Solving an interesting polynomial with degree 4?
Solve for $x$ in $6x^2-25x+12+\frac{25}{x}+\frac{6}{x^2}=0$
Is the set of all finite sequences of letters of Latin alphabet countable/uncountable? How to prove either? Today in Coding/Cryptography class, we were talking about basic definitions, and the professor mentioned that for a set $A=\left \{ \left. a, b, \dots, z \right \} \right.$ (the alphabet) we can define a set $A^{*}=\left \{ \left. a, ksdjf, blocks, coffee, maskdj, \dots, asdlkajsdksjfs \right \} \right.$ (words) as a set that consists of all finite sequences of the elements/letters from our $A$/alphabet. My question is, is this set $A^{*}$ countably or uncountably infinite? Does it matter how many letters there are in your alphabet? If it was, say, $A=\left \{ \left. a \right \} \right.$, then the words in $A^{*}$ would be of form $a, aa, aaa, \dots$ which, I think, would allow a bijection $\mathbb{N} \to A^{*}$ where an integer would signify the number of a's in a word. Can something analogous be done with an alphabet that consists of 26 letters (Latin alphabet), or can countability/uncountability be proved otherwise? And as mentioned before, I am wondering if the number of elements in the alphabet matters, or if all it does is change the formula for a bijection.   P.S. Now that I think of it, maybe we could biject from $\underset{n}{\underbrace{\mathbb{N}\times\mathbb{N}\times\mathbb{N}\times\dots\times\mathbb{N}}}$ to some set of words $A^{*}$ whose alphabet $A$ has $n$ elements? Thanks! I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (2,1,0) x (0,2,2) period 12. I'm a little confused with how to go about this. I would prefer an equation involving $Y_t , e_t, θ$ and $Θ$. Why can a 1 element set be a member of another set but not a subset of it? Windows 8 removes Grub as default boot manager I have a Sony VAIO S series with Windows 8 preinstalled, and I installed Ubuntu 12.10 on a new partition. When the PC boots Grub is display, and I can choose between Windows 8 (didn't worked at the beginning, had to change Grub settings) and Ubuntu 12.10. When I select Ubuntu 12.10 everything is OK, but when I use Windows 8, and I restart Grub isn't displayed anymore (Windows 8 boots immediately).  I booted a Ubuntu 12.10 LiveUSB, used efibootmgr, and found out that Windows 8 (each time it boots) changes EFI default bootloader from Grub to Windows Boot Manager.  How do I change this in Windows 8? I read something about bcdedit, but it does not work or I don't know how to use it... MySQL Case problem I am trying to run a SQL code (I use MySQL). What I want to do is to set DATE_REACT a value when the first condition is satisfied, and a different value when the first condition is not satisfied. The problem is that the first condition is executed always, even when it shouldn't. What I am doing wrong?  UPDATE BILLS SET STATE = 2, DATE_REACT = CASE  WHEN (DATE_EM &lt;= CURTIME() &lt;= ADDTIME(DATE_EM, '00:02:00')) THEN ADDTIME(CURTIME(), '00:13:00') ELSE ADDTIME(DATE_REACT, '00:13:00') END WHERE STATE = 1; Prove $\sin^2\theta + \cos^2\theta = 1$ How do you prove the following trigonometric identity: $$ \sin^2\theta+\cos^2\theta=1$$  I'm curious to know of the different ways of proving this depending on different characterizations of sine and cosine. Please help understanding the difference between force and kinetic energy for an object hitting a wall? If a car hits a wall at a speed of $v$, and an identical car hits a wall at a speed of $2\,v$, with the kinetic energy equation $E_K = \frac{1}{2}mv^2$ (the speed goes from $v$ to $0$) the second car will lose 4 times the energy, and therefore cause 4 times the damage, but with the force equation $F = ma$ (the car hits the wall and decelerates), it will hit with 2 times the force, and cause 2 times the damage.  How can this be explained? Equivalent definition of metric compatibility for a connection: what does $\nabla g$ mean? So the definition I know for metric compatibility is:  $$Xg(Y,Z)=g(\nabla_XY,Z)+g(Y,\nabla_XZ),$$   which make sense, as $g(Y,Z)$ is a smooth function from the manifold to reals and we think of $X$ as a derivation. So now I read this apparent equivalent definition that says $\nabla g=0$. Can someone explain what this means? How can I do $\nabla$ of $g$ I thought $g_p$ is an element of $T_p^*M\otimes T_p^*M$ at every point. Furthermore after you explain the meaning of this can you show me that these two definitions are indeed equivalent? Deriving a QM expectation value for a square of momentum $\langle p^2 \rangle$ I already derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle=  \int\limits_{-\infty}^{\infty} \overline{\Psi}  \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And I can read clearly that operator for momentum equals $\widehat{p}=- i\hbar\frac{d}{dx}$. Is there an easy way to derive an expectation value for $\langle p^2 \rangle$ and its QM operator $\widehat{p^2}$? Automatic line breaking of long lines of text? Here, it is just a example. I have a line:  aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa   Now, I want to let LaTeX automatically wrap the line according to the width of the text block/margins. Why is it differential equations exist on an interval instead of a domain? I understand a domain is the set of input elements a function is defined for (and can have breaks in it e.g. union of 2 sets) and a interval is a continuous range of real numbers. Why do we speak of the solution to a differential equation over an interval instead of an domain? If the solution to an ODE is just a function, and we normally speak of functions as having a domain, then why wouldn't we use domain? When I open the terminal on my Mac, this is what it shows:  australia:~ rod$   I don't live in Australia, don't have anything to do with Australia, nor have ever setup terminal as Australia.   Where does that name come from, why is it there, what does it mean and how do I change it (or should I even change it at all)? Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. (using disk/washer) Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. (using disk/washer)  I saw no example of this problem anywhere.. I saw an example how to solve it without calculus but I'm afraid that'll be deductions on my test.. I have the volume of a cylinder and the method of area between two curves but this is out of my reach.... I don't know what I can try... How do properties work in Object Oriented MATLAB? I am trying to create a MATLAB class with a member variable that's being updated as a result of a method invocation, but when I try to change the property within the class it (apperently, from what I understood from MATLAB's memory management) creates a copy of the object and then modifies it, leaving the original object's property untouched.  classdef testprop       properties           numRequests=0;       end       methods           function Request(this, val)               disp(val);               this.numRequests=this.numRequests+1;           end       end   end     .  &gt;&gt; a=testprop; &gt;&gt; a.Request(9); &gt;&gt; a.Request(5);   &gt;&gt; a.numRequests    ans = 0 What is the relationship between symmetry and degeneracy in quantum mechanics? I would like to create a virtual device in Android Studio but I can't because hardware acceleration is disabled.  I went to the BIOS and there are two option :  AMD-SVM AMD-IOMMU   Both are enabled.  I also downloaded the HAXM installer from the SDK manager and tried to run it from the   C:\Users\%user%\AppData\Local\Android\Sdk\extras\intel\Hardware_Accelerated_Execution_Manager  with intelhaxm-android file.  I got an error telling me :   This computer does not support Intel Virtualization technology VT X or it is exclusively used by Hyper V. HAXM cannot be installed. Please ensure that hyper V is disabled in windows feature   It makes sense that I can't activate Intel Virtualization technology because I have AMD Ryzen 7 2700U.  With my previous computer it worked just fine but I had an Intel processor.  Some tutorials online suggested to enable windows Hyper-V feature but it's only available for windows 10 pro.  Does anyone know a way to activate hardware acceleration with AMD processor and without Hyper-V feature? Check for column name in a SqlDataReader object How do I check to see if a column exists in a SqlDataReader object?  In my data access layer, I have create a method that builds the same object for multiple stored procedures calls.  One of the stored procedures has an additional column that is not used by the other stored procedures.  I want to modified the method to accommodate for every scenario.  My application is written in C#. I've been trying to track a footage taken by my Samsung Galaxy Note 8.0 (GT-n5100) tablet. It has a good 5 mp camera and I tracked the footage well. But the problem arises at the time of solving the camera. The solve error is too high (more than 2). I don't know the width the tablet's camera sensor or the focal length or any other specifications. So my question is, has anybody been able to solve the camera on footage shot by a smartphone and if yes,  what camera and lense specs did you feed to the Blender? How do I sort a vector of pairs based on the second element of the pair? If I have a vector of pairs: std::vector&lt;std::pair&lt;int, int&gt; &gt; vec;  Is there and easy way to sort the list in increasing order based on the second element of the pair? I know I can write a little function object that will do the work, but is there a way to use existing parts of the STL and std::less to do the work directly? EDIT:  I understand that I can write a separate function or class to pass to the third argument to sort.  The question is whether or not I can build it out of standard stuff.  I'd really something that looks like: std::sort(vec.begin(), vec.end(), std::something_magic&lt;int, int, std::less&gt;()); Why is document.write considered a "bad practice"?