What is my real weight?
What is the difference between weight and mass?
Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$ What is the acceptable similarity in a mathematics PhD dissertation when checking by Turnitin? I have checked the originality of my PhD thesis in mathematics using . The similarity was 31%. Is this percentage acceptable by most committees? Understanding the differential $dx$ when doing $u$-substitution Let $(x_n)_{n=1}^{\infty}$ be a sequence such that $|x_{n+1} - x_n| &lt; r^n$ for all $n \geq 1$, for some $0 &lt; r &lt; 1$. Prove that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.  I understand that a Cauchy sequence means that for all $\varepsilon &gt; 0$ $\exists N$ so that for $n,m \ge N$ we have $|a_m - a_n| \le \varepsilon$. But this one is really giving me a headache.  I tried doing something like: let $ m &gt; n$. Therefore $x_n - x_m$ =  $(x_n - x_{n-1}) + (x_{n-1} - x_{n-2}) + ... + (x_{m+1} - x_m) $ and then somehow using the triangle inequality to compute some sum such that $x_n - x_m$  &lt; sum which would be epsilon?  any help is appreciated, thank you. What is the geometric meaning of the determinant of a matrix? I know that "The determinant of a matrix represents the area of ​​a rectangle." Perhaps this phrase is imprecise, but I would like to know something more, please.  Thank you very much. Polynomial contrasts for regression I have a table with a column for ID, Date and Frequency of occurrence for that particular date and ID.  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-20      1 4     2014-05-18      6   I'm looking to insert the dates for each ID that aren't currently there (assuming that the date ranges from 2014-05-18 to 2014-05-20) and add a value of 0 in Frequency for those.  For example, you can see that  ID 1 has an observation for all three dates;  ID 2 is missing 2014-05-18 and 2014-05-19;   ID 3 is missing 2014-05-19;   ID 4 is missing 2014-05-19 and 2014-05-20.  Therefore, the output should look like this  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-18      0 2     2014-05-19      0 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-19      0 3     2014-05-20      1 4     2014-05-18      6 4     2014-05-19      0 4     2014-05-20      0   I've attempted the following from . However, that will only add dates with 0 Frequency that aren't present throughout the entire table instead of on an ID level.   DECLARE @s DATE = '20140518', @e DATE = '20140520';  SELECT c.date, Frequency = COALESCE(a.Frequency,0) FROM dbo.Calendar AS c LEFT OUTER JOIN dbo.table AS a ON c.date = s.[date] WHERE c.d &gt;= @s AND c.d &lt; DATEADD(DAY, 1, @e); I just purchased a D5100 and I am  slowly learning the basics.  I mostly shoot landscape/scenery shots.    I have been trying to capture the full moon unsuccessfully.  It looks focused in the viewfinder and I've experimented with slow shutter speeds and large apertures but the resulting image always comes out as a bright glare.  I'm never able to see the details of the moon.  How can I improve my shots? (currently deleted (visible only to 10kers)) is a great example of a duplicate question that should not be deleted. [Note: this question was later merged into , which resulted in the original being hard-deleted. This issue with merging  ] The titles of the duplicates are completely different.  Having duplicates around greatly aids search hits on the site. We need to keep questions like this around for the benefit of the community. Both questions have around 4K views.  They are both relevant.  I cannot believe that a question with over 3K views is being deleted. Edit Search for python continue line and python line break in google.  Both answers are top hits.  They should both be open. I have county data in which the &quot;FIP&quot;s (actually State &quot;FIP&quot;s and County &quot;FIP&quot;s combined). I have data imported as CSV with the sames &quot;FIP&quot;s data titled 'STCounty'. However, the shapefile &quot;FIP&quot;s is listed as a Real and the CSV came in as an Integer and the Join function does not seem to work.  The drop boxes are greyed out/empty. So the bigger questions is how do you change the attribute type in a table? I tried to create a new column in the shapefile (county data) and set it to an integer and then multiply the &quot;FIP&quot;s*1, but got a column full of NULL. I am new to QGIS and have a lot of experience in MapInfo, so the join concept is not new to me, just the syntax in QGIS. Why would spacetime curvature cause gravity? Change the selected value of a drop-down list with jQuery I have a drop-down list with known values. What I'm trying to do is set the drop down list to a particular value that I know exists using jQuery.  Using regular JavaScript, I would do something like:  ddl = document.getElementById("ID of element goes here"); ddl.value = 2; // 2 being the value I want to set it too.   However, I need to do this with jQuery, because I'm using a CSS class for my selector (stupid  client ids...).  Here are a few things I've tried:  $("._statusDDL").val(2); // Doesn't find 2 as a value. $("._statusDDL").children("option").val(2) // Also failed.      How can I do it with jQuery?     Update  So as it turns out, I had it right the first time with:  $("._statusDDL").val(2);   When I put an alert just above it works fine, but when I remove the alert and let it run at full speed, I get the error     Could not set the selected property. Invalid Index   I'm not sure if it's a bug with jQuery or Internet Explorer 6 (I'm guessing Internet Explorer 6), but it's terribly annoying. I have shown that a smooth solution of the problem $u_t+uu_x=0$ with $u(x,0)=\cos{(\pi x)}$ must satisfy the equation $u=\cos{[\pi (x-ut)]}$. Now I want to show that $u$ ceases to exist (as a single-valued continuous function) when $t=\frac{1}{\pi}$.  When $t=\frac{1}{\pi}$, then we get that $u=\cos{(\pi x-u)}$.  With single-valued function is it meant that the function is 1-1 ?  If so, then we have that $\cos{(2 \pi-u)}=\cos{(4 \pi -u)}$, i.e. for two different values of $x$, we get the same $u$, and so for $t=\frac{1}{\pi}$, $u$ is not 1-1.  But if this is meant, how are we sure that for $t \neq \frac{1}{\pi}$ the function is single-valued? I need to draw a tree, and constantly using dotty and including the PNGs is starting to be a pain. Is there a way to get LaTeX to draw it's own trees that doesn't involve learning an entirely new language like TikZ? How can I determine file type without an extension on Windows? Issue with Sorting Layers with an NPC and Tilemap I have a weird thing happening, that I can't quite explain.  I have two scenes, my starting town, and an Arcanist's shop.  When I go into the Arcanist's Shop, the Arcanist NPC stays on the same sorting layer (background layer 0) as my checkered tiles, and the table is background layer 1.  When I start the game, the NPC will switch between being "behind" the table, or on top of it whenever I reenter the Arcanist's Shop scene.  It seems to switch between background layer 0 and 1 with no cause.  I've double checked my sorting layers, they're all where they should be.  I've checked the camera's culling mask, it's fine.  I've checked to see if there are any weird components on anything in my shop scene, and there aren't  See the image attached, this is the same instance of the game, just different times when I enter the Arcanist's Shop.    Screenshot of my tilemap setup: What is the shortest way to compute the last 3 digits of $17^{256}$? What is the shortest way to compute the last 3 digits of $17^{256}$ ?  My solution: \begin{align} 17^{256} &amp;=289^{128} \\ &amp;=(290 - 1)^{128}\\ &amp;=\binom{128}{0}290^{128} -  ... +\binom{128}{126}290^2 - \binom{128}{127}290 + \binom{128}{128} \end{align}  Computed the last 3 terms whose last 3 digits gave the last 3 digits of $17^{256}$.  Is there any shorter method to do this(which requires much less computation) ? I got this $$ f=a(x-1)(x-2)...(x-101) $$ knowing a and that $1 ,2 \ldots ,101$ are it's roots ... I need the roots of $f'$ , how should I do it ? More specifc how can I derivate a polynomial like that, is there a formula or something ? Can I start and stop a tile floor job? I am tiling my bathroom floor and don't soon have a full day to dedicate to the job. Is it ok to lay down a few tiles each day and come back to the job when I have time? I would only lay mortar for the tiles I have time to lay each day.    My concern is that the mortar wouldn't properly "join" to the previously laid sections of tile and cause an inferior result, but I'm not really basing this concern on any facts. That is what I'm hoping to learn with this question. What is a single word for a person who, as a habit, exaggerates a lot when relating information?