Numbers Definition and 1000 Threads

$x,y\in R$ $if: \sqrt {3x+5y-2-m}+\sqrt {2x+3y-m}=\sqrt {x-200+y}\,\times\sqrt {200-x-y}$ $find:\,m=?$

Homework Statement problem in a pic attached Homework Equations The Attempt at a Solution i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got...

Wikipedia is not very clear on this. Is there a known computable normal number? I found this paper: http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf But I'm not sure if it's been peer reviewed.

What is the significance/physical interpretation of Fractional Occupation Numbers in DFT?

Homework Statement Prove the formula xcscx=2B(ix)-B(2ix)Homework Equations B(x)=x/((ex)-1) sinx= (eix-e-ix)/2i The Attempt at a Solution I know that it makes sense to use the formula for B(x) with x=ix and x=2ix, and rewrite xcsc(x) as x/sin(x), plugging the above relevant equation in for...

I want to solve y''+y'+y=(sin(x))^2 and try to use y=Ae^{ix} but then when I square it I get A^2 e^{2ix} I found y' and y'' and solved for A and it didn't work I guess I could use the formula for reducing powers but I would like to try and get around that.

Parition function for Boson "gas" with two quantum numbers Let's say that we have a system of non-interacting Bosons with single-particle energies given by, \epsilon_{p,m} = \frac{p^2}{2m} + \alpha m where m = -j, ... ,j and we want to calculate the partition function of this...

Okay, so this is a problem I've been pondering for a while. I've heard from many people that pi doesn't repeat. Nor does e, or √2, or any other irrational or transcendental number. But what I'm wondering is, how do we know? If there truly is an infinite amount of digits, isn't it bound to...

Homework Statement Let f(z) = z3-8 and g(z) = f(z-1). This information applies to questions 1-5. 1. Express g(z) in the form g(z) = z3+az2 +bz + c 2. Hence, solve g(z) = 0. Plot solutions on an Argand diagram. Homework Equations Factorisation i2=-1 The Attempt at a Solution I have done...

Homework Statement Hello Assume that we have n complex numbers u: u_1,u_2,...,u_n, and n complex numbers v:v_1,v_2,...v_n I would like to prove that: |\Sigma_{i=1}^nRe(u_i\bar{v_i})| \le |\Sigma_{i=1}^nu_i\bar{v_i}| I guess this can be written simpler: |\Sigma_{i=1}^nRe(z_i)| \le...

Hello :smile: Homework Statement The orbital quantum number for the electron in the hydrogen atom is l = 4. What is the smallest possible value (in eV) for the total energy of this electron? (Use the quantum mechanical model of the hydrogen atom.) Homework Equations The Attempt at a Solution...

Hello my name is Dax, I'm currently in the world building stage of a science fiction I am writing and I came here to bounce some questions off of you fine people. My question is regarding atomic numbers of elements on the periodic table and weather it could be possible that negative atomic...

Find natural numbers a and b such that $2^a-3^b = 7$

Homework Statement This is the solution, the question was find its domain. Homework Equations How does |X| (less than or equal to) 4, when a negative number is inputed into -2x how does that = a positive number?The Attempt at a Solution On the graph to me All X values < 0 should be negative...

Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$

can you help me solve this just using one variable the sum of two numbers is 9 and their difference is 6. what are the numbers? thanks!

I noticed that there are some odd looping numbers in pi Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn ) The process is...

Homework Statement Is there a real number c such that the series: ∑ (e - (1+ 1/n)^n + c/n), where the series goes from n=1 to n=∞, is convergent? The Attempt at a Solution I used the ratio test by separating each term of the function as usual to find a radius of convergence, but that doesn't...

The problem is as stated: Prove that $$F_1*F_2+F_2*F_3+...+F_{2n-1}*F_{2n}=F^2_{2n}$$ But earlier in my text I proved by induction that $$F_{2n}=F_1+F_2+...+F_{2n-1}$$. Do I need to use this earlier proof in my current proof. I tried adding $$F_{2n+1}F_{2n+2}$$ to the right and left hand side...

I have been looking at material properties such as thermal expansion of metals which usually involves very small coefficients. The general equation of thermal expansion is usually L_\theta = L_0 ( 1 + \alpha \theta) where L is the length and theta is the temperature change. The coefficient...

I just finished reading the "Reality Bits" in a recent copy of NewScientist. It discusses attempts to purge mathematics of the need for complex numbers. Started me thinking(danger, danger) of not how to get rid of the square root of negative one, but, more easily, simply find out where it enters...

Homework Statement Solve the equations: 3(z-2) = 2j(2z+1) and (i-2)z-z*=3i+1 where z* is the complex conjugate of z. (I am assuming z and z* are the unknowns. i and j are basically the same since they're defined as i2 = j2 = -1?) Homework Equations Rules for solving...

this is the program which i wrote: #include<iostream.h> #include<conio.h> #include<stdlib.h> void prime(int p) { if(p==0||p==1) { cout<<"neither prime nor composite"<<endl; getch(); exit(1); } for(int i=2;i<p/2;i++) { if(p%i==0) { cout<<"composite"<<endl; break; } else...

I understand the definition of real numbers in set theory. We define the term "Dedekind-complete ordered field" and prove that all Dedekind-complete ordered fields are isomorphic. Then it makes sense to say that any of them can be thought of as "the" set of real numbers. We can prove that a...

Hi, We know that if we have two complex numbers in polar format (i.e., magnitude and exponential), that for two complex vectors z1 = A*exp(iB) z2 = C*exp(iD) If z1 and z2 are equal, then A = C and B = D. However, this is assuming these values are all real. What if they are complex...

Hi everyone, i am just wondering why I cannot find a list of Charge Conjugation and Parity numbers for all the appropriate particles? I mean, I can look online and sift through sources for individual particles (for example, after some research I have found the the photon has a charge...

Hello everyone, I'm new to this forum. I have this Linear Algebra question that I have no clue how to solve. Any help would be much appreciated. :) The question goes as follows: The polynomial p(x) = x3 + kx + (3 - 2i) where k is an unknown complex number. It is given to you that if p(x) is...

Homework Statement . Prove that, given constants ##A_1,A_2, \phi_1## and ##\phi_2##, there are constants ##A## and ##\phi## such that the following equality is satisfied: ##A_1\cos(kx+\phi_1)+A_2\cos(kx+\phi_2)=A\cos(kx+\phi)## The attempt at a solution. I've tried to use the...

Hello I am writing a program where program will randomly generate a three digit number from 100 to 999 and then user will be asked to guess that number. If the number is matched exactly, then the highest prize is given to the user, if all digits in a guess are also in the original number...

I am studying programming for the first year so I don't have whole lot of experience. I am interested in how to work with super-large numbers, numbers that are much, much larger then the included Int or _int64. I mean some 100, 1000 .. 17 million (largest prime) digit numbers. How do they do...

I talked with an old friend of mine. We discussed prime numbers and Ulams Spiral, and the mathematical patterns that surround us all. He brought up something called the Zeta-Function and something about -1 1/2 and how this all related to prime numbers. I did a google search and found some...

An easy question. All "odd" number can be expressed as a sum of consecutive natural numbers. Example: 35=17+18 35=5+6+7+8+9 35=2+3+4+5+6+7+8Question: Demonstrate that prime numbers (except for the "2"), can only be expressed as the sum of two consecutive natural numbers.

$x_0,x_1,-----,x_{2004} \in Z , \, x_0=0, \mid x_n \mid =\mid x_{n-1}+1\mid $ $for, \,\, 1 \leq n \leq 2004$ (1) $find :\,\, min\mid x_1+x_2+x_3+ ------+x_{2004}\mid $ (2) get a set of numbers $ x_1,x_2,-----x_{2004} $ satisfying your answer

Hi lovely people, I recently came across a video http://www.youtube.com/watch?v=w-I6XTVZXww that said if you add all of the natural numbers from 1 to infinity, the answer is... What do you think it is? Infinity or something like that? They said it was -1/12. I watched the proof but I don't...

HI - what is the best textbook, website or another resource to learn about ordinal numbers (Alph -0, Alph-1, etc) and their properties? I don't even know if there is a specific subfield of set theory that they fall under. Thanks!

Hi, In BIDMAS (brackets, indices, division, multiplication, addition, subtraction) it shows clearly that indices should happen before subtraction, so why does -52=25? Because the real working (according to BIDMAS) should put the square first and then put the negative sign on, which would mean...

How to calculate <n_i ^2> for an ideal gas by the grand partition function (<n_i> is the occupation number)? In other words, I like to know how do we get to the formula <n_i>=-1/\beta (\frac{\partial q}{\partial\epsilon}) and <n_i ^2>=1/Z_G [-(1/\beta \frac{\partial }{\partial\epsilon})^2 Z_G]...

How would it make any sense to use dimensionless numbers to represent physical things? From wikipedia: If you are comparing the strength of forces, and you are using these numbers to do so, I would have thought that these numbers would represent units of - well, force. Clearly I must...

The set of the real numbers is closed. For me this is nearly trivial (*) but perhaps I miss something; a colleagues insists that there are some deeper considerations why this is far from trivial - but I don't get his point (*) A) A set is closed if its complement is open; the complement...

Compute $\sqrt{2000(2007)(2008)(2015)+784}$ without the help of calculator.

Homework Statement Show that (a^b)^c can have more values than a^(bc) Use [(-i)^(2+i)]^(2-i) and (-i)^5 or (i^i)^i and i^-1 to show this. Homework Equations The Attempt at a Solution I'm writing out the second one as the first one is long: i^i = e^ilni lni = i (\pi...

I am studying complex numbers and, hard as I try, I cannot see great difference between them and the conjugate numbers known and used since 500 B.C. (http://en.wikipedia.org/wiki/Quadratic_formula#Historical_development) to solve a quadratic equation p/2 \pm \sqrt(p/2 ^2\pm q) where the sum...

Homework Statement convert 14.334 to the base 16 to a no. to the base 10 Homework Equations sum ofeach no.*its poand take position weigth The Attempt at a Solution the integer part 14 will be 4*16^0+1*16^1=20 to the base 10 the decimal part 0.334 is my problem i multiply 0.334 *16...

Homework Statement z=1-i e^{iz} = ? I have to solve this problem and than picture it. Homework Equations The Attempt at a Solution e^{iz} =e^{i(1-i)}=e^{i+1}=e^i*e I don't really understand how to picture this result. I assume their is an other way, in which the result has a...

I know I am jumping ahead, as I am still working through part 1 of Spivak's Calculus, and am absolutely not properly equipped to prove his properties (if they are indeed provable). However, as I am trying to work on my proofing skills, my interpretation thus far has been, that these 12...

http://en.wikipedia.org/wiki/GE_Wind_Energy The rotor swept area is 4657 m^2, and wind speed is 11.5 m/s. Produced power 1.5MW. I assumed that the air density is 1.2kg/m^3, and computed, that the theoretical upper limit for produced power would be 4.25MW. This was obtained by computing the...

Can someone explain in simple terms "K mixing level" and "K selectivity" in nuclear decay processes ? ...as it relates to the "K quantum number". And does it relate directly to the nuclear angular momentum?...and selection rules? How so? Dumb it down for me please. Thank you kindly.

Homework Statement If m and x are two real numbers where m ε Integers, then e2micot-1x{(xi+1)/(xi-1)}m, (where i=√(-1)) is equal to : (a) cos(x) + isin(x) (b) m/2 (c) 1 (d) (m+1)/2 Homework Equations The Attempt at a Solution I seriously have no clear cut idea of how to...

Hi When we talk about a fluid moving at low Mach numbers, it is said to be incompressible. But does this mean that the flow is incompressible (i.e., material derivate is zero) or does it imply that the fluid itself is incompressible (constant density)? If anybody has a reference (book...

What are the critical numbers of f(x) = (x2+3)/(x-1) I took the derivative and found f'(x) = (x+1)(x-3)/(x-1) so I thought the critical numbers were 3, ±1 ...sadly, this is incorrect. I always thought the definition of a critical number was where f'(x) = 0 or DNE. But for this to be...