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tikz pgf - how to align nodes in multiple \tikzpictures? - tex


the reason for this is of course that the leftmost labels have different widths. hence, a workaround is to set the text width of all the labels to the same, with e.g.every label/.style={text width=3cm,align=center} the 3cm may have to be adjusted, depending on the labels themselves.addendum: strictly speaking, you only need to do this for the leftmost node, as aboammar points out in his answer.hence, you could just modify your code to have, e.g. for the first diagram,label={[text width=3cm,align=center]below:alternate past} or, for the code i posted below, remove the text width=3cm,align=center from the widelabels style, and use \node [place,"alternate past" {widelabels,text width=3cm,align=center}] (n1) {};just for fun, here is a suggestion for an alternative approach to drawing ...






geometry - what is a simple (or not) way of finding the lengths of the diagonals


as i mentioned in the question, here are the two ways that i have found to solve this problem.method 1: trigonometryif we draw in the diagonals, we get the following image, and we know that each diagonal bisects the other as well as the angles of the rhombus:that means that we can say \begin{align*} a &= 25\sin(22.5^{\circ})\text{ mm}\\ b &= 25\cos(22.5^{\circ})\text{ mm}, \end{align*}meaning that the diagonals are \begin{align*} 2a &= 50\sin(22.5^{\circ})\text{ mm}\approx 19.13 \text{ mm}\\ 2b &= 50\cos(22.5^{\circ})\text{ mm} \approx 46.19 \text{ mm}. \end{align*}method 2: (messy) geometryhere i started by drawing a line perpendicular to the top connecting to the lower right angle. since the upper right angle is $45^{\circ}$ we know that ...






algebra precalculus - algebraic identities


we can expand $$(a+b)^2+(b+c)^2+(c+a)^2$$ to get $$2 a^2 + 2 a b + 2 a c + 2 b^2 + 2 b c + 2 c^2 $$we can rearrange this to be more useful:\begin{align}2 a^2 + 2 a b + 2 a c + 2 b^2 + 2 b c + 2 c^2 &= 2 a^2 + 2b^2+2c^2 + 2 a b + 2 a c + 2 b c\\ &=2(a^2+b^2+c^2)+2(ab+ac+bc)\end{align}we know the value of $ab+ac+bc$, so we can say that \begin{align}2(a^2+b^2+c^2)+2(ab+ac+bc)&=2(a^2+b^2+c^2)+2\end{align}now we need to find the value of $a^2+b^2+c^2$. we can do this as follows:\begin{align}(a+b+c)^2&=2^2\\ a^2 + 2 a b + 2 a c + b^2 + 2 b c + c^2&=4\\ a^2+b^2+c^2+2(ab+ac+bc)&=4\\ a^2+b^2+c^2+2\times 1&=4\\ a^2+b^2+c^2&=2\end{align}so now we can say that \begin{align}2(a^2+b^2+c^2)+2&=2\times 2+2\\ &=6\end{align}






adobe illustrator - why do triangles do this with alignment


illustrator's align options use the bounding box as the area of definition, not the center point.therefore, when you click the align buttons, illustrator is centering the triangle's bounding box within the circle's bounding box. it's not paying any attention to the actual center points.the guides here represent the bounding boxes. (art shifts a bit when aligning, but they are the same size as you'll see at the end of the animation). in addition, when you draw holding the option/alt key down, you draw from area center - meaning everything moves outward equidistant from that center point. when you align, you align on visual center (which is what the bounding box center is). you'll notice the triangle's bounding box center is not actually centered in the triangle's area, it's visu...






yeehaw! you'll never guess what these cowboys love most about coming to the big


don’t be fooled by all that singing about “home on the range.” even cowboys like a little taste of urban living every now and then. check out what these hard-ridin’ cattle drivers like to do in the big city when they bring those doggies to market!angus“there’s so many different kinds of things to lasso in the city. yesterday, i roped a halal cart!”jed“out there, all alone on the ranch, i feel like the master of my domain, but here i can get on the subway and feel like an itty-bitty little bug!”tex“i can finally get me some honest to goodness dim sum.”rex“the billboards are incredible. giant, sexy ladies in their under-things. huge bottles of coca cola. it’s so, so close to this reoccurring dream of mine.”skinny pete“three words: no. dang. coyotes.”hank“i like going to a warby parker and tr






align different equations on different equal signs - tex


i am using the \begin{align*} command to structure equations such that they align along the first equal sign. i want to be able to change from one equal sign to another, such that i centre equations a to w on the first equal sign, and then centre the z equation on the second equal sign. attached is the output i'm getting. any pointers?\begin{align*} a&=b\\ c&=d\\ e&=f+g+h+j=w\\ x&=y\\ z&=0\\ \end{align*} i would like to be able to align the first three equations on the first equal sign and the last two equations on the second equal sign like so: a=b c=d e=f+g+h+j=w x=y z=0






8 bizarre but real road signs from keaton patti


the goal of a road sign is to quickly and clearly convey a message to drivers. however, some road signs can be downright confusing. here’s a helpful guide to the meanings of some of the more bizarre road signs.road entering curvethe road curves to the left with a side road entering from the right. drivers should approach the intersection with extra caution. bizarre, right?garfield is ahead with lasagnawithin 100 feet, the driver will encounter garfield with a fresh lasagna. the driver should slow down, if safe, in order to have a chance at stealing the lasagna. disregard this sign on a monday. y crab warningyou’ll be seeing a very y crab soon. remember to keep your eyes on the road and not the seductive crab. 90% of road accidents occur due to y crabs.no snowman zonethis sign signifies tha






geometry - family quiz has us baffled!


let $d$ be the length of the segment $dc$, and $r$ the radius of the larger circle. thanks to the geometric mean theorem of elementary geometry we can write:$$ \begin{align} d \cdot r &= (r-5)^2 \\ d+r &= 2r - 9 \enspace. \end{align}$$ this simplifies to $$ \begin{align} d \cdot r &= r^2 - 10r + 25 \\ d &= r - 9 \enspace. \end{align}$$ therefore the radius of the larger circle is $25$ cm and the radius of the smaller circle is $(2\cdot 25 - 9) / 2 = 41/2 = 20.5$ cm.






send it like beckham! the most shocking leaks from david beckham's email from ry


this weekend it was revealed that david beckham’s private emails had been ed! while much of the “beckileaks” controversy has centered around the english soccer superstar’s now-questionable charity work with unicef and his obsession with being knighted, we found a few more bombshells that’ll knock your cleats off!






functions and sequences problem - mathematics stack exchange


for $k \ge 2$ we have: \begin{align} f(2k) &= f(k) \\ f(2k+1) &= f(k) \end{align} this means $$ f(n) = f(\lfloor n / 2 \rfloor) \quad (*) $$ for $n \ge 4$. if we are using base 2 numbers this means we have a word of length $m$ with at least three bits $$ n = (1 b_{m-1} \dotsb b_2 b_1)_2 \quad (b_i \in \{0, 1\}) $$ and $(*)$ means we can shift right the word (dropping the bit at the end) and keep the value of $f$: $$ f((1 b_{m-1} \dotsb b_2 b_1)_2) = f((1 b_{m-1} \dotsb b_2)_2) \quad (m \ge 3) $$ we repeat until we have less than three bits.in other words \begin{align} f(n) &= f(1 b_{m-1}) \\ &= \begin{cases} f(3), & \text{for } b_{m-1} = 1 \\ f(2), & \text{for } b_{m-1} = 0 \end{cases...






kerning - why is the distance between plus or minus and the number different? -


the reason is that \cee does a different scanning than usual and gets tricked by +, which does have a special meaning inside \ce or \cee, because it's used for reactions.indeed, if you try putting that part outside \cee (which it should be), the problem doesn't show.here's a better version.\documentcl {article} \usepackage[version=3]{mhchem} \usepackage{siunitx} \sisetup{retain-explicit-plus} \begin{document} \begin{align} e&=-0.1\\ f&=+0.1 \end{align} \begin{align} \cee{fe^2+_{(aq)} + 2e- -> fe_{(s)} &\ (reduction)} & e^0 &= \si{-0.41}{\v} \\ \cee{al_{(s)} -> al^3+_{(aq)} + 3e- &\ (oxidation)} & e^0 &= \si{+1.66}{\v} \\ \cee{3fe^2+_{(aq)} + 2al_{(s)} -> 2al^3+_{(aq)} + 3fe_{(s)} & \ (overall)} & e_{\mathrm{cell}} &= \si{+1.25}{\v} \end{






you might be a fascist if... from pitch


when the waiter asks “may i take your order?” you scream back “yes, you must take orders!!”






linear algebra - sum of two rank deficient matrices


noting that $\qquad\text{im}(a+b)\;\text{is a subspace of im}(a) + \text{im}(b)$, an easy sufficient condition is $\qquad\text{rank}(a)+\text{rank}(b) < n$, since then \begin{align*} \text{rank}(a+b) &=\dim(\text{im}(a+b))\\[4pt] &\le\dim(\text{im}(a) + \text{im}(b))\\[4pt] &\le\dim(\text{im}(a)) + \dim(\text{im}(b))\\[4pt] &=\text{rank}(a) + \text{rank}(b)\\[4pt] &






10 things abraham lincoln says while kicking your from pitch


“your will little note, nor long remember what i say here, but it will never forget what i did here.”






real analysis - solving an infinite sum using integration or derivation


note that we have $\int_0^x t^{n-1}\,dt=\frac{x^n}{n}$. then, we can write$$\begin{align} \sum_{n=1}^\infty \frac{x^{2n}}{n^2}&=\sum_{n=1}^\infty \int_0^x t^{n-1}\,dt\int_0^x s^{n-1}\,ds\\\\ &=\int_0^x\int_0^x \frac{1}{1-st}\,ds\,dt\\\\ &=-\int_0^{x} \frac{\log(1-sx)}{s}\,ds\\\\ &=-\int_0^{x^2} \frac{\log(1-s)}{s}\,ds\\\\ &=\text{li}_2(x^2) \end{align}$$evaluating at $x=1/\sqrt{2}$ yields$$\sum_{n=1}^\infty \frac{1}{n^2\,2^n}=\text{li}_2(1/2)=\frac{\pi^2}{12}-\frac12\log^2(2)$$and we are done!to evaluate $\text{li}_2(1/2)$, we exploit the relationship$$\text{li}_2(1-x)=-\text{li}_2\left(1-\frac1x\right)-\frac12\log^2(x)$$letting $x=1/2$ yields$$\text{li}_2(1/2)=-\text{li}_2\left(-1\right)-\frac12\log^2(1/...






a complete guide to football referee hand signals from alex pearson


football refs make a lot of gestures, and not all of them make sense. here’s a quick guide to what they all mean:forgetting to wear a watchnetworking with an opposing playerexcessive rubbingyou missed two cl es, and no homeworkbeing too jackedstop play: ducks crossing the fieldwarning: time is a flat circleyour name’s not on the liststomach growling during the national antheminsulting the ref’s soul patch






25 teen vaping trends even cooler and more dangerous than dripping from alex pea


a new study says a fourth of teens who vape use an alarming technique known as “dripping.” but here are 25 even cooler and more dangerous trends for teens who vape:1. slurpingdrinking e-liquid through a straw you found in the trash2. sprinklingemptying a watering can full of steaming vape liquid directly on your head3. vape bombingpouring an e-cigarette into a pint of guinness and chugging4. knife fightingdipping a heated blade in e-juice and challenging a rival to a “beat it” style knife fight5. tattooingusing nicotine ink to mark your skin permanently with the name of someone you are dating, but not exclusively yet6. scuba divingfully submerging in a pool of e-juice, without tying your drawstring7. neti pottingpouring a small pot of nicotine liquid into the nostril, vape amoebas be damne






how to tell if this mansion is haunted from pitch


the decapitated child standing on the ceiling tells you she also saw that creepy puppet moving on its own






our country is falling apart, but at least we still have pizza from evan waite


america has had a rough go of it lately. the most vulnerable among us are being targeted by an administration seemingly hell-bent on inflicting pain against them for no discernible reason, and we are stirring up trouble abroad with short-sighted decisions. but on the other hand, pizza is delicious, and we have thousands of places dedicated to making it!we are in no danger of running out of dough. that’s not nothing.while it’s true that the recent muslim ban goes against the very principles of religious liberty our government was founded on, one thing that remains unchanged is that you can get a slice pretty much anytime you want. these days, most pizza joints will deliver right to your house, so you don’t even have to change out of your sweatpants or make an effort to look presentable. bas






amid boycott of ivanka trump-branded products, her perfume is a bestseller on am


a trump adviser’s move from fringes of washington to the west wingsebastian gorka, a former breitbart news editor, occupies a senior job in the white house, and his controversial ideas — especially about islam — drive the president’s populist approach to counterterrorism and national security.






things to say during the super bowl that'll have your friends saying "this perso


“i hate to interrupt the game, but i would like to propose marriage to sports!”






horizontal alignment - how to align text in the middle of \items? - tex


\documentclass[a4paper,10pt]{article} \begin{document} \begin{itemize} \item enfranchise \item talisman \item noxious : abrasive \item billowing : replete \item tangent : abasement \end{itemize} \end{document} what i would like is to align the words abrasive, replete, and abasement only, without introducing any other additional spacing anywhere else (that align seems to do in between the new lines?)






her twin’s hat fell from a world trade center escalator. she reached — and plung


trump undertakes most ambitious regulatory rollback since reaganas the administration targets dozens of obama-era policies, business leaders are thrilled, saying president trump is responding to long-standing complaints. but the campaign has alarmed labor unions, safety advocates and environmental activists as the fallout ripples across the federal bureaucracy and u.s. economy.






you won’t believe where these 2013 puppy bowl puppies are now! from claire coope


penelope, teimmediately after puppy bowl ix penelope s to fame as one of the recurring hosts of fox nfl sunday. you can catch her, along with michael strahan and terry bradshaw, every sunday at 12pm et on the fox network. wiggles, wrafter being named most valuable puppy of 2013, wiggles was well poised for an illustrious career in sports. that was until the 2014 off-season when he signed on as a contestant with dancing with the stars and tore his acl. the damage was irreparable, forcing the spritely prodigy into early retirement. wiggles is currently being treated for depression and opioid addiction at a luxury rehabilitation center in costa rica.crumbs, rbshortly after puppy bowl ix, crumbs met and fell in love with aleisha, a whimsical spoodle with a penchant for whistles. crumbs and ali






javascript - apply click method to outer div but not inner div


in this example i want the alert to be triggered when the black outer div is clicked but not when anything inside the inner div is clicked.currently when i click the inner button it triggers the alert.$("#outer").click(function() { alert("triggered"); });#outer{ position: absolute; width: 100%; height: 100%; background-color: #000; display: flex; justify-content: center; align-items: center; } #inner{ background-color: #fff; width: 300px; height: 300px; text-align: center; } inner button i want inside the inner div nothing to trigger the alert. how do i do this?(for some reason inner button isn't showing in snippet, here is codepen link: https://codepen.io/guerrillacoder/pen/pmvmqx)






a guide to who you are supposed to tip and how much from keaton patti


waitersalways tip your waiter. 15% of the cost of your meal is considered standard, but you can lower or raise that number based on the service. if your waiter is amazing and helpful, a 25% tip could be deserved. if your waiter is slow, rude, eats half of the steak you ordered and then says “that’s just how steaks look, dude” while pieces of steak drop out of his mouth, and during the meal he hits on both your mom and dad, but neglects to hit on you, a 10% tip may be in order.bartendersalways tip your bartender. a dollar for a normal drink and perhaps two dollars for a fancy tail is expected. if they do any cool tricks where they juggle liquor bottles and flip gl es in the air, tip them by reminding them this isn’t a circus. sometimes they forget.movers always tip your movers. if someone i






these 10 people guess how old tom brady is from alex pearson


we asked these 10 people the same question: “how old is tom brady?”“just by looking at him, i’d say he’s in his twenties or his thirties or his forties. definitely under sixty.”“no clue, but i know his wife is 36, which is kind of creepy considering how much older or younger than her he might be.”“the patriots have been around since 1960. tom brady is the new england patriots. therefore, by deductive reasoning, tom brady is immortal.”“it’s kind of a benjamin on situation, except he was born one age and will always be that age. until his tenth super bowl, when he will suddenly wither and die.”“are you counting the time belichick keeps him suspended in the cryo-pod or not?”“i find that the best way to tell a person’s true age is their eyes, which in this case is useless because i dare not ga






12 ways to make sure everyone remembers you at your high school reunion from pit


sever one of your limbs and walk around all night saying “geez, i know i’m missing something, but what is it??”






how prejudice by whites may keep black college sports stars from getting paid


white house tries to gain a sense of order amid misstepsalthough there have been some successes, the administration remains dogged by slip-ups, half-truths and bombshells, some of them set off by the president himself.






how prejudice by whites may keep black college sports stars from getting paid


trump’s white house tries to gain a sense of order amid misstepsthough there have been some successes, the administration remains dogged by slip-ups, half-truths and bombshells, some of them set off by the president himself.






her twin’s hat fell from a world trade center escalator. she reached — and plung


as flynn faces growing pressure over russia contacts, trump remains silent“the knives are out” for president trump’s national security adviser, an administration official said, after reports that michael flynn misled administration officials about his discussions with the russian ambassador. scrutiny is mounting and neither trump nor his advisers have publicly defended flynn.






fastest-growing new jobs in 2017 from pitch


physical therapist for people with repetitive stress due to throwing their hands in the air in abject despair






math mode - mathematical symbol looks bad in glossary - tex


i have a mathematical symbol that looks good when i use the align-environment. but not when i put the symbol inside $$. this makes the symbol look bad in the glossary, because i can not use align in the glossary. here is a picture, the first symol is using align, the second is using $$. here is the code:\documentclass[a4paper]{memoir} \usepackage{amsmath} \begin{document} \begin{align*} \sum\limits_{\tau=-\infty}^{t}\mathop{}_{\mkern -25mu \delta} \end{align*} \center{$\sum\limits_{\tau=-\infty}^{t}\mathop{}_{\mkern -20mu \delta}$} \end{document} how can i get the first symbol inside the glossary?here is how it is in the glossary:here is the code for the glossary\documentclass[a4paper]{memoir} \usepackage{amsm...






math mode - how to make a nice fraction in subscript? - tex


don't forget nicefrac. and, as erik notes, \sfrac of the xfrac package. finally, i added a \scriptscriptstyle\frac{}{}.\documentclass[11pt]{article} \usepackage{amsmath} \usepackage{nicefrac,xfrac} \begin{document} \begin{align*} m_{\nicefrac{1}{2}}&= \text{ nicefrac}\\ m_{\sfrac{1}{2}}&= \text{ sfrac}\\ m_{\scriptscriptstyle\frac{1}{2}}&= \text{ \texttt{scriptscriptstyle frac}} \end{align*} \end{document}






flabby heart keeps pumping with squeeze from robotic sleeve


this 21-year-old is mayor of an outer d.c. suburba year and a half ago, voters in indian head, md., approved a revolution. they threw out longtime leaders and chose people who had never held elected office. brandon paulin, who was 19 at the time, won in a landslide. in the largely ceremonial job, the part-time college student — and state’s youngest mayor — estimates he works more than 30 hours a week for $6,000 a year.






lethal injection drugs are scarce. arizona wants its death row inmates to bring


this 21-year-old is mayor of an outer d.c. suburba year and a half ago, voters in indian head, md., approved a revolution. they threw out longtime leaders and chose people who had never held elected office. brandon paulin, who was 19 at the time, won in a landslide. in the largely ceremonial job, the part-time college student — and state’s youngest mayor — estimates he works more than 30 hours a week for $6,000 a year.






calculus - finding the expression of a power series.


i thought it might be instructive to present an approach that uses pre-calculus tools only. to that end, we proceed.note that $n=\sum_{m=1}^{n-1} (1)$. therefore, we have$$\begin{align} \sum_{n=1}^\infty (-1)^{n-1} nx^{2n}&=-\sum_{n=1}^\infty\sum_{m=1}^n(1) (-x^2)^n\\\\ &=-\sum_{m=1}^\infty\sum_{n=m}^\infty (-x^2)^n \,\,\,\,\dots\,\,\text{interchange summation order}\\\\ &=-\sum_{m=1}^\infty\frac{(-x^2)^m}{1+x^2}\,\,\,\,\,\,\,\,\,\,\dots\,\,\,\text{sum inner geometric series}\\\\ &=\frac{x^2}{(1+x^2)^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\dots\,\,\text{sum geometric series} \end{align}$$and we are done!






trump jokes with sheriffs about destroying a texas legislator’s career over et f


dhs chief predicts travel ban will be reinstated, acknowledges misstepsahead of a key court hearing at 6 p.m. est, homeland security secretary john kelly said that if he were given a second chance, he might do things differently in rolling out the order. “i should have — this is all on me, by the way — i should have delayed it just a bit, so that i could talk to members of congress,” he said.






trump aides might be considering a major change to the president’s maternity lea


dhs chief predicts travel ban will be reinstated, acknowledges misstepsahead of a key court hearing at 6 p.m. est, homeland security secretary john kelly said that if he were given a second chance, he might do things differently in rolling out the order. “i should have — this is all on me, by the way — i should have delayed it just a bit, so that i could talk to members of congress,” he said.






a man charged onto the runway at honolulu airport. later, he was pronounced dead


for decades monticello hid jefferson’s mistress. now the estate is making room for sally hemings.the founding father, who wrote in 1776 that “all men are created equal,” was the master of a 5,000-acre working plantation. over the course of his life, thomas jefferson owned 607 slaves. a $35 million restoration of the charlottesville site will showcase their lives.story by krissah thompson | photos by norm shafer7 hours ago