Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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0
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1answer
117 views

Let $x = 2441921$. Factor $x$ into a product of primes.

Let $x = 2441921$. Factor $x$ into a product of primes. I found that: $1519^2 −x=−134560= −2^5 ·5 · 29^2$ and $1541^2 −x=−67240= −2^3 · 5 · 41^2$. I am trying to figure out what to do from here. ...
1
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3answers
58 views

Solve the equation: $\frac{z}{z-5}+\frac{1}{3}=-\frac{5}{5-z}$

Solve the equation: $\frac{z}{z-5}+\frac{1}{3}=-\frac{5}{5-z}$ First $z$ cannot be equal to $5$. First, I multiplied $z$ with $3$, $1$ with $z-5$ and $-5$ with both. Eliminating the denominators ...
0
votes
3answers
42 views

Dividing line segments with ratios vs. fractions [on hold]

I know that 2:3 is actually 2/3. So when you split a line segment by a ratio, you would add 2 and 3 to get a fraction of 2/5 that will be used to solve the problem. I can't really seem to find much ...
0
votes
1answer
36 views

Determining the infinite limit of a Riemann' sum

I need to evaluate the following $f(x)=x^2 + 2x - 5$, on $[1,4]$, by using the riemans sum and limiting it to infinity. I have set up everything $\Delta x=\frac{3}{n}$. $x_i=1+\frac{3i}{n}$, I would ...
1
vote
1answer
37 views

Finding a closed subset in $\mathbb{R}^2$ such that its image is not closed in $\mathbb{R}$

I am trying to find an example of a subset $S\subset\mathbb{R}^2$ such that the image $\pi_1$(S) is not closed in $\mathbb{R}$. I define the image $\pi_1$ as: $\pi_1 : \mathbb{R}^n \to \mathbb{R} ...
1
vote
0answers
17 views

using stone-weierastrass theorem for completely regular space

Let X be completely regular .If K is a compact subset of X, define $$p_K(f)=\sup\{|f(x)|;x\in X\}$$ then $\{p_k; \text{K is a compact }\}$ is a family of seminorms that makes $C(X)$ into a Locally ...
0
votes
1answer
22 views

Given that the graph of $f$ passes through the point $(1, 6)$ and that the slope of its tangent line at $(x, f(x))$ is $2x + 1$, find $f(2)$.

As in the title - we assume that the graph of $f$ passes through $(1,6)$ (i.e. $f(1) = 6$) and that the slope of its tangent line at $(x, f(x))$ is $2x + 1$ and we are asked to find $f(2)$. How does ...
1
vote
0answers
23 views

Maximal flow in flow-networks

I want to do the task (b),(c) and (d)in the picture above. I have done (b) correctly. For (c) I only found one (s-t) augmenting path, namely (s,1),(1,3),(3,2),(2,4),(4,t) and I only can push one ...
0
votes
1answer
44 views

Getting a p-value from a histogram?

A hypothetical HIV vaccine trial involving 20,000 participants—10,000 in the vaccine group and 10,000 in the placebo group—had the following results: 6.3 infections per 1000 in the vaccine group and ...
1
vote
1answer
42 views

integrating square root of tanx [duplicate]

$\int \sqrt{\tan (x)}dx $ Let $\tan(x)=t^{2}$ then $dx$ will become $\frac{2t}{1+t^{4}}$ Hence $\int \sqrt{\tan (x)}dx =\int\frac{2t}{1+t^4} dt $ ...
0
votes
1answer
44 views

Find $\sin(x+y)$, given $\tan x$ and $\cos y$

Given that $\tan x= -2$ and $\cos y= 1/2$ where $x$ and $y$ are in the 4th and 1st quadrants respectively. Find, without evaluating angles $x$ and $y$, a) $\sin (x+y)$ Here is what i have done so ...
0
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0answers
27 views

Miscellaneous questions about trees

I want to know which of the following claims are true: 1) Let T be a minimal spanning tree in G for a weight function w. Then T is also a minimal spanning tree for the weight function obtained from w ...
4
votes
2answers
76 views

Please help me to reduce this equation $6xy + 8 y^2 -12x-26y + 11 = 0$ to canonical one of a second-order curve

I have this polynom $$ 6xy + 8 y^2 -12x-26y + 11 = 0 $$ and I need to reduce it to a canonical equation of a second-order curve. The correct answer from the textbook is that it is a hyperbola $$ ...
2
votes
1answer
26 views

Relations examples (reflexivity, symmetry, transitivity)

I've found the two textbooks I'm using to to be particularly unhelpful in explaining these concepts, especially as they relate to English examples (non-existent). The first few following questions ...
0
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2answers
36 views

Find 3rd side, given two sides and bearings

The bearing from A to B is N $42^\circ$ E. The bearing from B to C is S $44^\circ$ E. A small plane traveling $65$ miles per hour, takes $1$ hour to go from A to B and $2$ hours to go from B to C. ...
0
votes
2answers
22 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
1
vote
1answer
64 views

Solving the differential equation $y' \tan y = \frac1x$

Express the differential equation $$\tan y\,\frac{dy}{dx}=\frac{1}{x}$$ in a form not involving $\frac{dy}{dx}$. I undersand the concept of a differential equation (though, as a student, I am ...
0
votes
1answer
48 views

Correct proof of supremum property?

Let $u$ be an upper bound of non-empty set $A$ in $\mathbb{R}$. Prove that $u$ is the supremum of $A$ if and only if for all $\epsilon > 0$ there is an $a \in A$ such that $u-\epsilon < a$. ...
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0answers
39 views

Topic = Numbers ,{Simple But difficult for me :) } [on hold]

Question= There are how many different "a" natural number ?
0
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0answers
30 views

The set of rational numbers, each point is point accumulation

Please let us help someone by telling you a precise formulation is below, and then someone please tell me solution that has since become like that with a few days my friend we debates, here my ...
1
vote
1answer
124 views

Showing that planes intersect

let there be two planes $$2x-y-5z+11=0$$ and$$2x+2y+z-1=0 $$ show that they intersect attempt at a solution: If planes do not intersect they are parralel hence there is a $t\in R$ such that ...
0
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0answers
19 views

Question about Boundary points of the sets in metric space

Let A be a metric spaces. Prove the following properties: The boundary of $A$ equals $A'-A$ The boundary of $A$ is the closed set. $A$ is closed if and only if it contains its boundary. Where ...
-3
votes
1answer
40 views

Calculus use of integral [on hold]

Assume that the price of a product is at a constant value of $\$100$ per unit or the marginal function is $MR=f(x)=100,$ where $x$ equals the number of units sold $a)\ $ What is the total revenue ...
1
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0answers
37 views

Using the method of characteristics to find a general solution to PDE

I want to find the general solution to $3U_x-4U_y = x^2$ using the method of characteristics. I'm given the answer which is $U(x,y)=\frac{x^3}{9}+F(3y+4x)$ but I'm having trouble getting to this ...
-1
votes
2answers
55 views

Maclaurin series of the function $\frac{x^2}{2+3x^2}$

I got this question: Find the Maclaurin series of the function $\frac{x^2}{2+3x^2}$ and find its domain of convergence. I tried using the binomial series $(1+x)^m = 1 + \sum_{k=1}^{\infty}{m \choose ...
1
vote
3answers
107 views

Evaluate $\int_0^\infty\frac{dl}{(r^2+l^2)^{\frac32}}$

How to evaluate the following integral $$\int_0^\infty\frac{dl}{(r^2+l^2)^{\large\frac32}}$$ The solution is supposed to look like this, unfortunately I can't derive it. $$ ...
3
votes
1answer
43 views

Question about the Betti numbers

can someone explain me this definition from :http://en.wikipedia.org/wiki/Betti_number The $n^{th}$ Betti number represents the rank of the $n^{th}$ homology group, denoted $H_n$ "which tells us the ...
0
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0answers
22 views

Find the Fixed points

Let $L=\mathcal P(\mathbb N)$ be a complete lattice of subsets of $\mathbb N$. Find the smallest and the greatest Fixed Point: 1) $F(X)=\left\{ x \mid x+1\in X \right\}$ 2) $F(X)=X \setminus \left\{ ...
0
votes
0answers
33 views

What is the linear combination of B?

I have a problem where I am finding $A^n$B where B=$[3,1,1]^t$. I know the steps in solving, but I do not remember how to find linear combination. I do not see it. There has to be a way to calculate ...
3
votes
2answers
432 views

The sum of two irrational square roots

This is very similar to this question, but I was wondering if there was a simpler proof. In particular, a proof that would prove that $\sqrt{x}+\sqrt{y}$ is an irrational number if both $\sqrt{x}$ ...
1
vote
4answers
80 views

How to compute 1/7 in base 8?

This is probably a very basic question but nonetheless I choked when I got in a math for programmers class. I was taught how to convert from base to base but I have no idea how to convert fractions to ...
2
votes
3answers
220 views

Summation of Infinite Geometric Series

Determine the sum of the following series: $$\sum_{n=1}^{\infty } \frac{(-3)^{n-1}}{7^{n}} $$ My work: $$\sum_{n=1}^{\infty } \frac{(-3)^{n-1}}{7^{n}} = \sum_{n=1}^{\infty } \frac{-1}{7} ...
1
vote
1answer
26 views

Prove existence of Diagonalizable Matrix

Suppose R, T $\in L(F^3)$ each have 2, 6, 7 as eigenvalues. Prove that there exists an invertible operator S $\in L(F^3)$ such that $R=S^{-1}TS$. What I got so far is that since R and T have three ...
2
votes
2answers
95 views

How to I write $\frac{7^{2n}}{4^{3n}}$ as a geometric series?

I am trying to write $$\frac{7^{2n}}{4^{3n}}$$ as a geometric series which has the form:$$\sum\limits_{i=0}^n{ar^n}$$. I'm not sure if I should get in the form $$\left(\frac{7}{4}\right)^{2n}$$ ...
1
vote
3answers
57 views

If one number is thrice the other and their sum is $16$, find the numbers

If one number is thrice the other and their sum is $16$, find the numbers. I tried, Let the first number be $x$ and the second number be $y$ Acc. to question $$ \begin{align} x&=3y &\iff ...
0
votes
2answers
46 views

Geometric meaning of results obtained in (a) and (b)

The task: Plot the function $\sqrt{1-x^2}$. What does it look like? What is the geometric meaning of the results you obtained in (a) and (b)? Can anybody help me with geometric mean? I can't ...
1
vote
3answers
72 views

How does $-\sqrt {\frac{{2 - \sqrt 2 }}{{2 + \sqrt 2 }}} $ simplify to $1 - \sqrt 2 $?

I've the answer for a question in my textbook to be: $-\sqrt {\frac{{2 - \sqrt 2 }}{{2 + \sqrt 2 }}} $ which i've then simplifed to: $-\sqrt {3 - 2\sqrt 2 } $ However my textbook states $-\sqrt ...
2
votes
1answer
39 views

Finding conditional distribution

Let $X$ and $Y$ be independent $Exp(1)$-distributed random variables. Find the conditional distribution of $X$ given that $X + Y = c$ ($c$ is a positive constant). this is my idea: $$f_{X \mid ...
3
votes
4answers
43 views

Prove a property about the centralisator

Let G be a group and $U \subseteq G$ a subgroup. Let $x \in G$ be arbitrary. How to show that $C_G(xUx^{-1})=xC_G(U)x^{-1}$ where $C_G(U):=\{g\in G : gu=ug$ $\forall u\in U\}$ For the first ...
2
votes
0answers
37 views

What is a good technique for evaluating this double integral?

The integral is: $ \int_0^1 \int_0^1 \frac{x^2 - y^2}{(x^2 + y^2)^2} dxdy $. I'm having difficulty finding an appropriate technique for evaluating it. I initially thought that polar coordinates ...
0
votes
0answers
20 views

Absolute integrability questions (can someone check my answers?)

Started working through some textbook problems and have some questions about a collection of related questions. It has been a long time since I have done any analysis and I am feeling very rusty and ...
0
votes
2answers
56 views

Does the definition range remains the same?

In solving this inequality (transcribed from here) $$\left(\frac23\right)^{\log_{0.5}(x^2+4x+4)}<\left(\frac94\right)^{\log_2(x^2-3x-10)}$$ we eventually reach the point where $ ...
3
votes
1answer
41 views

Finding derivative form the definition

I want to find the derivative of the function $f:\mathbb R^n\to \mathbb R^m$ at a point $x_0\in \mathbb R^n$, where $f(x)=c\in \mathbb R^m$, is a constant function. What I did is as follows: If $f$ ...
0
votes
1answer
60 views

Every Cauchy sequence is bounded

Please help me to understand step-by-step how this example is proven. The statement is follows: Every Cauchy sequence is bounded. since I do not understand how verified, please help me, thank ...
0
votes
2answers
33 views

Could anybody provide a more detailed explanation of a tangent equation in its general form?

In my textbook I'm currently at the topic of a tangent line to an ellipsis and hyperbola. And there I've encountered this statement: If a curve has an equation $$ y = f(x) $$ then an equation of a ...
0
votes
1answer
36 views

Doubts about locus and its equation

Two points A and B with $(1,1)$ and $(-2,3)$ respectively are given.find the locus of point P.So that area of $\Delta$PAB is 9 square units. answer is :- $2x+3y+13=0$ or $2x+3y-23=0$. how i tried:- i ...
1
vote
2answers
38 views

Find the Fixed points (Knaster-Tarski Theorem)

Let $L=\mathcal P(\mathbb N)$ be a complete lattice of subsets of $\mathbb N$. a) Justify that the function $F(X)=\mathbb N \setminus X$ does not have a Fixed Point. I don't know how to solve this. ...
0
votes
3answers
70 views

The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$

$$\lim_{x\rightarrow 0}\frac{(1+x)^{1/x}-e+\frac{ex}{2}}{x^2}=\,?$$ by directly substituting $x=0$ i got $\infty$ by using L-H's rule, i got $-1/8$ the given options are $a)\frac{24e}{11}$ ...
0
votes
2answers
55 views

Grade 4 level arithmetic maths problem that I can't work out

My grade 4 son was given this problem as homework, except I can't even seem to work it out! Any help is appreciated. Each student in year 4 was asked to bring a paint tin, a paint brush and glue for ...
2
votes
1answer
38 views

Question on continuity with [x]

given the function $f(x)=\frac{2[x]}{3x-[x]}$ the question is to find continuity of the function at $x=1$ and $x=\frac{-1}{2}$ note: [x] denotes the largest integer which is less than or equal to x. ...