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Linux Mastering Development Ubuntu

Wacom Intuos S only recognized in Android Mode

The original title of this question was “Only left half of Wacom Intuos S is working”. The text of the original question preserved below. I have since figured out part of the problem, so I am updating this question. I am using a Wacom Intuos S on Ubuntu 18.04. If I plug it into the […]

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Does the prevalence of COVID-19 infections in West Europe compared to East Europe prove that BCG vaccine is helpful against Coronavirus?

Particularly, we see the apparent difference between East and West Germany: This also may explain why in Germany and in Israel it is the younger people who are mostly affected by the coronavirus (the both countries formerly had mandatory BCG, West Germany stopped the practice in 1975).

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Unable to think about a quiz question

I am asking about a quiz question which I am trying to solve but not able to think about. Please note any number of options in it can be true. What I thought -> since first order derivative is non singular, so f is 1-1 . But I am unable to think about any of […]

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Mean and Variance of subset of a data set

I have a data set of position measurements of an object. However, the data set is split into subsets. The subsets have equal size. I want to find the mean and variance of the whole data set only with access to the subsets, and the not the whole data set at once. How would I […]

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Derivative of Vector from the derivative of its norm

It is known from previous question that, $\frac{d}{d x} \left \| \vec{x} \right \| = \frac{\vec{x}}{\left \| \vec{x} \right \|} \cdot \vec{\dot{x}}$ How can I get the vector derivative $\vec{\dot{x}}$ from the norm derivative $\frac{d \left \| \vec{x} \right \| }{d x} $ ?

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radius and center of curvature of parametric curve

Find radius of curvature and center of curvature of curve whose parametric coordinates are $x=t,y=t^2,z=4t^3$ at $t=1$ My try Given $r(t)=ti+t^2j+4t^3j$ First we calculate $T$ from velocity vector $v=i+2tj+12t^2k\Longrightarrow |v|=\sqrt{1+4t^2+144t^4}$ So $$T=\frac{v}{|v|}=\frac{i+2tj+12t^2k}{\sqrt{1+4t^2+144t^4}}$$ $$\kappa=\frac{1}{|v|}\bigg|\frac{dT}{dt}\bigg|$$ $$\kappa=\frac{1}{(1+4t^2+144t^4)}|2j+24tk|$$ at $t=1$ We have $\displaystyle \kappa= \frac{\sqrt{580}}{149}$ So radius of curvature is $\displaystyle \frac{149}{\sqrt{580}}$ How do i find centerof curvature Help […]

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Elementary Combinatorics+Recursion Olympic Problem

In the city there was one person infected with a virus. Every day every sick person is visited by all his healthy friends, they become infected with the virus and get sick the next day. And all patients recover the next day and are immune to the virus for exactly one day. $\cdot$Prove that the […]

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Understanding Why a Limit (w/ Factorials) Approaches 0

I am given the following limit: $\lim_{x \to \infty} \frac{a^{x+1}}{(x+1)!} $ I am aware that this limit approaches $0$ after plugging large enough numbers on the calculator, but I am looking for a more mathematical approach. Do I need to use L’Hôpital’s rule for this as it looks like the fraction is approaching $\frac{\infty}{\infty}$? I’m […]

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René Schilling’s proof for backwards submartingale $L^1-\lim_{n} w_{-n} = w_{-\infty}$ $\iff$ $\inf_{n \in \mathbb{N}_0} \int w_{-n}d\mu > -\infty$

I am reading René Schilling’s Measures, Integrals, and Martingales. Let $(w_l, \mathscr{A}_l)_{l \in -\mathbb{N}_0})$ be a backwards submartingale and assume that $\mu|_{\mathscr{A}_{-\infty}}$ is $\sigma$-finite. Then we have the following. (i) $\lim_{n \to \infty} w_{-n}=w_{-\infty} \in [-\infty, \infty)$ exists a.e. (ii) $L^1-\lim_{n \to \infty} w_{-n} = w_{-\infty}$ if, and only if, $\inf_{n \in \mathbb{N}_0} \int w_{-n}d\mu […]

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An extremum product in a circle

Let $(C)$ be a circle of radius $R$ and center $O$, $[A’A]$ a diameter. Let $OC’A$ be an equilateral triangle with $C’$ and $A$ on $(C)$ and $C\in [OC’]$ let $[BC] $ be a segment inside $(C)$ such that $ [A’A]$ is its perpendicular bissector. Finally let $P$ a point in the small arc $C’A$. […]