Simplify Definition and 385 Threads

I have tried two attempts at this and the strange this is - depending on where and how I apply my algebraic simplification (multiplying by s/s), I get a different answer. In attempt 1, I lose the integrator s=0 pole some how but in attempt 2, it's all fine. Attempt 1 Attempt 2 PS: I have...

This is the first time I am doing logic so the question is probably stupid, but could I just factorise (p∨t)∧[(r v¬r] or perhaps you cannot do that in Boolean algebra?

$$Re(e^{2iz}) = Re(\cos(2z)+i\sin(2z))=\cos(2z)$$$$e^{i^3} = e^{-i}$$ $$\ln (\sqrt 3 + i)^3=\ln(2)+i(\dfrac {\pi}{6}+2k\pi)$$ Can't I simplify these more? Are they correct? Final one:## (1+3i)^{\frac 1 2}## Can I write in in term of ##\sin x## and ##\cos x## then use ##(\cos x+i\sin x)^n=\cos...

For the dipole moment I calculated $$\begin{aligned} M &= \int \rho(\mathbf{r}) \mathbf{r} \times \mathbf{E}(\mathbf{r}) d^{3} \mathbf{r} \\ \mathbf{E}(\mathbf{r}) &\approx \mathbf{E}(\mathbf{0}) + \sum_{i=1}^{3} \nabla E_{i}(\mathbf{0}) \cdot \mathbf{r} \\ \mathbf{M}_{D} &= \mathbf{p} \times...

I know that ##∇(A⋅v)=(A⋅∇)⋅v+(v⋅∇)⋅A+v×(∇×A)+A×(∇×v)## The third term ##v×(∇×A)## simplifies to ##v×B##. I'm just now sure how to "get rid" of the other terms. I tried checking for some vector identities but couldn't make any headways. Any guidance?

I know that 1/sqrt(2) can be multiplied by sqrt(2)/sqrt(2) to give sqrt(2)/2 How can I do something similar with 1/cuberoot(2) ?? What is the trick?

I'm trying to prove the statement ##n^2 + 1 < n!## for ##n \geq 4##. My proof by induction looks way too contrived. Is there a way to simplify it? Here's what I got. For n = 4, ##n^2 + 1 = 17 < 4!##. So, the statement is true for n = 4. Now let's assume it's true for n = k, that is, ##k^2 + 1 <...

hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my...

Basically surface B is a cylinder, stretching in the y direction. Surface C is a plane, going 45 degrees across the x-y plane. Drawing this visually it's self evident that the normal vector is $$(1, 1, 0)/\sqrt 2$$ Using stokes we can integrate over the surface instead of the line. $$\int A(r)...

I am evaluating this formula, it's real value is 0. but maple can't further simplify it?

Hi, This is a pretty simple question, but I am new to Mathematica so I am not sure if I am missing something obvious. Question: How do I make the expression ## e^{log(z)} ## return z? Attempt: I have used all of the following combinations and all of them return ## e^{log(z)}##. Are there any...

So this is the circuit. And here i tried to calculate Uout/ Uin , any suggestion how to simplify this term?? I used Uout= Uin * (1+ Z2/Z1)

simplify $\left(\dfrac{a^2b^3-2a^{-3}b^3}{2a}\right)^2=$ OK this could get confusing quickly but I don't think we want to square it first

$\tiny{8.aux.27}$ Simplify the expression $\dfrac{{\cos 2x\ }}{{\cos x-{\sin x\ }\ }} =\dfrac{{{\cos}^2 x-{{\sin}^2 x\ }\ }}{{\cos x\ }-{\sin x\ }} =\dfrac{({\cos x}-{\sin x})({\cos x}+{\sin x\ })}{{\cos x}-{\sin x}} =\cos x +\sin x$ ok spent an hour just to get this and still not sure suggestions?

eg ##\cos (\sin x)## Asking this question out of curiosity.

See attachment. I don't understand the solution given by David Cohen. I am sure this is a shortcut explanation. I don't like shortcut explanations. 1. What in the problem indicates that x > 1? 2. What in the problem indicates that x < 2?

I don't know how to start with the factorization. $$\frac{(-1)^{2/9} + (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}{(-1)^{2/9}- (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}$$ Any hints would be nice. Thank you.

I'm a bit confused on the derivation above. I understand what the goal of the derivation is, as it derives Gauss's Law using the solid angle, but i was wondering if someone could kind of fill in the steps the author skipped and explain the use of the solid angle.

I'm not sure how to simplify this without spending a lot of time on it. Is there a pattern that I need to weed out?

I tried to find logic behind how do we simplified the circuit as given for 2 hours and I unable to find any clue. I can do it just by following rules but I am unable to get intuition. I tried to make sense of it but how can we even make two points as one.

The following is the questions given. I solved the first one, which steps are shown below. But I am not sure if this is how the question wants me to solve the problem. Would you tell me if the way I solved the problem is the proper way of simplifying the expression using euler's formula...

I could simplify the expressions in the numerator and denominator to (1+x^n)/(1+x) as they are in geometric series and I used the geometric sum formula to reduce it. Now for what value of n will it be a polynomial? I do get the idea for some value of n the simplified numerator will contain the...

Hi all, I'm new to Demorgan's theorem and hence am dumbfounded on how people actually simplify the equation by just looking at it. I was wondering if there are any tricks to doing so and I will appreciate it if someone can teach me. In the example of this question, what I can only simply come...

Let's see how many people can answer this one right. Give your answer, with no work so that everyone will get a chance to answer it fairly! The problem is:Simplify:(1 + i)^8, given that i is an imaginary number.Answer will be posted in a few days!"Sciences are the laws by which God set the...

I recently saw a threat that stated:"For the present you just have to accept that in particle physics the mathematics are way ahead of the explanation and no one is prepared to play 'catch up'."after just two days lurking around on this forum, i'd have to say they this quotation is one of the...

Hi, I've just started getting into physics but a lot it still confuses me. I was wondering if any of you smart people could help me. Since I'm only an 8th grader if you dummied it down to the most simplest form as possible that would be great. Thanks

Hello,I am trying to describe the following in terms of a sum of cos and sin:cos(Wa*t + Phia) * cos(Wb*t + Phib)Hope that i did everything correct, what i get is:= cos [(Wa - Wb)*t + Phia - Phib]+ (1/2) * cos [(Wa - Wb)*t + Phia - Phib]+ (1/2) * cos [(Wa + Wb)*t - Phia - Phib]+ (1/2) * cos [(Wa...

Vectors with magnitudes and angles, seems a little complicated, perhaps someone could explain it to me how to do it in trig?Thanks.

k is a constant that can be reduced in half until you get the smallest value with which to evaluate the functions. The slope of a nonvertical line can be found by dividing: y/x, and a triangle with a hypotenuse h a base b and the other leg l has the property of: l/b=h._____________________Late...

1) Integral (del X V) dot d(sigma) = 0 if S is a closed surfaceYeah I kind of stared at this one, then moved on, im sure there is a very simple relationafter applying stokes theorem, but I cant see it.2) Show that A= (1/2)(Bx r) B = del X A is satisfied by any constant vector B (any...

Hello, I am having difficulty matching my answer to text book for the following question. Anyone?Simplify the following:(e^x+e^-x)(e^x+e^-x) - (e^x-e^-x)(e^x-e^-x)/(e^x+e^-x)^2The answer in the text is 4/(e^x+e^-x)^2Thanks for the help!!

Simplify the following:(A or B) and (B or C) and (C or D) and (D or A)42 is just another number

Hey, I am having a really rough time with this question and was hoping that someone out there could lend me a hand. The question is as follows:Using the Fresnel equation:r(perpendicular) =- sin(theta(incident) -...

I have an assignment that has a problems I must solve by means of quadratic approximation.I really hate my Calculus book and I plan to burn it one of these days because it rarely (if ever) explains anything.How would you use quadratic approximation to approximate something like...

alright. This isn't a hard problem but for some reason I can't figure it out. So someone help simplify this expression....The cube root of x (or x to the 1/3 -- I mention it both ways so there's no confusion but it's written as the cube root of x) times the square root of x cubed, all over the...

By substitution I've solved that $$z_u = 0$$ (which is correct according to textbook) which leads me to try find z by integrating $$z = \int z_v \,(dv ?)$$ and I'm just stuck here. Dont know how to integrate that.

Solve the boundary value problem Given u_{t}=u_{xx} u(0, t) = u(\pi ,t)=0 u(x, 0) = f(x) f(x)=\left\{\begin{matrix} x; 0 < x < \frac{\pi}{2}\\ \pi-x; \frac{\pi}{2} < x < \pi \end{matrix}\right. L is π - 0=π λ = α2 since 0 and -α lead to trivial solutions Let u = XT X{T}'={X}''T...

i can get to 3i+1/1-3i but no further. I take it this is the correct way to start

I see that when n is an even number, the product can be represented as ## \frac {2n} {(n+1)} ##. When n is an odd number, the denominator seems to be changing and I am not able to define an expression for it. How should I go about solving this? Thanks

four variables a,b,c,d here is the equation: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd) wondering if this can be simplified to something much smaller

f(x)=2xand g(x)=2^x Find the composite function of fg(x) fg(x) =f(g(x)) =f(2^x) =2(2^x) I don’t understand how this in turn equals to 2^(x+1) [Moderator's note: Moved from a technical forum and thus no template.]