# complete

1. ### Are complete groups abelian?

Hi: Let $G$ be a group and $G'$ it's commutator subgroup. Then $G > G' > 1$ is a series of normal subgroups of $G$. Suppose $G$ is complete. Then, if I'm not wrong, $Aut(G)$ is the stabilizer of that series. But then, by a theorem, $Aut(G)$ is nilpotent of class <= 1, that is $Aut(G)' = 1$ and...
2. ### Factor out the GCF of the three terms, then complete the factorization

Ok, I don't even kind of understand this problem... Please help! (Cool) Factor out the GCF of the three terms, then complete the factorization of x4+9x3+14x2.

Hello, I wanted to know about the total course of Mathematics. So I was just trying to create an entire list of Mathematics Courses. Here is the broad section I have devided. 1. School Mathematics 2. BSc Mathematics 3a. MSc Pure Math 3b. MSc Applied Math But when I am going to list each section...
4. ### prove q are not complete

From the definition : Q is complete iff every non empty bounded from above,subset of Q HAS A sUPREMUM IN Q,WE CAN INFER that Q is not complete: if there exists a non empty,bounded from above subset of Q that it has no Supremum belonging to Q. So the main idea is to find a non empty ,bounded...
5. ### Eigenvalues of complete partite Graphs.

The eigenvalues of complete bipartite graph(Km,n) is given by the expression ±√m*n , 0(with multiplicity k-2). Where k is number of nodes in the graph. I am looking for generalization of the expression for eigenvalues of complete n-partite graphs. Does such a expression exists for complete...
6. ### Complete the square

My question is in the image.
7. ### How Many Days to Complete Work

A contractor joined 60 men to build a house in 60 days. After 16 days, he was joined by 70 more men. In how many days will the work be completed? I need the equation set up.
8. ### complete space

Hi, I need help to prove that the space of sequences of natural numbers X={xk} endowed with the following metric is complete: d(X,Y)=1/min{k:xk is different from yk} Thanks in advance
9. ### Find Indefinite Integral: Complete the Square

Must I complete the square of the denominator? If so, after completing the square my answer is (x+1)^2 + (1/2). I then set a to be sqrt(1/2) and u to be x+1, which means dx = du. Is this right so far. Can someone rotate this picture for easy reading?
10. ### Using matrix to complete the square

Given a quadratic form: x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2, find the symmetric matrix that defines this, row reduce this matrix into row echelon form, and use this upper triangle matrix to complete the square and write the quadratic form as the sum/difference of squares...
11. ### Graph or complement contains complete graph

I am trying to prove that given any graph G on 4^n vertices, either G or its complement contains K_n (the complete graph on n vertices) as a subgraph. I am tutoring students who have not had any graph theory, and they are supposed to approach the problem combinatorially (supposedly just applying...
12. ### Structural Induction on complete quaternary trees.

question is little bit computer science related and long , but i will try to explain if there is any question. SO basically , we have to prove a complete quaternary tree and colour its leaf node(the bottom node) with 3 colour . There exists a binary complete tree that has a pair of node with...
13. ### How do you complete the square with a negative coefficient?

Hi guys basically I have got a bit of a problem with completing the square... If I had to complete the square of x2-14x+36=0 I would form the square of (x-7)2 I would then expand the brackets to get x2-14x+49 I would then combine this with the original equation to get x2-14x+49+36=0...
14. ### Do we have a complete knowledge of calculus or is it a study in development?

I was wondering since I never hear of anyone studying mathematics to do advance "calculus". More generally, can calculus be categorized as a pure math?
15. ### Exdraft - Complete worked solutions to first year math problems

Hi everyone, Exdraft is a website, but in essence it is web-based software that provides full step-by-step solutions to math problems typically encountered in first year university. The cool part is that you can plug in your own values for these problem templates, and obtain worked...
16. ### Give a complete graph of each polar equation

Give a complete graph of each polar equation and also identify the type of polar graph. I have no idea how to do this problem and how the solutions came up with all these answers for cos theta and r = 2+2costheta r = 2+2costheta In the solutions manual, it says its a "cardioid" polar...
17. ### complete

good evening or good morning
18. ### How many functionally complete ternary connectives are there?

Knowing that Nand and Nor are the only functionally complete binary connectives, how many ternary connectives are there?
19. ### Complete the square to find center and radius of the sphere

I have an odd problem in my book that i am trying to solve but dont have the solution to. Can anyone help me? Find the center and radius of the sphere whose equation is: x^2 + 2x +y^2 - y + z^2 = 0 Attempt: (x^2 + 2x + 1) -1 (y^2 - y - 1/4) + 1/4 + z^2 = 0 (x^2+1)^2 + ( y^2 - 1/2)^2 + z^2 =...
20. ### Number of subgraphs within a complete graph

How many subgraphs with at least one vertex does K3 (a complete graph with 3 vertices) have? I know that K3 is a triangle with vertices a, b, and c. From asking for help elsewhere I was told the formula for the number of subgraphs in a complete graph with n vertices is 2^(n(n-1)/2) In this...