Division Definition and 469 Threads

Spivak's "Calculus," chapter 3 - problem 7 - a Homework Statement Prove that for any polynomial function f, and any number a, there is a polynomial function g, anad a number b, such that f(x) = (x - a)*g(x) + b for all x. (The idea is simply to divide (x - a) into f(x) by long division, until...

Homework Statement Show that for every integer n the number n33 - n is divisible by 15 Homework Equations The Attempt at a Solution Not sure what to do. I was thinking it might have something to do with both numbers are divisable by 3 ie the power = 3 x 11 and the divisor...

I know this is a silly question for a 12th grader to ask but I don't know the exact rules. If we divide 950 by 121, the first digit of quotient is 7, then we place a decimal after 7 and bring one 0 down, which is correct way. In the division of 21780/704, the first digit of quotient is 3...

Homework Statement how come that 16/64=.25 166/664=.25 1666/6664=.25 and any 1then n number of sixes / the same number of sixes then 4 = .25 same thing with 19 / 95 is there other strange division patterns?

Homework Statement Let R = { [ a + b*sqrt(m) c + d*sqrt(m) ] } [ n(c - d*sqrt(m)) a - b*sqrt(m) ] (Sorry if the matrix is unclear... I can't get it space nicely. r11 = a + b*sqrt(m) r12 = c + d*sqrt(m) r21 = n(c -d*sqrt(m))...

Im reading a paper about use of electron beams in oncology and it says: "The mechanism of neutron production in the region of electron beam energies under consideration is determined by photodivision of nuclei by bremsstrahlung photons and the small contribution of electrodivision by...

Hi. I'm a second year physics and astronomy major. I'm beginning to worry that I have entered these two majors with unrealistic expectations. The problem is that I developed my passion for physics throughout high school by reading popular science books like The Elegant Universe and Many...

Homework Statement Suppose that two people are dividing two cakes using the following rules: 1. The first person divides the first cake into two pieces in any fashion. 2. The second person then chooses which of the two cakes they will get to choose the first piece from. 3. The first person...

For some time I've been trying to get a geometric appreciation of why normed division algebras only exist in dimensions 1,2,4,8 (namely R,C,H,O). As always Baez provides the most elegant answer: http://math.ucr.edu/home/baez/octonions/node6.html" Allow me to descibe the key point of the...

what is: [log(log x)] / [log x]i would guess logx/1 but not sure

There is an article on wikipedia (http://en.wikipedia.org/wiki/Fourier_division" ) about Fourier division algorithm, but there is something that confuses me. When they compute the so called "b terms" they have to divide 2 numbers. Let's call them x and y, and x/y=q+r. To compute q and r they use...

Homework Statement Find the least positive rest in division of 7^35 with 5 Homework Equations (7^35)/5 The Attempt at a Solution 7^35=378818692265664781682717625943 => 378818692265664781682717625943/5... Uhhhhh this is not the way I am supposed to take right? :cry:

How do you get a vector to the power of negative one? I.E. : V ^ (-1)? Or inversion if that's what it's called? Thank you.

Consider the function g(t) = f(t)/t on [0,1], where f is measurable on [0,1]. Does it follow that g is measurable on [0,1]? I know there's a problem -- namely, division by zero -- only on a set of measure zero -- namely, \{0\} -- and that g agrees with the measurable function g_0 = g|_{(0,1]}...

Why division is not possible between vectors? We have seen in many books that there is vector addition, subtraction and multiplication .. but division between two vectors or more vectors is not anywhere... what is the reason of not having division in vectors.does it have any connection with...

Hello everyone, When a cell divide, do the organalles divide, or does DNA divide first, and using that DNA information new cells synthesize organalles. Thanks :smile:

Hello everyone, Quick question. I can understand proteins are needed to make everything in the cell, so if you inhibit bacterial protein synthesis, cell division can not occur. However my question is does the DNA replicate and divide, and then the cell can not make other things they want so...

I'm pretty much a beginner trying to wrap my head around the concept of voltage division within a circuit. To help myself out, I've come up with the following circuit. [PLAIN]http://img401.imageshack.us/img401/801/voltagedivision.gif I am having trouble determining the voltage between...

is it possible? I'm reading a proof where A is a local ring and f is a monic polynomial, v another polynomial in A[x] then the author says there is q,r with v=qf+r and degf<r. I thought the algorithm required divison of coefficients?! Maybe it's true we can always do this with f monic? thanks

Homework Statement Calculate v (refer to attachment). Homework Equations Voltage division: Vout = Vin x R2 / R1 + R2 The Attempt at a Solution V1 = V1 x R2 / R1 + R2 = 15 x 5 / 10 + 5 = 5V V2 = V2 x R4 / R3 + R4 = 5 x 2 / 10 + 2 = 0.83V V = 5 + 0.83...

Let R be a ring . Suppose that e and f=1-e are two idempotent elements of R and we have R=eRe \oplus fRf (direct sum ) and R doesn't have any non-trivial nilpotent element . Set R_1=eRe and R_2=fRf . If R_1=\{0,e\} and R_2 is a local ring , then prove that R_2 is a division ring . (note that e...

Find the quotient and the remainder when 15 is divided by 29. Use the division algorithm to write your answer as a linear equation (i.e., use the division algorithm to write 15 divided by 29 as a linear equation) I wrote 15=29*0+15 but this problem was marked wrong when I submitted it...

Something odd i noticed while playing around with primes. We have the set of prime numbers P and a p ∈ P. Define a function f:Q → N that will give the period of the repetition in the decimal expansion of some number r ∈ Q. 1) ∀ p ∈ P: ∃ n ∈ N: ∀ q ∈ P, q < p: f(q/p) = n. So n is...

Homework Statement I forgot how to divide this 1.) x^2 + 15 -8x divided by 3 - x I don't know how to start since 3 has nothing to do with x^2. The result from the book is 5 - x. I also don't understand this problem which uses trigonometric identities. if x = a sin theta then...

Homework Statement Let p(z) = \sum_{j=0}^{n} a_{n-j}z^j be a polynomial of at least degree 1 thus n \geq 1. Show that if z\neq 0 then 1/z is a root of the polynomial p. Homework Equations Fundamental theorem of Algebra The Attempt at a Solution If a expand the polynomial...

Homework Statement how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx Homework Equations using long division The Attempt at a Solution x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure

Homework Statement Show that g(x) = x^3 + 1 divides f(x) = x^{9999} +1. Homework Equations The Attempt at a Solution g(x) can obviously be factored into the irreducible polynomials (x+1)(x^2 - x + 1) in Z[x], and since f(-1) = (-1)^{9999} + 1 = 0, the factor theorem gives that (x+1) divides...

Homework Statement Problem 3.5.2 Let R be a ring such that the only right ideals of R are (0) and R. Prove that either R is a division ring or that R is ring with a prime number of elements in which ab = 0 for every a, b \in R. Homework Equations The Attempt at a Solution...

[SIZE="1"]This has been posted in another, but the wrong, section of the forum. That's why there are already quotes in it. Hello, Homework Statement I don't understand a step in the following integral: ∫(x-1)/(2x+1)dx = ∫(1/2)dx − (3/2)∫1/(2x+1)dx = (1/2)x − (3/4)ln|2x+1| + C The...

Homework Statement Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd. Let m be a positive integer. Show that a mod m = b mod m if a ≡ b(mod m) Homework Equations | means "divides," so a | b means "a divides b" or "b can be divided by a" mod gets the...

Homework Statement M and N are positive integers with M>N. The division algorithm for integers tells us there exists integers Q and R such that M=QN+R with 0\leqR<N. The division algorithm for real polynomials tells us that there exist real polynomials q and r such that xM - 1 = q(xN - 1) +...

Hi everyone, I was questionning myself about a problem that I have surely learn in school but I want to know if it's possible to solve a division with imaginary numbers without using the polar transformation. Example: \frac{2+2i}{1-i} So with the polar tansformation we have...

cosh = \frac{e^x + e^{-x}}{2} In the above definition, why there is division by 2? Is it there so that when x=0, y could be 1?

I am currently looking at a Tyco Electronics Multimode Relay MT. (Schrack division). I am wondering what it means in the description when it mentions CO contact configuration.

(Thread should be named: Question about proof of the division algorithm, sorry about that) Hi, I am reading this proof of the division article: http://xmlearning.maths.ed.ac.uk/lecture_notes/polynomials/division_algorithm/division_algorithm.php" I will write some of it here in case you don't...

What's the worst case for the factorisation of n using trial division? Worst case in terms of arithmetic operations that is. Many places tell me that it's n=pq with p and q prime and close to each other (and hence close to root(n) ), but I can't prove it. Help would be appreciated.

Well, I took a junior level classical mechanics course. We used Marion (the 4th edition). I guess I’m retarded or something because it just didn’t make a whole lot of sense to me… My professor didn’t help much either (most students “got him” but he just didn’t mesh with my learning style)…...

So I kinda got painted into a corner this upcoming quarter. I am trying to do a Math/Physics double major and with all the req's for both majors, I pretty much got no time to be taking easy quarters (unless I want to waste time going to school an extra year. I am 31 y/o, I still want to do grad...

Homework Statement Find tan(z) up to the z^7 term, where tan(z) = sin(z)/cos(z) Homework Equations sin(z) = z - z^3/3! + z^5/5! - z^7/7! + ... cos(z) = 1 - z^2/2! + z^4/4! - z^6/6! + ... The Attempt at a Solution Hi, Seeing as sin and cos have the same power series as for when...

Homework Statement For all x>2, \frac{2x²+2x-12}{x-2} simplifies to: 2(x - 2), x + 3, 2(x + 3)(x - 2), x - 2 or 2(x + 3). (Problem taken from http://www.analyzemath.com/practice_tests/act/act_sample_1.html" , question five). Homework Equations None, AFAIK. The Attempt at a...

Divide the polynomials by using long division. (-9x^6+7x^4-2x^3+5)/(3x^4-2x+1) When I attempted it I started by pulling using 3x^2 . multiplied that by the (3x^4-2x+1) and from there I had to use a fraction of 7/3 or something and then couldn't divide into x cubed. If anyone can...

Homework Statement Is mitosis the same as cell division? Homework Equations The Attempt at a Solution I want to say yes because mitosis is a type of cell division and when you speak of mitosis, it's usually referred to cell division. However, mitosis doesn't include all of cell...

Homework Statement When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2. Determine the remainder when the polynomial is divided by (x+2)(x-1). EDIT: Took out my attempts lol, there were way off. This was a "Math...

Homework Statement Theorem Let \alpha\neq0 and \beta be Gaussian integers. Then there are Gaussian integers \tau and \rho such that \beta=\tau\alpha+\rho and N\left(\rho\right)<N\left(\alpha\right) Problem Show that the Guassian integers \tau and \rho in the Theorem are unique if and only...

3rd roots in denominator Homework Statement \frac{ \sqrt[3]{25} + \sqrt[3]{5x} + \sqrt[3]{x^2} }{ \sqrt[3]{x} - \sqrt[3]{5} } Rewrite the expression with no roots in the denominator and it being simplified as far as possible.Homework Equations The Attempt at a Solution I'm.. stumped...

The question is "without a calculator, long divide 425/836. Round to the nearest hundredth. Estimate your answer before starting." My attemp at a solution: Well, my estimate would be approximately one half, since 400 divided by 800 would be 0.5; however, I'm not sure how to long divide a...

I am trying to solve: \frac{x^6+6x^3-2x^5-7x^2-4x+6}{x^4-3x^2+2} Using the polynomial long division algorithm. I order first the terms of the divident, and leave one blank space between -2x^5 and +6x^3 My problem is, I first put x^2 to the quotient, so I get x^4 * x^2 = x^6, but then I...

When finding the current in a 4+j3 balanced load star connected circuit. with 400V line voltage at 50Hz. Do you find the current by dividing the phase voltage approx. 230V by 4+j3 ohms? and if so. how do you divide normal numbers with complex numbers? your help is appreciated.

I assume everyone who saw this thread first rolled their eyes. Sorry for that. My question is an innocent one, as I am completely uneducated in number theory. My understanding is that numbers are grouped in a sort of Russian doll fashion, with each successive group encompassing all previous...

I apologies if this is in the wrong place! I'm a Computer science person with a keen interest in maths and occasionally the two topics cross paths. I am working on an matrix manipulation package in Java/C but seriously require some help with the maths, I am witting into it, parallelization at...