Simplify Definition and 371 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...

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.]

How? Taken from HiSet free practice test

Hi I have to simplify this square root fraction: 10/√5 + √20 The answer is 4√5, but I do not get to that answer. Please help.

3m+m=4m 4m +2k =6mk Is this correct, help please if not correct Thanks

Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5 This one throws me off because I don't know how to deal with the z, as only on the right side of the divide

Hey, I have this chaotic system. It is a modified Hamiltonian Chaotic System and it is based on Henon-Heiles chaotic system. So I have this functions (as shown below). I want to know how can I make it as a discrete function. Like, how can I know the value for x dot and y dot. 1. Prefer to know...

Homework Statement [/B] Homework Equations [/B] The Attempt at a Solution Could someone check my answer please ?

Homework Statement Simplify the Boolean expression : Homework Equations - The Attempt at a Solution [/B] Here is my work : Could someone check my answer please ?

I'm trying to simplify the combination defined as : \binom{n}{\frac{n}{2}}. I did some calculations, starting from the factorial formula \frac{n!}{(\frac{n}{2})!(\frac{n}{2})!} and i found this form : 2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})... but i don't know how to continue...

Problem 1: 1 / (2x-y) - 2 / (x+2y) = ? The answer is: (4y-3x) / (2x^2+3xy-2y^2) Please explain.Problem 2: f(x) = 4x/(1-x) and g(x) - 2/x, then f(g(x)) = ? The answer is 8/(x-2) Please explain.Problem 3: Square Root of a / (1+ Square Root of a) = ? The answer is (Square Root of a - a)...

How does r∪(-p∩q∩-r) simplify to r∪(-p∩q) ? The second expression is just the first with the "-r" gone at the end. I'm not seeing how to get from the first expression to the second using any of the basic laws like distribution, de morgan, tautology, etc. What am I missing?

Please help with this algebra II question. It needs to be simplified. Thank you.

In the above equation for Dirac energy, is it trivial to note that given: Principal quantum number n Orbital angular momentum quantum number l(max) = n - 1 Total angular momentum quantum number j = l + 1/2 = n - 1/2 Then nr = n - j - 1/2 = n - (n - 1/2) - 1/2 = 0 and the energy expression...