In A New Hope  they needed to go through the trench. This meant they lost almost all of their maneuverabiltiy and were easy targets in there due to the narrow width of the trench itself. Now I'm wondering...why did they do that and not fly just outside the trench and then dive bomb onto the shaft and torp it that way? Is there any in universe reason? (out of universe I guess it was the rule of cool that succeeded there).
We all know how to blow up the first Death Star: Fire a couple of proton torpedoes into the thermal exhaust port.  It's ray shielded, so only torpedoes will do.  To do this, the Rebel pilots had to fly down a very long trench, where they were vulnerable to fire from any TIE fighters to the rear.  In fact they were so vulnerable that most of the pilots on this run were blown up once the Imperial forces started responding to the attack. This battle is in space, so the fighters can, if necessary, come to a dead stop and hold their position while firing.  Also, when Luke fired his torpedoes, they took a 90 degree turn and went straight into the port.  So the torpedoes didn't have to be fired from in the trench. We also didn't see any gun emplacements firing at the fighters from near the exhaust port, but if there were, the Rebels could have targeted them and taken them out or run interference to make it hard for the towers to fire at a fighter targeting the exhaust port.  (They were already dodging fire in the trench as well.) A fighter could have easily flown directly at the exhaust port, firing torpedoes multiple times on approach and, if not under fire (or if protected by other fighters), could have actually stopped and taken time to target the exhaust port before firing. Is there any valid in-universe reason that the pilots had to fly down the trench before firing on the port?  And if there is, is there any reason they had to enter the trench so early? Just for reference, here is the  on YouTube.  There's no explanation given for having to fly in the trench.
Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ Recently, I encountered a problem about infinite series. So my question is how to know whether the infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ is convergent? Can awakened mind be used with suggestion? Can the warlock class feature "awakened mind" be used in conjunction with the suggestion spell, allowing the warlock to make the suggestion telepathically?  Awakened Mind, Player's Handbook p. 110:     You can telepathically speak to any creature you can see within 30 feet of you. You don't need to share a language with the creature for it to understand your telepathic utterances.   Suggestion, Player's Handbook p. 279:     You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you.   If it works with suggestion, would it also work with mass suggestion?  To be clear, I am not asking about the verbal component of the spell, only the method the caster "suggests a course of activity". $\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this? I came across a question where I needed to find the sum of the factorials of the first $n$ numbers. So I was wondering if there is any generic formula for this? Like there is a generic formula for the series: $$ 1 + 2 + 3 + 4 + \cdots + n = \frac{n(n+1)}{2} $$ or $$ 1^{2} + 2^{2} + 3^{2} + 4^{2} + \cdots + n^{2} = \frac{n(n+1)(2n + 1)}{6} $$  Is there is any formula for: $$ 1! +2! +3! + 4! + \cdots + n! $$ and $$ {1!}^2 +{2!}^2 +{3!}^2 + \cdots + {n!}^2 $$?  Thanks in advance. If not, is there any research on making this type of formula? Because I am interested. Least rank of a matrix Let $A$ be a $7\times 7$ matrix such that it has rank $3$ and $a$ be $7\times 1$ column vector.  Then least possible rank of $A+(a a^T)$ is? ($a^T$ is transpose of the vector)  Intuitively I think it's $2$ as $a a^T$ has rank $1$, and the most it could affect is one row of $A$. YA coming-of-age fantasy series, protagonist keeps pigs I lost a series books during a move and I'm thinking I might like to get them for my son.  They are about a teenage orphan who lives with a (sort of) wizard who's primarily known for his prize pig. There is a "bad guy" but he doesn't do much - he starts off the action in one by scaring the pig, and the boy has to chase after it. He goes on several such adventures, notably one to "find his true nature" that ends with him staring into a pool.  I suppose it could be the early books of , but I'm pretty sure I read them in the 1980s, not 90s, and title seems wrong. And unlike the Wiki description, in the series I'm thinking of, there's no real magic to speak of - its "out there" but does not seem to be part of the action that I recall. No internet after upgrade to 17.10 ReaderWriterLockSlim vs. Monitor I have an IDictionary&lt;TKey,TValue&gt; implementation that internally holds n other Dictionary&lt;TKey, TValue&gt; and distributes that insertions by the HashCode of the key to the invidual sub-dictionaries. With 16 sub-dictionaries, the number of collisions is pretty low on a 4-core machine.  For parallel insertions, i locked the Add-method with a ReaderWriterLockSlim, locking only the individual sub-dictionary:    public void Add(TKey key, TValue value)         {             int poolIndex = GetPoolIndex(key);             this.locks[poolIndex].EnterWriteLock();             try             {                 this.pools[poolIndex].Add(key, value);             }             finally             {                 this.locks[poolIndex].ExitWriteLock();             }         }   When inserting items with four threads, i only got about 32% cpu usage and bad performance. So i replaced the ReaderWriterLockSlim by a Monitor (i.e., the lock keyword). CPU usage was now at nearly 100% and the performance was more than doubled.   My question is: Why did the CPU usage increase? The number of collisions should not have changed. What makes ReaderWriterLock.EnterWriteLock wait so many times? Does Java Connection.close rollback? Does Java Connection.close rollback into a finally block?.  I know .Net SqlConnection.close does it.  With this I could make try/finally blocks without catch...  Example:  try {     conn.setAutoCommit(false);     ResultSet rs = executeQuery(conn, ...);     ....     executeNonQuery(conn, ...);     ....      conn.commit(); } finally {    conn.close(); } Program does not wait before output Why isn't the product rule used in the definition of mechanical work? Looking for old book, SF, artificial world, different zones for different species that visitors "inhabit" I read this book at least ten years ago.  Any help identifying it would be appreciated.  Characters are teleported to an artificial world where each take over the mind of a different species.  I remember a moving sentient plant, a faun-like character, and a wasp-like character.  The planet is subdivided into different zones designed for each species.  One of the characters had long sharp fingernails with poison in them.  Thanks for any help, steve I want wp_link_pages (mutli-page posts) to display the page numbers, the word "previous" before those numbers, and a "next" after those numbers.  It would look like this:  Prev 1, 2, 3, 4 Next  I'm attempting to do this without a plugin.  Here's what I've tried so far, but it isn't working, it is only displaying numbers.  &lt;?php wp_link_pages(array(     'before' =&gt; '&lt;span style="clear:both; display:block"&gt;Pages',      'after'  =&gt; '&lt;/span&gt;',     'next_or_number'=&gt;'number',     'previouspagelink' =&gt; 'previous',     'nextpagelink'=&gt; 'Next' )); ?&gt; Responsive Breakpoints? Twitter Bootstrap uses these break points for responsive design:  Large Display: 1200px Default: 980px Tablet: 768px Mobile: 480px  A client said they are using 1280px for their Large Display breakpoint.  Is there an industry standard for these or are they just made up as we go right now? How to find correctly the .bib file? How to make a multiboot CD that will start a user-chosen ISO file I have many CD ISOs downloaded from the Internet. They are each about 100 MB in size and consist of repair/diagnostic programs and other tools. Some of them are Linux-based; others are based on DOS clones, like FreeDOS. I want to put all of the ISOs onto one bootable DVD, so that when I use the DVD, I will get a menu prompting me to select the ISO I want to boot. How can I do this? I've seen some rescue CDs that are combinations of other people's ISOs, but I have no idea how they were made.  Regarding bounty: I, a different person than the OP, have placed a bounty on this question for a solution that meets ALL of these criteria:  Is for DVDs (not flash drives!!!) Is free Works with any ISO file, regardless of original OS How to open a PDF form file that says Please wait...? I posted a question recently regarding my Windows 10 upgrade which ended up with a black screen and cursor.   I reverted back to Windows 8.1 using the "Revert to previous build" option in recovery, and all seems fine, except that Virtualisation is disabled.  I tried to open BIOS settings but it just boots into Windows. I've tried the usual F2 key and Shift F2, all the other F keys, tried pressing B and Shift+B but no luck.  I tried pressing the Lenovo key on the laptop when it is powered down, which shows a menu to either boot into BIOS, recovery, or show boot menu. I choose BIOS and it just boots into Windows.  I tried going into advanced startup options from Windows (Shift+Restart) and choosing "UEFI FIRMWARE SETTINGS" but it just reboots back into Windows.  Before the Windows 10 upgrade it was working perfectly.  Lenovo G580 laptop - Core i3 with Intel 4000 graphics. 8GB of RAM and a Crucial MX100 512GB SSD (replaced the original hard drive with this SSD). I've been wondering why I've never seen any official specifications of the maximum allowed torque that can be exerted upon lens mounts. It seems to me like a very useful specification, but I can't seem to find it from any manufacturer.  indicates that there might be no specifications for Nikon mounts. Are there really no manufacturer that publish these specification of their mounts? So i have this $3\times 3$ matrix  $$     \begin{pmatrix}     -2 &amp; 0 &amp; 0 \\     3 &amp; 1 &amp; -6 \\     0 &amp; 0 &amp; -2 \\     \end{pmatrix} $$  I want to check if the matrix is diagonizable. First thing i do is find the roots : namely $\lambda_1 = −2$ of multiplicity $2,$ and $\lambda_2 = 1$ of multiplicity $1.$  In order to ensure that the matrix is diagonalizable we need to find a basis of $\mathbb{R}^3$ whose elements are eigenvectors for $A.$ In particular, since we have the eigenvalue $\lambda_1=-2$ having multiplicity $2$ we need to check that the dimension of the eigenspace $E(\lambda_1)$ is equal to $2.$ We compute the eigenspaces of $A.$  $\DeclareMathOperator\Nul{Nul}$On the answer sheet is says that we need to find $\Nul(A+2Id)$... but why $2Id?$ Isn't is supposed to be $-2,$ so $\Nul(-2Id-A)$??   I do not understand this $\Nul(A+2Id).$ I always thought that we should compute $\Nul(-2Id-A),$ so what do i need to do ?   $\Nul(-2Id-A)$ gives me a different result from $\Nul(A+2Id).$  Does that mean that since $-2$ has a multiplicity of $2,$ we need to work with $2$ and not $-2$?  Somebody please help with a clear and simple explanation ! Thanks! Has any Dark Force user/ally ever said "May the Force be with you"?