Numbers Definition and 1000 Threads

The real numbers $$x$$ and $$y$$ satisfy $$x^3-3x^2+5x-17=0$$ and $$y^3-3y^2+5y+11=0$$. Determine the value of $$x+y$$.

Prove that all polynomials with real coefficients, having complex roots can occur in complex conjugates only. It's easy to prove in a quadratic equation... ## ax^{2} + bx + c = 0 ## ## \displaystyle x = \frac{-b \pm \sqrt(b^2 - 4ac)}{2a} ## But how to prove the same in general? Please...

Hi, I have some theories about physical facts derived from the size of powers in physics, compared to the first fraction of an irrational number. I do not know if this is redundant with present day science, but I am curious about it. Regards, Justin

I have a list of chaos numbers Average each 10 results as display below Sum each 10 results as display below Average the 30 results as displayed below here’s my question: I believe that I can see as the average goes up we have larger sums So I think I can predict something from the last...

Hi everyone, I've been bumping on this problem for a while and wondered if any of you had any clue on how to approach it. My question is whether the following equality is possible for 4 distinct prime numbers : PxPy + Pw = PwPz + Px where Px, Py, Pw, Pz are odd prime numbers, and each...

Determine all 3 digit numbers P which are divisible by 11 and where $$\frac{P}{11}$$ is equal to the sum of the squares of the digits of P.

Homework Statement An eight digit number is a multiple of 73 and 137. If the second digit from the left of the number is seven, find the 6th digit from the left of the number. Homework Equations N.A. The Attempt at a Solution I don't know any clear method for solving this problem...

"Simple" Line Integral in Complex Numbers If anyone could please double-check my final result for this question it would be greatly appreciated. Rather than write out each step explicitly, I'll explain my approach and write out only the most important parts. "[E]valuate the given...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...

you can list and match up all rational numbers with irrational numbers this way.. lets say i have an irrational number 'c'. Rational->Irrational r1->cr1 r2->cr2 . . . rn->crn There exists an irrational number that is not on this matching, (not equal to any of the crx's) this...

I'll write down what i know and point it out if I'm wrong.So we normalize the wave function because -∫|ψ(x,t)|^2dx should always be equal to 1 right? Has this anything to do with transition from ψ to ψ^2?

I can find for example Tan(2x) by using Euler's formula for example Let the complex number Z be equal to 1 + itan(x) Then if I calculate Z2 which is equal to 1 + itan(2x) I can find the identity for tan(2x) by the following... Z2 =(Z)2 = (1 + itan(x))2 = 1 + (2i)tan(x) -tan(x)2 = 1...

we all know Fibonacci numbers,just for information they are the numbers of sequence whose $$t_n=t_{n-1}+t_{n-2}$$ and $$t_0=t_1=1$$ $$\text{PROVE THAT:}$$ $$1+S_n=t_{n+2}$$ where, $$S_n=\text{sum up-to n terms}$$ $$t_n=\text{nth term}$$

Please I have read texts about changing the bases of numbers but still I have difficulties in doing, may s'body instruct me for example.. Change 3145 to base 8 Thanx..

This is a solved problem and I am having a hard time working through the answer. Question . Choose two numbers uniformly but without replacement in {0,1,...,10}. What is the probability that the sum is less than or equal to 10 given that the smallest is less than or equal to 5? Answer...

I guess the best way to start this is by admitting that my conceptual understanding of the Cauchy-Schwarz Inequality and the Lagrange Identity, as the title suggests, is not as deep as it could be. I'm working through Marsden's 3e "Basic Complex Analysis" and it contains a proof of the Cauchy...

I have found some trouble in trying to prove this question.please help mw with that. Q1) If (a+b)/2 is a rational number can we say that a and b are also rational numbers.? Justify your answer. I have tried the sum in the following way. Assume (a+b)/2=p/q (As it is rational) Lets...

I keep hearing even by very brilliant Engineering co-students that they require a lot of text-based theory before going into numbers. However, there is also a good deal of good Mathematicians that state they can think in numbers, requiring theory, but not strictly in a text form, or at least an...

I was recently given the challenge to take a string of numbers (ages) and + x - / to equal another number (age). As part of the challenge each number can only be used once and you must only use numbers here to do multiply, add to, subtract from or divide by. NUMBERS 7 9 11 37 45 45 47 75...

Sorry about the intriguing title; this is just a continuation of the discussion in https://driven2services.com/staging/mh/index.php?threads/5216/ from the Discrete Math forum. The original question there was how to introduce mathematical induction in a clear and convincing way. Since the current...

There are lots of examples of numbers where "is it a rational number" has been an open question for a while before being proved as not being rational. Pi and e being famous examples. Some of them are still open, like pi+e, or the Euler-Mascharoni constant, but I think the general consensus is...

Can the arithmetic mean of a data set of complex numbers be calculated? if so, can the method be demonstrated?

Hi All, I'm trying to figure out the probability of winning the lotto. 8 numbers are drawn between 1 and 45. The first six are 'winning' numbers, the last two are the 'supplementary' numbers. To win division 1, you need to get all six winning numbers right: \binom {45}6 = 8145060 Hence...

Find all 10-digit numbers ##a_1a_2a_3a_4a_5a_6a_7a_8a_9a_{10}## (for example, if ##a_1= 0##, ##a_2## = 1, ##a_3 = 2## and so on, we get the number 0123456789), such that all the following hold: - The numbers ##a_1,~a_2,~a_3,~a_4,~a_5,~a_6,~a_7,~a_8,~a_9,~a_{10}## are all distinct - 1 divides...

I'm trying to understand the notation (3, 1, 2/3) for the up quark and (3, 2, 1/6) for the left-handed up and down quarks... Is the first number related to SU(3), the second SU(2) and the third I believe is the hyper charge... Not sure what the significance is of the first two numbers... I...

Homework Statement Graph the following numbers on a complex plane. A) 3-2i B)-4 C)-2+i D)-3i D)-1-4i Can smomeone help me how to get started on this question? I'm not sure what it wants me to do

How do you prove/disprove the following: For any integer n higher then 1, there exists at least one prime number in interval [n+1, n^2]?

Homework Statement If ##f## is continuous on ##[a,b]## and ##f(a) < f(b)##. Prove that there are numbers ##c, d## with ##a \le c < d \le b## such that ##f(c) = f(a)## and ##f(d) = f(b)## and if ##x \in (c,d)## then ##f(a) < f(x) < f(b)##. Homework Equations The Attempt at a...

First I'll write what I know: Algebraic number: one of the roots to a polynomial over rational numbers. Polynomial: A function for x. Example: ##f(x) = x^2-2## although I won't write the ##f(x)## part when writing a polynomial. Root of a polynomial: All values for x where the polynomial is...

is there any way to prove or disprove the statement: y=3x^2+3x+1 is prime for all x belongs to natural numbers...

draw on a argand diagram |arg(z + 1)| = \dfrac{\pi}{2} I got the correct drawing... but I'm not sure why it's correct. What I thought was arg(z + 1) = \dfrac{\pi}{2} and that's a half line from the point (-1,0) going upwards, and arg(z + 1) = -\dfrac{\pi}{2} and that's a half life...

Homework Statement Prove that their are an infinite amount of primes by observing that in the series 2^2+1, 2^{2^2}+1,2^{2^3}+1,2^{2^4}+1,... every 2 numbers are relatively prime. The Attempt at a Solution I was going to take 2 of the numbers in the series and look at their difference...

a + b + c = a * b * c where a, b, c are positive integers. I can think of only one solution to this. {1, 2, 3}. Is there any other solution to it? Can you prove or disprove?

I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...

Arrange the numbers: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 such that the summation of each two successive numbers is a complete square easy interesting question

I took the prime numbers from this link: http://nl.wikibooks.org/wiki/Wiskunde/Getallen/Lijst_priemgetallen I did take the first three lines I did the following with the numbers The prime 11 = 1+1 = 2 The prime 13 = 1+3 = 4 The prime 17 = 1+7 = 8 and so on This is the result for the...

Let E(x) denote the number of numbers relatively prime to x. Please help me prove that the function E(x) is multiplicative,i.e., E(xy)=E(x).E(y)

http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

My linear algebra uses "Kyle Numbers" to compute some kernels. But it does not elaborate on what they are and how they are used to compute the kernel? Please help.

I have a question about the HUP. As I understand the HUP, it only applies to conjugate attributes that do not commute, such as position and momentum. However, many good quantum numbers do commute, so does this mean that the HUP does not apply to simultaneous measurement of such good quantum...

Given n numbers x1,x2...xn belong to N. x1+x2+x3...xn=m How many different combinations of x1,x2,x3...xn are there?Is there any formula useful here? Note:x1,x2,x3... need not be distinct and also can be 0. Thanks

Let's start with: $$ \int \frac{dx}{1+x^2} = \arctan x + C $$ This is achieved with a basic trig substitution. However, what if one were to perform the following partial fraction decomposition: $$ \int \frac{dx}{1+x^2} = \int \frac{dx}{(x+i)(x-i)} = \int \left[ \frac{i/2}{x+i} -...

Let p[n] be the following property of Fibonacci numbers: p[n]: f_{n+1} * f_{n-1} - (f_{n})^{2} = (-1)^{n}. Prove p[n] by induction. This is the proof I wrote. i used regular induction. Is weak induction sufficient to prove it or do I need to prove this by strong induction? proof: BASE STEP...

matrix inversion with complex numbers?? or faster way? Homework Statement The Attempt at a Solution i managed to get the answer, but it took me like 30min. to work this by hand. i probably worked it differently than my instructor's method above, but wat i did was get the coefficients of V...

Problem Statement: Do the sieve of Eratosthenes from 2 to 100 and find all the primesSo I'm trying to do the sieve of Eratosthenes in fortran 90 (I'm using Plato IDE)My efforts to solve this/ method to use: Obviously, I want the program to do a LOOP starting with every whole number from 2...

Hi guys, I've been trying to help a friend with something that I learned in class but I'm now finding it hard to solve myself. The problem goes as follows: Use geometry to show that |z3-z-3| = 2sin3θ For z=cisθ, 0<θ<∏/6 Now, I chose ∏/12 as my angle and plotted all this on an Argand diagram...

Homework Statement The question : http://gyazo.com/7eb4b86c61150e4af092b9f8afeaf169 Homework Equations Sup/Inf axioms Methods of constructing sequences ##ε-N## ##lim(a_n) ≤ sup_n a_n## from question 5 right before it. I'll split the question into two parts. The Attempt at a...

Are Transfinite numbers accepted as genuine numbers?

Homework Statement I'm trying to convert something like 1.25^-03 into it's standard number composed of standard decimals using a calculator (0.0125) - if you know what I mean. Thanks.

Let me start by writing about the natural or counting numbers. The story of how, where and when we invented them is lost in the misty dawn of history. But perhaps our African ancestors, like our living simian cousins (and some other animals) evolved the ability to distinguish between few and...