# Tagged Questions

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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### maths question on levers [closed]

If someone is holding a 2kg weight in their hand at a distance of 35cm from the elbow (fulcrum) and the downward force (load) due to the weight is 20 newtons. Calculate the effort in newtons that the ...
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### Prove that these 3 points are in a straight line.

A triangle ABC is inscribed in a circle $\omega$. $BB_1$ bisects $\angle ABC$ (and so $M$ is the midpoint of the arc $AC$ ($B \notin AC$, where $AC$ is the arc)). $B_1K \perp BC$ ($K\in\omega$). ...
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### Relating a transformed exponential random variable to its standard density

Suppose $X$ is a random variable that follows exponential distribution with rate $\lambda=1$; hence its pdf is $f_X(x) = e^{-x}$. If $Y = \mu + \sigma X$ where $\sigma >0$ is exponentially ...
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### Convergence of $\sum_{n=2}^{\infty}n^2\left(\frac{1-i}{2+i}\right)^n$

Does this sequence converge/diverge and if so, does it in a (not)absolute way? $$\sum_{n=2}^{\infty}n^2\left(\frac{1-i}{2+i}\right)^n$$
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### Find the minium of function

Find the minimum of $f(x)=(x-1)(x-2)(x-3)(x-4)$ without using the calculus, I know it's easy to find it using the derivative, but I need to fiugre out how to solve it without it. I know that the ...
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### Characteristic function of a exponential random variable, problems with complex integral.

I tried to compute the characteristic function of a random variable, which is exponential distributed with parameter $\lambda$: \begin{align*} \varphi(t) &= \mathbb E[e^{itX}] = ...
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### Probability of World Series - Using Pascal and Fermat “Problem of Points”

This is a question I have for a history of math class, but I can't figure it out. I need to use the three method that Pascal and Fermat used on their problem of points, and it doesn't seem to work ...
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### Convergent Sequences involving functions

Let $f: (M,d) -> (N,p)$ be a function and suppose that {${f(Xn)}$} is a convergent sequence, whenever $Xn -> a$. Prove that $f$ is continuous at $a$ My thinking is that since Xn converges to ...
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### Can anybody correct this derivative exercise for me

It's just that I'm solving a list of exercises but they don't have the answers. I want to know if I'm going about this one the correct way. At $x$ years after 2005, the average building tax over an ...
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### Using $E(S) = E(E(S|Y))$ to find $E(S)$ - gamma and exponential distribution [closed]

I have a word problem that seems so simple but I am struggling to get my head around it. The time between passing their test and their first car accident varies from driver to driver depending on ...
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### Probability and statistics /Homework [closed]

Consider a hash table with "$N$" slots, currently occupied by "$n$" records, resulting in a load factor of $a = n/N$. That is, a is the probability of a slot picked at random being filled. Secondary ...
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### Question about Graph with cos

Can you help me with this question? and can you tell me what's the subject that this question belongs to? So I can study it. Thank you very much
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### Closed subset of R^2

Show that the set A = {(x,y): $x^3$ $>=$ $y^5$} is closed as a subset of $R^2$. I defined a closed set as a set whose complement is open. So the complement of the above set is {(x,y): $x^3$ ...
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### Find the area under the curve with a sketch

I am trying to find the value but do not know how because I am not given an intial value.. Any help?
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### Composite Numerical Integration- Numerical Analysis

I am currently stuck on this problem. I keep trying to put it in maple but instead of it giving me the value its giving me the function. So, I must be doing it wrong, also I am a bit unsure of how to ...
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### Two isomorphism questions

Let G = (C - {0}, mult.), and let U be the subgroup U = {x+yi such that x^2 + y^2 = 1}. Use the Fundamental Theorem to show that: a) G/U is isomorphic to (R>0, mult.) b) G/R>0 is isomorphic to U. ...
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### How many blue balls must you choose to guarantee that you have at least $3$ light blue balls?

A bag contains $4$ light blue balls, $5$ dark blue balls, and $10$ sea blue balls. How many blue balls must you choose to guarantee that you have at least $3$ light blue balls? My first reaction ...
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### How to know if $(8,7,7,6,5,5,4,3,3,2,1,1)$ is a Simple Graph w/o using Havel-Hakimi Algorithm

I've used the Havel-Hakimi Algorithm to show this sequence $(8,7,7,6,5,5,4,3,3,2,1,1)$ is simple, but is somewhat time consuming for a test. Is there a way to determine without using algorithms? Or ...
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### Matching infinite matrices

Can any one solve this problem that I have. I have been sitting with this problem for a while now. Completely confused. "For inifinite matrices a complete matching may not be possible even though ...
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### Gived y[n], a discret signal, using Z transform, get the general expression.

i hope you can guide me in this mess i have. Gived this signal $y[n+2]-y[n+1]-30y[n]=(1/5)^n+1; \qquad (n \in \Bbb N, n>= 2)$ $y[0]=0,$ $y[1]=1.$ get the general y[n] expression. Applying Z ...
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### Prove that the union of countably many countable sets is countable.

I am doing some homework exercises and stumbled upon this question. I don't know where to start. Prove that the union of countably many countable sets is countable. Just reading it confuses me. ...
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### Is a convergent sequence?

Is the sequence $\{z_n\}\subset \mathbb{C}$ defined by $$z_n=\cos\left(n\frac{\pi}{3}\right)+i \sin\left(n\frac{\pi}{3}\right)$$ a convergent sequence?
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### Norm of a matrix equals greatest eigenvalue

How do I prove that the norm of a matrix equals the absolutely largest eigenvalue of the matrix? This is the precise question: Let $A$ be a symmetric $n \times n$ matrix. Consider $A$ as an ...
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### Convert HEX to BIN

How to convert the number $fada.cafe_{16}$ to binary? I used Wolfram understand it, but when I type $fada.cafe_{16}$, it changes to $fada.cafdfffffd..._{16}$. Why that?
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### Find a direct way to calculate recursive elements (simple problem with matrices)

I nearly solved this question, I just need a hand with the last part since it is a bit confusing. We are given the recursive sequences $\{a_n\}$ and $\{b_n\}$ like this: $a_1=1$, $b_1=2$ ...
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### Question on Curl F

The problem in the book asks what the curl of $\operatorname{curl}\vec F(\vec r)= \frac {\vec r}{\|\vec r\|}$. Can someone give me a good explanation on why the curl will be zero? I would really ...
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### Vector bundle on a quadric $Q$

The problem: Consider the smooth quadric $Q=V(X_{0}X_{1}+X_{2}X_{3}+X_{4}^{2})\subset\mathbb{P}^{4}$ and the line $L=V(X_{0},X_{2},X_{4})$ contained in it. Prove that there exists a vector bundle $F$ ...
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### Proving a combination of differentiability

$f:\mathbb{R}\to \mathbb{R}$where$$f(x) = \begin{cases} \dfrac{P(x)}{x^n}e^{-1/x^2}& \text{if x\ne 0}, \\ 0 &\text{if x = 0}.\end{cases}$$ Where P(x) is a polynomial and $n\geq 0$ is an ...
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### percentage puzzle from shakuntala devi-

The High-Rise while in Canada, I visited a beautiful high-rise building in the Metropolitan City of Toronto. The manager of the building told me that the building consisted of different kinds of ...
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### Nilpotent Pseudoinverse

I am trying to write up solutions for my linear algebra students and I'm currently stuck on the following proof: Let $A$ be a square matrix such that $A^2 = O$. Prove that $(A^\dagger)^2 = O$. ...
### Prove that $M_{n}(F)\otimes _{F}M_{m}(F)\simeq M_{nm}(F)$ .
Suppose $F$ is a field. Then prove that $$M_{n}(F)\otimes _{F}M_{m}(F)\simeq M_{nm}(F)$$ as $F$-algebras. I know that I should take $$\alpha :M_{n}(F)\otimes _{F}M_{m}(F)\rightarrow M_{nm}(F)$$ ...