How to solve $x^2 +\left(\frac{x}{x-1}\right)^2 =8$?
Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$
How can I assign the output of a command to a shell variable? I want to assign the result of an expression (i.e., the output from a command) to a variable and then manipulate it – for example, concatenate it with a string, then echo it.  Here's what I've got: #!/bin/bash cd ~/Desktop; thefile= ls -t -U | grep -m 1 &quot;Screen Shot&quot;; echo &quot;Most recent screenshot is: &quot;$thefile;  But that outputs: Screen Shot 2011-07-03 at 1.55.43 PM.png Most recent screenshot is:   So, it looks like that isn't getting assigned to $thefile, and is being printed as it's executed. What am I missing? Putting a piece of code in between two html tags in Solaris How to show this equality of $\rho(X,Y)$ Let I have $(S,\Sigma,\mu)$ be a probability space, then $X,Y \in \Sigma$. Define $\rho (X,Y)$ by $\rho (X,Y)$ = correlation between random variable $I_X$ and $I_Y$, where $I_X$ and $I_Y$ are the indicator function of $X$ and $Y$. Express $\rho (X,Y)$ in term of $\mu (X)$, $\mu (Y)$, $\mu(XY)$. Conclude that $\rho(X,Y)=0$, if and only if $X$ and $Y$ are independent.      How to show that: $$\rho(X,Y)= \frac{\mu(XY)\,\mu(X^cY^c)-\mu(XY^c)\,\mu(X^cY)}{(\mu(X) \,\mu(X^c)-\mu(Y) \,\mu(Y^c))^{1/2}};0&lt;\mu(X)&lt;1;\,0&lt;\mu(Y)&lt;1$$ I have two raster images, Boolean classified (1 or 2).  They overlap in given areas.   I need a raster that is only the overlapping sections.  Using Arcinfo 10.  Answer can only use raster methods, no converting to polygons, points, etc... Explain what is a transistor in plain English! Can somebody explain "leveraged debt investment positions" and "exposures" in this context for me, please? "The strong bond performance has led to a surge in leveraged debt investment positions that are ultimately funded by the banks' interbank exposures and WMPs. But nobody really knows how levered these positions are, who has financed them, and by how much," S&amp;P said. "The contagion risks for the financial sector could be high."  source: TeX editor with line-spacing preferences Why don't absorption and emission lines cancel out in our Sun? I was looking at  on why  and emission lines don't cancel out:      An experiment shining light on the material and looking at the   reflected spectrum will see absorption lines at those frequencies,   because the relaxation of the excited electrons will emit back   radiation all around randomly, whereas the reflected spectrum is at a   specific angle.   However it is not totally convincing to me. The photons that get emitted towards the center of the Sun (by the electrons in higher energy states that absorbed a photon earlier) would get absorbed again when they hit a different electron (and then re-emitted) and would eventually make it out. So why don't absorption and emission lines cancel out in our Sun? Textbook on the Geometry of Special Relativity I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance. When we implement the Always Encrypted feature in SQL Server 2016, do the .mdf files, .ldf files and .bak files get encrypted as well?  I would like to know if the data/log/backup files gets encrypted or not. Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$ I would like to show $\lim\limits_{r\to\infty}\int_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$.  Now, of course, the integrand does not converge uniformly to $0$ on $\theta\in [0, \pi/2]$, since it has value $1$ at $\theta =0$ for all $r\in \mathbb{R}$.   If $F(r) = \int_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta$, we can find the $j$th derivative $F^{(j)}(r) = (-1)^j\int_{0}^{\pi/2}\sin^{j}(\theta)e^{-r\sin\theta}\text d\theta$, but I don't see how this is helping.  The function is strictly decreasing on $[0,\pi/2]$, since $\partial_{\theta}(e^{-r\sin\theta})=-r\cos\theta e^{-r\sin \theta}$, which is strictly negative on $(0,\pi/2)$.  Any ideas? Quitting a job in the US on a work visa, going to Canada and re-entering on a tourist visa (ESTA waiver) I have been working in the USA on an E-3 visa and intend to return home to Australia, but I want to travel around the US before I do so. I am under the impression that after leaving my current company, I will have 10 days to leave the country.   Will I be able to go into Mexico or Canada and re-enter with an ESTA waiver as a tourist? How to stop iPhone users from sending iMessages and send SMS instead I used to have an iPhone, but I changed to an android (shock, horror!). Unfortunately Apple refuses to let me go and whenever friends message me the messages get sent as iMessages (unless they remember to specifically chnge the format). I never get these messages. They never get resent as SMSs automatically as is supposed to happen. How can I get my phone number deleted from the iMessage list. I've turned off iMessage on the old iPhone. 'chmod u+x' versus 'chmod +x' What is the difference between chmod u+x and just chmod +x?  I have seen a ton of tutorials that say to use u+x to make scripts executable.  However, omitting the u doesn't seem to have any effect. In  thread, the question was to find a $f: \mathbb{R} \to \mathbb{R}$ such that  $$f(f(x)) = f(x) + x$$  (which was revealed in the comments to be solved by $f(x) = \varphi x$ where $\varphi$ is the  $\frac{1+\sqrt{5}}{2}$).    Having read about  shortly before though, I came up with this train of thought:  $$f(f(x)) = f(x) + x$$ $$\Leftrightarrow f^2 = f^1 + f^0$$ $$f^2 - f - f^0 = 0$$  where $f^n$ denotes the $n$'th iterate of $f$.  Now I solved the resulting quadratic equation much as I did with plain numbers  $$f = \frac{1}{2} \pm \sqrt{\frac{1}{4} + 1}$$ $$f = \frac{1 \pm \sqrt{1+4}}{2} = \frac{1 \pm \sqrt{5}}{2}\cdot f^0$$  And finally the solution $$f(x) = \frac{1 \pm \sqrt{5}}{2} x .$$  Now my question is: *Is it somehow allowed to work with functions in that way?** I know that in the above, there are denotational ambiguities as $1$ is actually treated as $f^0 = id$ ... But since the result is correct, there seems to be some correct thing in this approach.  So can I actually solve certain functional equations like this? And if true, how would the correct notation of the above be? Why can't I log into minecraft with a mojang account? I created a Mojang account and downloaded the Minecraft launcher, but when I started it up, I couldn't log in. Since the log in fields did not require a username, I tried typing in my email, and still couldn't log in. I've tried after resetting my password, but that didn't work either. What am I supposed to do to log in and play? What are drawbacks or disadvantages of singleton pattern? The  is a fully paid up member of the 's , but it lately seems rather orphaned by the developer world. I still use quite a lot of singletons, especially for , and while you have to be a bit careful about multithreading issues (like any class actually), I fail to see why they are so awful.  Stack Overflow especially seems to assume that everyone agrees that Singletons are evil. Why?  Please support your answers with "facts, references, or specific expertise" Show that $C[a,b]$ is a complete space under the metric $d(f,g)=\sup_{t\in [a,b]}|f(t)-g(t)|$. I hava Lenovo g580 laptop. I want to change disk to SSD drive, but I'm not sure if my laptop support SATA 3 (6Gbps).  I write following output:  dmesg | grep SATA [    3.190743] ahci 0000:00:1f.2: AHCI 0001.0300 32 slots 6 ports 6 Gbps 0x5 impl SATA mode [    3.199450] ata1: SATA max UDMA/133 abar m2048@0xd3617000 port 0xd3617100 irq 43 [    3.199455] ata3: SATA max UDMA/133 abar m2048@0xd3617000 port 0xd3617200 irq 43 [    3.518365] ata1: SATA link up 3.0 Gbps (SStatus 123 SControl 300) [    3.857921] ata3: SATA link up 1.5 Gbps (SStatus 113 SControl 300)   Is that means I Can use SSD disk in SATAa 6Gbps mode? I applied for a standard visitor visa to the UK for seven days. I earn £278/month and have been working at the same organization for more than a year. I have saved up enough funds for the trip and I attached bank statements to prove it. The ECO refused my visa stating:      I note that you stated that your trip to the UK will cost you £1100, this is approximately 4 times your monthly income. I do not find it credible that you spend this amount on a trip.   I am a single woman, with no financial responsibilities and I saved up for this trip because I really wanted to visit the UK.  How do I prove to the ECO and the authorities that spending £1,100 for my trip wouldn't have caused me any financial harm neither would I have had to access UK government funds?    Another concern of mine is that if I reapply without the partial funding of my father or get sponsored by a different person, does the amount given by my father previously cause hindrance in my visa application?  Won't they still reject it on the basis of my pay being too insignificant?