For SQL Server 2012 where is better way to restrict rows (WHERE or JOIN)?
Is a join optimized to a where clause at runtime?
How can I identify what application is using a given file? Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple I know how to , but I'd like to add a bunch of different extensions and avoid the tedious job of adding every single one. Is there a command line tool or registry key I can use to accomplish this? What is the reason that the value "47" is so popular in electrical engineering? How do I resolve a recurrence relation when the characteristic equation has fewer roots than terms? I know how to solve "simple" recurrence relations. For instance, say you have:  $$c_0 = 20$$ $$c_1 = 30$$ $$c_n = 3 c_{n-1} - 2 c_{n-2}$$  We can write the characteristic equation as:  $$3x^{n-1} - 2x^{n-2} = x^n$$  Solving this with $n=2$, we get $x = 1$ or $x = 2$. This lets us write the relation $c_n = \alpha_1 1^n + \alpha_2 2^n$, and we can solve for $\alpha_1$ and $\alpha_2$ with the initial states $c_0$ and $c_1$.  However, this depends on the fact that $3x^{n-1} - 2x^{n-2} = x^n$ has two roots.  Now, I'm stuck on another problem where the characteristic equation has fewer roots than terms.  Say I have this recurrence relation instead:  $$a_0 = 0$$ $$a_1 = 2$$ $$a_2 = −1$$ $$a_n = 9a_{n-1} - 15a_{n-2} - 25a_{n-3}$$  The characteristic equation would be:  $$9x^{n-1} - 15x^{n-2} - 25x^{n-3} = x^n$$  However, solving with $n=3$, we only get two roots: $x=-1$ or $x=5$. There are not enough roots to write a relation in the form of $a_n = \alpha_1 r_1^n + \alpha_2r_2^n + \alpha_3r_3^n$. How do I proceed? "It was recommended that" + verb in present tense It was recommended that the international development partners develop guidelines or a roadmap to help countries take the necessary steps to select the right tool for their purposes.   Why is it using present tense "develop" in the sentence which is actually a past tense "It was recommended"? Does the alarm work when my phone is turned off? What resolution should a large format artwork for print be? How to check if specific column exists in an Access database table Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$ When should I implement IDisposable? AJAX call using admin-ajax URL is returning 400 bad request Why is the derivative of a vector orthogonal to the vector itself? $R(t) \cdot R'(t) = 0$, which is what every source I can find tells me. Even though I understand the proof I don't understand the underlying concept. If $R(t)\cdot R'(t) = 0$, then $R'(t)$ is orthogonal to $R(t)$, right?   But you use the same derivative to find the tangent of a curve. Then somehow if you differentiate the tangent itself, you get the normal to the curve.  I really can't wrap my head around this. Could someone help me understand? Must present perfect tense be used if the action takes place more than once? I was told that if an action is completed once in the past, the simple past is used. Ex:  I saw that movie.  If the action is completed more than once, the present perfect tense must be used. Ex:  I have seen that movie twelve times.    So, "I have seen that movie twelve times on Tuesday." is correct and "I saw that movie twelve times on Tuesday." is incorrect? Unitary map between sets of vectors How to show $d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}$ is a metric? $d_1(x_1,y_1)$ and  $d_2(x_2,y_2)$ are metric on $X$ and $d(x,y)$ is defined as: $$d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}.$$ I am trying to show this is a metric. Can you give me some clue about proving the triangle inequality for $d$ ? Thank you for your help. How to remove configuration files completely Recently I uninstalled some software using sudo apt-get --purge autoremove, thinking that this would remove all traces of it including unused dependencies and configuration files. However I discovered that a configuration file was left behind in my home folder.  Is there a more powerful command which would remove even that?   Also, is it safe to delete the hidden files and folders under home, if they are merely configuration files, or are there other kinds of files? Disable automatic screen turn-off during call Probability of $p(x_1<x_2<\max(x_3,x_4))$ Dual Canadian and British citizen - healthcare coverage in the UK?