{x-1} and then just add it to the derivative of \frac{x+1}{3x}...

By 'equivalence', I mean of the computational kind -- i.e. in the same way any universal computer can emulate any other. First of all, hi there, I'm not sure I put this question in exactly the right forum, but it seems to me that most dualities currently being discussed fall under the...

Ship A is located 3.3 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B? (b) Write an expression for the position of A relative to B as a...

Hello, geniuses! :) I am having a problem in chemistry... What is this systems equilibrium constant expression? And under what conditions (temperature, pressure, concentrations) you can most fully get rid of SO2? I really have no idea with what to start... :/

Homework Statement What is the totaly power emitted by the sun over all wavelengths (frequencies) according to the (incorrect) classical Rayliegh-Jeans expression for ρt(v) Homework Equations ρt(v)dv=8piv^2kT/c^3 dv The Attempt at a Solution I'm not sure how to start this one...