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2answers
2k views

convex and concave regions

I was doing this question and it quoted that "Given that the region OCB is convex..." but surely that region is concave as a basic way is that a line between two points can be drawn under the curve. ...
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votes
1answer
35 views

Determine for $f(x)=x^3-x+3$ a $n \in \Bbb Z$, sucht that $f(x)=0$, for a $x\ \in [n,n+1]$. [closed]

Determine for $f(x)=x^3-x+3$ a $n \in \Bbb Z$, sucht that $f(x)=0$, for a $x\ \in [n,n+1]$. I'm not sure how to tackle this problem for a $x\ \in [n,n+1]$. I was thinking about using the intermediate ...
-1
votes
2answers
143 views

Calculating Covariance when three coins are flipped [closed]

Three fair coins are flipped. Let x be the number of heads. Let y equal to 1 if all coins land the same outcome I.e hhh or ttt, and 0 if otherwise. Calculate Cov(X,Y)
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votes
1answer
134 views

There exist vectors $p$ and $d$ such that the line containing $a$ and $b$ can be expressed in the form $v = p+d t.$

Let $$a = \begin{pmatrix} 5 \\ -3 \\ -4 \end{pmatrix} \quad \text{and} \quad b = \begin{pmatrix} -11 \\ 1 \\ 28 \end{pmatrix}.$$ There exist vectors $p$ and $d$ such that the line containing $a$ and $...
-1
votes
1answer
45 views

Differentiation Product Rule

At the bottom of a proof I'm doing I end up with the following expression which equals zero. But I can't see how? I believe it has something to do with the product rule. If someone can show me ...
-1
votes
1answer
175 views

Separable Space [closed]

There is a vector space $X$ with two norms $\|\cdot\|_1, \|\cdot\|_2$ such that $(X,\|\cdot\|_1)$ is separable and $(X,\|\cdot\|_2)$ is not? In both cases, we will consider the topology induced by ...
-1
votes
1answer
29 views

What is the probability $P(Y=y | X=x) $ in this case? [closed]

In given n balls {$1,2,3,4,...,n$} in the jug, if I randomly take 2 balls with the return (Independent extractions) , and: X - the minimum value of the two extractions. Y - the maximum value of the ...
-1
votes
1answer
36 views

Can a shape be a fininte line? [closed]

Can mathematicians define a shape as a finite line? By which I mean moving in a direction that heads back towards the beginning point, but so that even if the line were infintely long it would not ...
-1
votes
1answer
124 views

Use induction to show that this improper integral exists [closed]

Let $m,n \ge 0$ be positive integers. Using induction on $n$ or otherwise, show that the improper integral $$\int_0^1 x^m \left(\log x\right)^n dx$$ exists, and give a closed-form expression for it. ...
-1
votes
1answer
594 views

standard Brownian motion. Calculate the probability that W(3) > W(2) > W(1). [closed]

Assume that W(t) is the standard Brownian motion. Calculate the probability that W(3) > W(2) > W(1). Hi I am really bad with BM so can anyone please help me here?
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votes
1answer
218 views

Group whose maximal subgroups are normal [closed]

Let $G$ be a group(not necessary finite) such that every maximal subgroup of $G$ is normal. Then Why $G^{\prime} \leq \Phi(G)$?
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votes
1answer
52 views

Can anyone please tell how $f(x)=x^2$ is neither even nor odd when $0<x<2\pi$?? [closed]

How can $f(x)=x^2$ be neither even nor odd when $0<x<2\,\pi$? I am struggling with this question. Please help me out with this.
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votes
1answer
256 views

Exponential Growth and Decay Word Problem [closed]

Annual sales for a clothing store are $270,000 and are increasing at a rate of 7% per year. Find out how much money is made in 3 years. Use the formula y=a(1+r)^t.
-1
votes
3answers
64 views

what does ^-1 mean?

Im kind of frustrated when I see the experession of (something)^-1 and its not really clear from context that it means 1 over something or the inverse of somethings. This issue shows up frequently in ...
-1
votes
1answer
488 views

How do I change the X-step on the TI-84 Plus?

I am trying to create a vertical line in my calculator, but it needs to be restricted to a certain height. I have an equation with a very high slope and I need to restrict its domain to hundredths. I ...
-1
votes
1answer
24 views

Determine if all infinite vectors which differ from the infinite zero vector in finite indexes is countable

i have the following question: let $A=${0,1}$^\mathbb{N}$. we define $v\in A$ ,$v_i$ is the i'th coordinate of the infinite vector, and $$R =\{ (u,v)|\{i|u_i\neq v_i\}is\space finite\}$$ Determine if $...
-1
votes
2answers
149 views

How to solve the following equation for $x$: $(3x-1)\ln4 =\ln3+ x\ln5$

$$(3x-1)\ln4 =\ln3+ x\ln5$$ Is there a way to solve this for $x$, without typing everything into a calculator, and getting the value that way?
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votes
1answer
39 views

$(\sum_j a_j |b_j|)^2 \leq \sum_j a_j |b_j|^2$

I have to prove this relation $(\sum_j a_j |b_j|)^2 \leq \sum_j a_j |b_j|^2$, where $b_j$ is a vector for every $j$ and $0<a_j<1$. The material which I am referring hints at the use of Cauchy-...
-1
votes
1answer
57 views

How to show that $\mathcal F$ is a $\sigma$-algebra

Let $\Omega:=[0,1]$ and $\mathcal F :=\{ A \subseteq [0,1] \,|\, A\,\, is \,\, countable\,\, or \,\, A^c\,\, is \,\, countable\}.$ How can I show that $\mathcal F$ is a $\sigma$-algebra?
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votes
1answer
79 views

Measurability of continuous function in R

In my textbook there is this claim: In $(\mathbb{R},\mathcal{M},m)$ where m is the Lebesgue measure, continuous function are measurable. Indeed, for every $\alpha \in \mathbb{R}$ the set $\{x\in\...
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votes
2answers
2k views

Prove an equation has exactly two real roots [closed]

If i want to prove and equation has exactly two real roots, how would i do so? What theorem would i use, Rolle's or Bolzano's or something else?
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votes
1answer
46 views

Prove that, If $p > 0$ and $\Bbb{E}(|X|^p )< \infty$, then $x^p \Bbb{P}(\{ |X|>x\}) \sim o(1)$ as $x \to \infty$

Prove that, If $p > 0$ and $\Bbb{E}(|X|^p )< \infty$, then $x^p \Bbb{P}(\{ |X|>x\}) \sim o(1)$ as $x \to \infty$ I tried to solve this question in class but I ended up with the difficult ...
-1
votes
1answer
31 views

What is the value of $ \ n\ $ such that $\ \xi_{n}= e^{\frac{2 \pi i}{n}} \ $

What is the value of $ \ n\ $ such that $\ \xi_{n}= e^{\frac{2 \pi i}{n}} \ $ has degree at most $ \ 3 \ $ i.e, $ [ \mathbb{Q}(\xi) : \mathbb{Q}]=3 $ . $$ $$ I have thought that - since $ [\...
-1
votes
1answer
252 views

First step argument of Markov Chain [closed]

Let $P$ be a transition probability matrix of a regular Markov Chain over a finite state space S. Let $M=(m_{ij})$ be a matrix of mean return times. a) Use first step argument to establish that $$m_{...
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votes
1answer
244 views

Complex numbers; omega

Hi I have trouble doing this exercise: Let $\omega=e^{2i\pi/5} $ Explain why $\omega^1+\omega^2+\omega^3+\omega^4=−1$ and show that $\omega+\omega^4= 2\cos(2\pi/5)$ and $\omega^2+\omega^3=2\cos(4\pi/...
-1
votes
1answer
35 views

Suppose that A is a linear transformation and p is a polynomial. Is it true that if p(λ) is an eigenvalue for p(A). Then λ is an eigenvalue for A?

Suppose that A is a linear transformation and p is a polynomial. Is it true that if p(λ) is an eigenvalue for p(A). Then λ is an eigenvalue for A? I already know that it is not true but I dont know ...
-1
votes
1answer
67 views

How do I show that $f(x)=\sqrt{x+1}$ is concave using $f(\frac{x+y}{2})\geq\frac{f(x)+f(y)}{2}$ .

I want to show that $f(x)=\sqrt{x+1}$ is concave using $f(\frac{x+y}{2})\geq\frac{f(x)+f(y)}{2}$ and not the second derivative argument. However, I get into the following trouble: \begin{align} f\left(...
-1
votes
3answers
41 views

Absolute Values and its Inequalities [closed]

Find $x \in \mathbb{R}$ that satisfies both $|2x - 3| < 5$ and $|x + 1| > 2$ simultaneously.
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votes
1answer
75 views

How to evaluate this limit when variable tends to infinity? [closed]

How to evaluate this limit when n tends to +infinity $(1^4+2^4+...n^4)/n^5 - (1^3+2^3+...+n^3)/n^5$ I tried using L hopital but got answer zero which is incorrect, then I tried to somehow use some ...
-1
votes
1answer
42 views

how can we prove this inequality??? [closed]

visit this post https://math.stackexchange.com/a/2279318/446173 due to this answer can we infer this equation? if yes how can we prove this??? $$I((X_1,\dots X_n);(Y_1,\dots Y_n))\ge\sum_{i=1}^n H(...
-1
votes
2answers
55 views

Problems solving equation [closed]

Let $(x,y) \in (0,1)^2$. How many solutions does this equation have? $$\sqrt3 \cdot x = \cos(xy)$$ I really have no idea on how to get to this
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votes
1answer
210 views

Cyclic group order 15

Let G be a cyclic group of order 15. Why must G contain at least 2 elements of order 3? Is it to do with Cauchy's theorem? Then once we know that it has one, the inverse of this element has order 3 ...
-1
votes
2answers
115 views

Find a correct trial function for undetermined coefficients. [closed]

Consider the DE $$\frac{dy}{dx} + 2y = xe^{-x}$$ Is this solvable by method of undetermined coefficients? If so, how do I find a correct trial function for it?
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votes
4answers
2k views

A tricky probability question (About drawing balls from boxes) [closed]

I found this question intriguing. "In a box, there are 6 red balls and 7 blue balls. Two blue balls are drawn in the first and second draw. Assuming the balls are not returned, what is the ...
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votes
1answer
66 views

Missing conclusion in proof convergence radius

If the limit of $\lim\limits_{n\to\infty} \left\vert\frac{c_n}{c_{n+1}}\right\vert$ with $c_n\neq 0$ exisits, then $R:=\lim\limits_{n\to\infty} \left\vert\frac{c_n}{c_{n+1}}\right\vert$ is the ...
-1
votes
1answer
29 views

ARC of the function - write an equation that represents the statement

I'm missing something on this problem: ...
-1
votes
1answer
374 views

How to find a density function of the sum of two independent random variables?

I have random variable X with uniform law of distribution in the interval $[0;1]$ . Also I have random variable Y and its density function with triangle distribution(or Simson distribution) is ...
-1
votes
1answer
19 views

Let $(X,F,\mu)$ be measure space with $\mu(X)=1$ [closed]

Let $f_n$ be sequence of measurable functions on $X$. Suppose that $f_n$ converges to measurable function almost every where $f$ on $X$. Suppose that $f_n$ cauchy in $L^2(X)$. Since $\mu(X)=1$, $...
-1
votes
1answer
33 views

Find the Polar equation of the curve made of all points P such that the distance from O to P equals the distance from A to B.

Crude picture but its the best i could do. Do not even know where to start with this particular problem. I'm almost positive it deals with cycloids but that is about it.
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votes
2answers
425 views

Let $w$ denote cube root of unity which is not equal to 1. Then the number of distinct element in the set {$(1+w+w^2+…+w^n)^m : m,n=1,2,3,.. $} [closed]

I know it follows part cycle mod 3 but I don't understand how to find different element in set, do I have to think of all possible values in the set?
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votes
1answer
97 views

Is the singleton closed in this topology?

let $\tau=\{0_{n}:n\in \mathbb{N}\}\cup\{\emptyset,\mathbb{Z}\}$ over $\mathbb{Z}$ s.t $O_{n}=\{n,n+1,n+2,...\}$ is a singleton is open in this topology? So we look at $\{n\}^{c}=\{i+1,i+2,...:i \in \...
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votes
1answer
605 views

Proof with characteristic function

If f : X → N,g : X → N xA(x)= {1. if x E A; {0 if x E X\A Write the functions χAχB, χA +χB − χA∩B,χA + χB − 2χA∩B in the form χC. Ive managed to get ...
-1
votes
2answers
2k views

Find the solution to the initial value problem…

Find the solution of the initial value problem $$ \frac{dy}{dt}=1-y^2,\;y(0)=y_0 $$ (i) in the case $y_0=1$; (ii) $y_0=-1$; (iii) in all other cases. Are there any $y_0$ such that the ...
-1
votes
2answers
43 views

A question about characteristic equation and digonalization [closed]

how do we solve this problem is that eigen values or 0 and 1..but i am not sure can any one help me this problem
-1
votes
1answer
2k views

How can we solve the following non homogeneous laplace equation 2D? [closed]

let we have the following non homogeneous laplace equation 2D $$u_{xx}+u_{yy}=q(x,y)$$ where $0<x<a$ and $0<y<b$ with the conditions $u(x,0)=f(x)$ where $0<x<a$ and $u(x,b)=g(x)...
-1
votes
1answer
52 views

Desperately Need Solution For This Proof, Anyone? [closed]

Suppose $f(x)$ and $g(x)$ are non-constant real-valued differentiable functions $\in\Bbb R$ Furthermore, suppose that $f(x + y) = f(x)f(y) − g(x)g(y)$ and $g(x + y) = f(x)g(y) + g(x)f(y)\ \forall\ x,...
-1
votes
1answer
87 views

How many digits are there before the hundredth $9$ in the following number: $97977977797777977777\cdots$

When I count from left of the following number, how many digits are there before the hundredth $9$: $$97977977797777977777\cdots$$ Before the 3rd $9$ there are $2$ sevens and before the 5th nine ...
-1
votes
1answer
78 views

If $α , β$ be two arbitrary complex number then $| α +\sqrt{α^2-β^2 } |+| α - \sqrt{α^2-β^2}|$ is equal to? [closed]

If $α$ , $β$ be two arbitrary complex number then $$| α +\sqrt{α^2-β^2 } |+| α - \sqrt{α^2-β^2}|$$ is equal to ?
-1
votes
3answers
48 views

How can I reduce this matrix $\left[\begin{smallmatrix}-2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \\\end{smallmatrix}\right]$?

I am trying to reduce this matrix to the reduced one $$ \begin{bmatrix} -2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \\ \end{bmatrix} $$ ...
-1
votes
1answer
62 views

Permutation and cycles decomposition

For the permutation cycle $\sigma = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 4 & 3 & 1 & 5 & 2 \end{pmatrix}$, they decomposed it into $(3 4)(13)(45)(25)$. I don't see how ...

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