Recent content by Mathick

Hi, thanks for your reply! That is what I thought - that this problem is incomplete. It says that we use a full alphabet (26 letters) and I also came to the conclusion that the statement can't be proven. I will try to find out where the typo is and come back.

Suppose that we are in the situation that Alice is using a Hill cipher consisting of a $2 \times 2$ matrix $M$ to send her message, which is $100$ ‘A’s. If Eve intercepts this message and knows that plaintext contained only one letter, and she also knows anyone of the entries of the matrix $M$...

I tried to understand the following problem: Consider a sequence of Bernoulli trials with success probability $p$. Fix a positive integer $r$ and let $\mathcal{E}$ denote the event that a run of $r$ successes is observed; recall that we do not allow overlapping runs. We use a recurrence...

Hello! I don't know exactly how to state my question so I'll show you what my problem is. Ex. Let T : R[x]_3 →R be the function defined by T(p(x)) = p(−1) + \int_{0}^{1} p(x) \,dx , where R[x]_3 is a vector space of polynomials with degree at most 3. Show that $T$ is a linear map; write down...

So you claim that (b) and (d) are equivalent to $ notA $ and (a) and (c) are not, don't you?

Let $A$ be the statement 'The sequence $(x_n)$ is bounded'. Use your mathematical intuition to decide which of the following statements are equivalent to $notA$. You don't need to give a justification. (a) There exists $C > 0$ such that $\left| x_n \right| > C$ for some $n \in \Bbb{N}$. (b) For...

If $X$ is a set, then the power set $P(X)$ of a set is the set of all subsets of $X$. I need to decide whether the following statements are true or false and prove it: (i) If $Z = X \cup Y$ , then $P(Z) = P(X) \cup P(Y)$. (ii) If $Z = X \cap Y$ , then $P(Z) = P(X) \cap P(Y)$. By examples I...

I appreciate that but I didn't ask for that...

Hello! I need to compute the following integral: $ \int \sec\left({x}\right) \; dx $ using the substitution $ t=\tan\left({\frac{x}{2}}\right) $ what I did. HOWEVER, they ask to compute the same integral knowing that $ \int \csc\left({x}\right) \; dx =...

Hello! We know from 'Binomial Expansion' that (1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+... for \left| x \right|<1 . Why doesn't it work for other values of x? I can't understand this condition. I would be really grateful for clear explanation!

W and c are constant, am I right? And it should look like $x = \frac{\sin[ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta) ] }{ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta)}$ ?

In the triangle a point $$I$$ is a centre of inscribed circle. A line $$AI$$ meets a segment $$BC$$ in a point $$D$$. A bisector of $$AD$$ meets lines $$BI$$ and $$CI$$ respectively in a points $$P$$ and $$Q$$. Prove that heights of triangle $$PQD$$ meet in the point $$I$$. I've tried to show...

Solve the system of $$n$$ equations with unknown $$x_1, x_2, ... , x_n$$, for $$n\ge 2$$: $$2x_1^3 + 4 =x_1^2 (x_2 +3)$$ $$2x_2^3 + 4 =x_2^2 (x_3 +3)$$ $$......$$ $$2x$$n-13$$+ 4 = $$$$x$$n-12$$(x_n +3)$$ $$2x_n^3 + 4 =x_n^2 (x_1 +3)$$ Can you help me?

Proof: the line $AB$ is tangent to the circle through $A$, $C$ and $D$ Knowing that $$BD=AC$$, $$AD=AE$$ and $$AB^2=AC\cdot BC$$, we get $$\frac{AB}{AC}=\frac{BC}{AB}$$ and then $$\frac{AB}{BD}=\frac{BC}{AB}$$. Thus, the triangles $$ABD$$ and $$CBA$$ are similar. So $$\sphericalangle...

Yes, I found it but there is one extra variation. You can choose either $$3n+1$$ or $$3n-1$$. Doesn't it have an influence on the result?