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How can I fix a 404 Error when using a PPA or updating my package lists?
A line is drawn through the point $A(1,2)$ to cut the line $2y=3x-5$ in $P$ and the line $x+y=12$ in $Q$. If $AQ=2AP$, find the coordinates of $P$ and $Q$.  I found the lengths of the lines $AQ$ and $AP$ in terms of $x$ and $y$ and used $AQ=2AP$ to get this equation $11x^2-40x-16=0$  Working: $AP=\sqrt{(x-1)^2+(\frac{3}{2}x-\frac{9}{2})^2}=\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $AQ=\sqrt{(x-1)^2+(-x+10)^2}=\sqrt{2x^2-22x+101}$  $AQ=2AP\Rightarrow \sqrt{2x^2-22x+101}=2\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $\Rightarrow 2x^2-22x+101=13x^2-62x+85\Rightarrow 11x^2-40x-16=0$  Using the quadratic formula I found $x=4,x=-\frac{4}{11}$  I then substituted these values into the two equations in the question to get the coordinates $(4,\frac{7}{2}),(-\frac{4}{11},-\frac{15}{11})$ or $(4,8),(-\frac{4}{11},\frac{136}{11})$  But the answers in the book are $(4,\frac{7}{2}),(7,5)$ or $(\frac{2}{5},-\frac{19}{10}),(\frac{11}{5},\frac{49}{5})$  I don't know where I went wrong in my method.  Edit: Found some errors in my method and calculation.  Using $x=4$ in $2y=3x-5$ gives $P(4,\frac{7}{2})$  Line with points $AP$ has equation $y-2=\frac{\frac{7}{2}-2}{3}(x-1)\Rightarrow y=\frac{1}{2}x+\frac{3}{2}$  $Q$ lies on the same line. Therefore, the intersection between $y=\frac{1}{2}x+\frac{3}{2}$ and $y+x=12$ is the point $Q$. Working: $\frac{1}{2}x+\frac{3}{2}=-x+12\Rightarrow x=7$ Therefore, $y=-7+12=5$. Point Q has coordinates $(7,5)$.  But $x=-\frac{4}{11}$ is not the other $x$ coordinate of $P$ according to the answers in the book. I have no idea where I went wrong at this point. Correct tracked camera orientation \bar vs. \overline - when to use what, semantically? Following the question "" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.  I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".  Then I just tried  \documentclass{article}  \begin{document}   \[ \bar{a} \overline{a} \]   \[ \bar{abc} \overline{abc} \] \end{document}   where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).  So, the question here is:  What does \bar represent semantically? And when to choose it over \overline and vice versa? In physics sometimes we find energy that is negative. What does the negative sign indicate? How to handle trigger recursion I have two objects A(parent) and B(child) related by a lookup relationship. I  need to update records in object A using data loader. There is an after update trigger on object A which updates some fields on related records of object B. On object B as well there is an after update trigger which updates a field on parent object A. How can i handle recursion. How to parse data in JSON format? How do I make money efficiently? In Oblivion, I had two favorite money-makers:   Dump all my stuff except some basic armor and potions, and raid an oblivion tower. The armor and weapons was worth lots, and selling it in Anvil made a lot of cash fast. Harvest an entire farm's worth of crops, create 'restore fatigue' potions and sell them.   Skyrim seems to spoil this:   Merchants have a max-amount per day/QOD/... instead of per item You can't carry as much (or maybe I have yet to discover the strength/feather spells) Alchemy is a lot harder (most common items go into food recipes now, which don't sell for those prices) On top of that, once a dungeon is cleared, it doesn't respawn - so no 'farming' familiar dungeons?   What are some easy/repeatable money making methods in Skyrim? Which are most efficient effortwise/real-life-time wise? Is there a word for saying "um" or "uh", etc, during speaking?  Or a word for "um" and "uh", etc? Removing a DE field when DE is used in a data relationship I have a Data Extension field I'd like to delete, but that DE is used in an attribute group/set in Contact Builder. So is it really necessary to delete the data relationship first before I can remove the field? Seems too risky if that's the case. Opposite of "trendy" without a negative meaning I am looking for an opposite to the word trendy without giving a meaning that those who adopted the trend are old-fashioned in hindsight. For example,     Service Oriented Architecture is the trend as of now. But what is trendy in 2014 can become ______ in 2015.   So in 2015, the trend becomes widespread to the extent that it is no longer trendy, but not necessarily old-fashioned.  Edit: I am currently thinking of using mainstream. But still any other thoughts are welcome! How to set a letter to the margin of the page and position it vertically according to alphabetical order? Android: Making Https Request How to change LCD brightness from command line (or via script)? To work around  (changing LCD brightness via hotkeys impossible), I'd like to have one command line query for increasing and one for reducing the brightness of my LCD. I could then map a hotkey to each one of this queries.  The problem is: I don't know how to increase and reduce the LCD brightness on the command line. Do you? How would you go about proving that $$\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$$  for any two integers $a$ and $b$?  Intuitively it is true because when you divide $a$ and $b$ by $\gcd(a,b)$ you cancel out any common factors between them resulting in them becoming coprime. However, how would you prove this rigorously and mathematically? Compare using Thread.Sleep and Timer for delayed execution I have a method which should be delayed running for a specified amount of time.  Should I use  Thread thread = new Thread(() =&gt; {     Thread.Sleep(millisecond);     action(); }); thread.IsBackground = true; thread.Start();   Or  Timer timer = new Timer(o =&gt; action(), null, millisecond, -1);   I had read some  about using Thread.Sleep is bad design. But I don't really understand why.  But for using Timer, Timer has dispose method. Since the execution is delayed, I don't know how to dispose Timer. Do you have any suggestions?  Or if you have alternative codes for delayed execution are also appreciate. Which packages should be loaded after hyperref instead of before? Why does a RegExp with global flag give wrong results? IDW Publishing are bringing out a , Assimilation2, set in ST:TNG (presumably the TNG in the timeline prior to the events of the 2009 movie) featuring the 11th Doctor.  Is the canon of these two universes at all compatible?  Both feature a lot of time travel, so we've seen the development of humanity through many centuries in the future.  Are there direct contradictions that make it impossible for these two universes to merge, without some sort of trick like having the Doctor come from an alternate universe?  Or, given the vast spread of time, is it possible that the events of the Star Trek stories have taken place between Doctor Who stories? How does "warp drive" not violate Special Relativity causality constraints? I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.) Make square image