I'm trying to get back to my graduation after a long time and i'm stuck on this problem using vectors: I want to find $\vec{x}$ knowing that $e = \vec{c}.\vec{x}$ and $\vec{v} = \vec{c} \times\vec{x}$. What is the best approach?
I was wondering if $\mathbf{A}\times\mathbf{C}=\mathbf{B}$ and $\mathbf{A}\cdot{\mathbf{C}}= p$, is it possible to express C in terms of A, B, and p?  Note: A, B, C are vectors and p is a scalar.  Sorry if this question has been asked before. If so, can anyone give me a link to it?
Is there a point of beating Vault of Glass raid on Hard after finishing on Normal? What kind of passport do I need when entering the USA? I heard that you need a biometric passport if you want to enter USA. However, my friend has a biometric passport, but no fingerprints in it. Is this enough? And how long has the passport to be valid? Is it okay if it expires on the day after his return date? If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square. Problem is as stated in the title. Source is Larson's 'Problem Solving through Problems'. I've tried all kinds of factorizations with this trying to get it to the form $$k^2l^2$$ but nothing's clicking. I tried Bézout but the same expression can be written as $$a^2 + (a^2 + 1)(a+1)^2$$ which would imply that there is no real root.  Would really appreciate some help, thanks. Prove that the equation $x^2-y^2 = 2002$ has no integer solution Selenium/PhantomJS raises error Fedora 25 and disabling whatever is listening on port 111 I've got a Fedora 25 x86_64 stand alone workstation. Something is listening on port 111 (identified with an nmap scan):  $ sudo lsof -i :111 COMMAND PID USER   FD   TYPE DEVICE SIZE/OFF NODE NAME systemd   1 root   36u  IPv4  15170      0t0  TCP *:sunrpc (LISTEN) systemd   1 root   37u  IPv4  15171      0t0  UDP *:sunrpc systemd   1 root   38u  IPv6  15172      0t0  TCP *:sunrpc (LISTEN) systemd   1 root   39u  IPv6  15173      0t0  UDP *:sunrpc   I disabled the Sun gear on the port with the following commands:  $ sudo systemctl disable rpcbind $ sudo systemctl disable sunrpc Failed to disable unit: No such file or directory   After reboot the port is still open.  It appears something other than Sun gear wants to listen on port 111. Or maybe systemd is not respecting my wishes to disable the unused service. Or maybe something else...  How do I determine what is trying to listen on the port, and how do I disable it?    From below:  $ sudo systemctl -a | grep -E "rpc|port"   var-lib-nfs-rpc_pipefs.mount          loaded    active   mounted   RPC Pipe File System   abrtd.service                         loaded    active   running   ABRT Automated Bug Reporting Tool   auth-rpcgss-module.service            loaded    inactive dead      Kernel Module supporting RPCSEC_GSS   fedora-import-state.service           loaded    active   exited    Import network configuration from initramfs   fedora-readonly.service               loaded    active   exited    Configure read-only root support   rpc-gssd.service                      loaded    inactive dead      RPC security service for NFS client and server   rpc-statd-notify.service              loaded    inactive dead      Notify NFS peers of a restart   rpc-statd.service                     loaded    inactive dead      NFS status monitor for NFSv2/3 locking. ● rpc-svcgssd.service                   not-found inactive dead      rpc-svcgssd.service   rpcbind.service                       loaded    inactive dead      RPC Bind   rpcbind.socket                        loaded    active   listening RPCbind Server Activation Socket   rpc_pipefs.target                     loaded    active   active    rpc_pipefs.target   rpcbind.target                        loaded    active   active    RPC Port Mapper I've got a project where I'm looking to tweak the standard lead conversion process.   Triggers and lead conversion has always been funky in past projects so I was hoping to start the design off by reviewing the order of execution, but after a long google search I'm coming up empty handed.   Anyone out there know the specific trigger order for lead conversion?    Edit: I'm not asking about trigger execution order for any object, but all the objects created in the lead conversion process.  I'd think it would be something like this:        Lead Before Update Triggers (isConverted = false, convertedAccountId = null, convertContactId = null, convertedOpportunityId = null)         Account Before Insert Triggers (not fired if merged with existing account)   Account After Insert Triggers (not fired if merged with existing account)   Contact Before Insert Triggers (not fired if merged with existing contact)   Contact After Insert Triggers (not fired if merged with existing contact)   Opportunity Before Insert Triggers (not fired if no opportunity) (OpportunityContactRoles null)   Opportunity After Insert Triggers (not fired if no opportunity) (OpportunityContactRoles = convertedContactId)   Lead After Update Triggers (isConverted = true, convertedAccountId = XXX, convertedContactId = XXX, convertedOpportunityId = XXX) multi-layer board copper pour I have a 6-layer board where the internal 4 planes are +15,GND,VCC,-15.  I was wondering if there was any advantage to doing a copper pour on the top and bottom layers?  I would probably leave them floating as I don't want to use micro-vias to say tie it to GND?    Is this actually a bad idea?  I.e. floating copper=antenna.  Would it be just as acceptable to have 4 layer board with the top layer having copper pour to VCC and the bottom having a pour to GND and keep the two internals as +-15?  Note that this is for a fairly low speed circuit which has some analog and digital parts. Answers in top Network Posts showing incorrect score There is already a question  which is posted around a month ago (which was fixed). My question reports a similar issue of showing inaccurate scores along with another bug.   A couple of answers in the Top Answers in my network profile are showing incorrect score.         As we can see they are showing a score of 10. But as of writing this question, the score of both the answers is 9.  and  both have a score of 9 instead of 10.  Even though the current score is 9, both these answers reached a score of 10 a few months ago and I was awarded  for both.         The vote was removed either when a user was removed or there was an unupvote. As far as I can tell, I don't remember an unupvote notification in the achievement box from these answers. My guess is the votes are removed when user accounts were deleted.   So, I suspect the score of answers in Top Network Posts is not updated either when there is an unupvote or a vote thrown away due to account deletion.   Is this the right reason why score is inaccurate? Can this be fixed? Problem of unbalanced data How to prevent LaTeX from line-breaking a phrase? How can I prevent LaTeX from putting line-breaks into a phrase?  I could replace dashes with  and spaces with non-breaking spaces, but I'm looking for a more general solution in case I need other characters in such phrases. Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$? It's well seen throughout the series that there is a “curse” on the DADA teacher position, that no one can hold that post for more than a year. But it seems like Quirrell has been around for longer than a year. What's up with that? I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? What is the rationale for all comparisons returning false for IEEE754 NaN values? I have a file, which was encrypted with AES-128 in ECB mode. I know the format of the original file and know that all files in this format have the same headers. So, I have an encrypted block and the original block.  Can I get the encryption key, using this information? What was Dumbledore's original wand made of? Rules for the usage of "me" VS. "myself"? What are general guidelines for the use of "me" and "myself"?     Did I describe me or did I describe Maria?   OR     Did I describe myself or did I describe Maria? How do I Sort a Multidimensional Array in PHP I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row. I need to use binary variables (values 0 &amp; 1) in k-means. But k-means only works with continuous variables. I know some people still use these binary variables in k-means ignoring the fact that k-means is only designed for continuous variables. This is unacceptable to me.  Questions:     So what is the statistically / mathematically correct way of using binary variables in k-means / hierarchical clustering? How to implement the solution in SAS / R?