Division Definition and 469 Threads

I am reading "Algebra: An Approach via Module Theory" by William A. Adkins and Steven H. Weintraub ... I am currently focused on Chapter 2: Rings ... I need help with an aspect of the proof of Corollary 2.4 ... ... Corollary 2.4 and its proof read as follows: In the above proof of...

As far as I know, vectors can only be added, subtracted, or “multiplied” by dot or cross product. Does this mean that you couldn’t divide f-> by a-> to get m using the vector form of Newton’s second law? This would require dividing a vector by a vector, which seems to not be allowed.

I am starting my senior year this spring semester. I have been looking at Applicant Profiles and Admission Results on physicsGre forum, and it honestly made me a bit depressed and anxious. I am an international student at a large state school known for its physics program. I have no research...

Is this true? If the remainder of f(x) / g(x) is a (where a is constant), then the remainder of (f(x))n / g(x) is an I don't know how to be sure whether it is correct or wrong. I just did several examples and it works. Thanks

Hey, I have often times wondered what is multiplication? Repeated addition is OK but for some reason it doesn't satisfy me. For example: 2*2cm is linear because it scales 2cm on the same dimension but 2cm*3cm is not scaling, it spans 2 dimensions. It seems as if the flow of operation takes a 90...

Hey everyone, The Short Story: I need to choose 5 classes from the below list that will make me marketable after graduation aside from an internship. The Long Story: I'll be entering my final semesters this coming year. I, mostly, have only electives left. I have to take at least 5 courses...

According to the synthetic division done below, what was the original polynomial and what number do we know is a root of that polynomial? Explain how you know to receive full points. I know what the polynomial is, but I thought the root of this polynomial would be 1 but it's actually -1 could...

Homework Statement Upper Bound[/B] If all of the numbers in the final line of the synthetic division tableau are non-positive, prove for ##f(b)<0##, no real number ##b > c## can be a zero of ##f## Lower Bound To prove the lower bound part of the theorem, note that a lower bound for the...

Hi, I am looking into Reed Solomon codewords and I am looking at this paper. On page 16 the author divides M(x) by G(x) I am struggling to see how he has arrived at 14501 with a remainder of 63. Would someone be able explain what he did?

Hello everyone. Iam working on a course in digital control systems and by reading my textbook I stumbled over this expression. C(z) = 0.3678z + 0.2644 : z^2 − 1.3678z + 0.3678 = 0.3678z^−1 + 0.7675z^−2 + 0.9145z^−3 + ... Now Iam wondering how the result of the polynomial division is...

Is there any chance someone can help me solve this? Music teacher with absolutely no idea how to solve this. Thanl you so much. ? w!81 = 26r3 (the goal is to find the first number, and explain how you figured it out)

Hi, First of all, if this is wrong forum, I apologize; please direct me to the correct one. I have 4 * 8-byte integers, representing 2 rational numbers (i.e. 2 pairs of a nominator & a denominator). The 2 rational numbers have the same mathematical value, but different nominator & denominator...

We know division by zero is not possible but what is the math reason why it is impossible to divide by zero?

Homework Statement Determine the current through each circuit element Homework Equations V = IR (Ohm's Law), The Attempt at a Solution I1 is .06A after plugging 6V and 100 ohms into V = IR, but I can't figure out the rest, because I don't know how the current splits. The left path obviously...

"A standard FDM scheme for telephone signals is to multiplex 12 voice channels, each occupying 4kHz bandwidth, into a group signal with 48kHz. The next basic building block is the 60-channel supergroup, which is formed by frequency division multiplexing five group signals. The next level of the...

Homework Statement Here we divide the mole balance by the volume ##4*\pi## ##*## r2##*##dr and take lim as dr->0(standard procedure) 1) How exactly he makes the transition from equation from 6 to 7? Exercise #2(see below please) Solution for Problem#2 2)Why does he divide here by...

First of all, I didn't know where to put this in general math or differential equations. Let's start with the basic, x/0 = α. Where α is every number and decimal number from -∞ to +∞, by rearranging, we get x = 0α, x= 0, therefore only 0/0 = α. Now, we can integrate this with graphs. Take the...

Homework Statement Hi I am trying to understand this http://math.stackexchange.com/questions/341406/how-do-i-obtain-the-laurent-series-for-fz-frac-1-cosz4-1-about-0 So the long division yields...

Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. public class SphereVolumeCalculator { public static void main (String [] args) { double piVal...

Hi everyone. I'll start my master's degree in physics next year. My plan is to continue my studies in theoretical condensed matter physics. So I've decided to increase my knowledge in this area. In my undergrad I took some courses like Intro. to QFT and Many-Body physics. Also I have studied...

Hello, I will take Classical Mechanics I (upper division) course fall of 2017. I have not seen Mechanics material since fall of 2014 and would like suggestions on how to review the concepts prior to taking the class. I was pretty good in that class and do not need to "re-learn" anything per...

Homework Statement Three identical balls fit snugly into a cylindrical can: the radius of spheres equals the radius of can, and the balls just touch the bottom and the top of the can, If the formula for the volume of a sphere is V = 4/3 PI * radius * radius * radius, what fraction of the...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with understanding some remarks that Matej Bresar makes in Chapter 1 ... The relevant text is as follows: My questions...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.3 ... ... Lemma 1.3 reads as follows: In the above text by Matej Bresar we read...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows: My questions related to the above proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

Homework Statement So I thought I knew how to do synthetic division but ran into this problem 4a^4+4a^3-9a^2-4a+16 / (a^2-2) Homework EquationsThe Attempt at a Solution [/B] All the examples I can find don't have a second degree polynomial in the denominator. i.e. they are a-3 or a+2. How...

The question is : If x > 0 and I divide x by y, the quotient is 3 and remainder is 7. If I divide y by x the remainder is 12. what is the value of x? So far I used long division quotient form to make 2 equations... 1. x/y = 3 + 7/y 2. y/x = Q(quotient) + 12/x so 1st equation i solve for y and...

{a,-a,0} ∈ Z For a set to have inverse under an operation, all elements must be able to be combined with another element of the set under that operation, after which the product of combination under said operation yields the identity element of that operation. My question is, this is a...

NO TEMPLATE BECAUSE MOVED FROM ANOTHER FORUM Hello, I've been trying to figure out how it works for complicated problems, I know how to use long division, but I'm not understanding how this process is done for a problem like I have. Instructions: Write the function in the form ƒ(x) = (x -...

for example 100,539/2 in mod 1,000,007. is there a systematic procedure to calculate this ??

Let P(x) be a polynomial of x. Show that there exists a polynomial Q(x) such that P(x)Q(x) is a polynomial of $x^3$

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows: In the above text, in part 4...

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows:In the above text, in part 4 of...

I read this interesting thread trying to find an answer to my questions (and I got even more confused). I study radiometry units in context of computer graphics. I have a few questions, starting from the basic ones: 1. Following AlexS's note, why is speed=distance/time and not distance*time? 2...

If two oocytes are considered, does taking the nuclear material of one and transferring to the other's nucleus start the division of it ?

why is vector division not possible?

I have column from E5 -->E35 which contains values for each box. another column from F5-->F35 contains values for each box I have a sums column, H5-->H35,, which contains values for the sums between the E and F boxes (E5+F5=H5 ;;; E6+F6=H6 etc...) I want a division column inside J5-->J35 which...

i am trying to divide x^3+(1-k^2)x+k by (x+k) but i can't do this can you show me how to.

Dividend: 4x^3 - 6x - 11 Divisor: 2x - 4 In this problem above, the dividend lacks a variable to the second power, so we have to add a 0x^2 to make it: 4x^3 + 0x^2 - 6x - 11 Question: Why do we add 0x^n? (n = missing powers) In regular long division, we do no such thing. Why do we have...

Hello! (Wave) I have applied a lot of times the euclidean division of $x^6-1$ with $x^2- \alpha^{a+1} (\alpha+1)x+ \alpha^{2a+3}, a \geq 0$, $\alpha$ a primitive $6$-th root of unity. But I don't get the right result... (Sweating) We are over $\mathbb{F}_7$. I got that $x^6-1=(x^2-...

Hey! :o Let $R$ be a finite non-trivial ring. We suppose that for each $r,s\in R$ with $rs=0$ then either $r=0$ or $s=0$. I want to show that $R$ is a division ring. Could you give me a hint how we could show that each element $x\in R\setminus \{0\}$ has an inverse? (Wondering)

During cell division there are different processes that take place like prophase,metaphase,anaphase etc...I don't understand about chromatin condensation and chromosomal condensation that happens during these processes.Can some one explain how the chromatin material changes itself in different...

Take a number r that is n-digits long where n is finite. so if r =2385813... $$r_1r_2r_3...r_n$$ $$r_1 = 2$$ $$r_2 = 3$$ $$r_3 = 8$$ etc.. I postulate (since I don't know this is true): Every such number can be expressed as a division between two other numbers, say a and b. $$r = \frac{a}{b}$$...

My question is: suppose you have a function ##F(x)## which has an asymptote at ##x=x*##. Can you decompose ##F(x)## so that $$F(x) = G(x) + H(x)$$ where ##G(x)## is defined at ##x=x*## and ##H(x)## contains the asymptotic behaviour at ##x=x*## and goes to ##0## at plus or minus ##\inf##? This is...

I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or...

Homework Statement Find the load resistor current for 4 different resistors. Homework Equations Current Division The Attempt at a Solution I need to use current division to find the load resistor current for 4 different resistors, but I am not sure how to apply it here. I have I_norton and...

I would love someone to verify the answer for equation 8 in this paper (bottom of page 263) http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2028.2002.00368.x/epdf For the sake of clarity here is the equation is LaTeX which you can render at the following link \frac{QC + Q\lambda \sigma -...