Mostly we some times uses silent words like knife, knock, knee etc i want to know is there any law in english please also inform me why these are silent? I am a new english language learner.
Why have a letter in a word when it’s silent in pronunciation, like the b in debt?  Can anyone please clarify my uncertainty here?
Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$ $$I_1=\int_{0}^{1} \left(1-x^{50}\right)^{100} dx$$ and $$I_2=\int_{0}^{1} \left(1-x^{50}\right)^{101} dx$$ Then find $\frac{I_1}{I_2}$  I tried by subtracting $I_1$ and $I_2$   $$I_1-I_2=\int_{0}^{1}\left(1-x^{50}\right)^{100}\left(1-(1-x^{50}\right))dx$$ so  $$I_1-I_2=\int_{0}^{1} \left(1-x^{50}\right)^{100} x^{50} dx$$ Now using Integration by Parts we get  $$I_1-I_2= \left(1-x^{50}\right)^{100} \times \frac{x^{51}}{51}\bigg|_{0}^{1} -\int_{0}^{1} 100 \left(1-x^{50}\right)^{99} \times -50 x^{49} \times \frac{x^{51}}{51} dx$$  So $$I_1-I_2=\frac{5050}{51} \times \int_{0}^{1}\left(1-x^{50}\right)^{99} x^{100} dx$$  Now $x^{100}=\left(1-x^{50}\right)^2-(1-x^{50}-x^{50})$ so  $$\frac{51}{5050}(I_1-I_2)=\int_{0}^{1} \left(1-x^{50}\right)^{99} \times \left(\left(1-x^{50}\right)^2-(1-x^{50})+x^{50}\right)dx=I_2-I_1+\int_{0}^{1} \left(1-x^{50}\right)^{99} x^{50} dx$$  Need a hint to proceed further. How do I cd into a directory in the home folder? How do I change directories to downloads, from the home folder, in the latest version Ubuntu 12.10? I tried cd /downloads, but it gave an error saying that there is no such directory. If $G/Z(G)$ is cyclic, then $G$ is abelian Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? single email limit exceeded salesforce very frequently..? my email limit is exceeded after sending 10-12 emails..what could be the problem..as i have seen the limit is 1000 emails/day.i am not able to find out what could be the problem..Can some give me some suggestions. As i also know we can send 10 emails in a single transaction.I am sending emails in a batch class.  I am calling this batch class on button click and filling emailList with emailsId's.                      String query='Select id from Lead';//No use of this query                     Batch_send_emails bse=new Batch_send_emails();                     bse.query=query;                                                         bse.resendEmails=emailList;                     database.executebatch(bse);           **Batch Class**           if(!resendEmails.isEmpty())           {               for(String s:resendEmails)                {                   emailsLeads.add(s);                }           }           Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();         mail.setToAddresses(emailsLeads);        // mail.setCcAddresses(ccAddresses);         String subject='GoToMeeting Invitation Details for '+subject;         String body='test';          mail.setHtmlBody(body);          mail.setSubject(subject);         Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });          } Determinant of a specially structured matrix ($a$'s on the diagonal, all other entries equal to $b$) I have the following $n\times n$ matrix:  $$A=\begin{bmatrix} a &amp; b &amp; \ldots &amp; b\\ b &amp; a &amp; \ldots &amp; b\\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ b &amp; b &amp; \ldots &amp; a\end{bmatrix}$$  where $0 &lt; b &lt; a$.  I am interested in the expression for the determinant $\det[A]$ in terms of $a$, $b$ and $n$.  This seems like a trivial problem, as the matrix $A$ has such a nice structure, but my linear algebra skills are pretty rusty and I can't figure it out.  Any help would be appreciated. I have a txt file which actually is a html source of some webpage. Inside that txt file there are various strings preceded by a "title=" tag.  e.g.   &lt;div id='UWTDivDomains_5_6_2_2'  title='Connectivity Framework'&gt;    I am interested in getting the text Connectivity Framework to be extraced and written to a separate file.  Like this, there are many such tags each having a different text after the title='some text here which i need to extract '  I want to extract all such instances of the text from the html source/txt file and write to a separate txt file. The text can contain lower case, upper case letters and number only. The length of each text string(in characters) will vary.  I am using PowerGrep for windows. Powergrep allows me to search a text file with regular expression inout. I tried using the search as        title='[a-zA-Z0-9]  It shows the correct matches, but it matches only first character of the string and writes only the first character of the text string matched to the second txt file, not all string.   I want all string to be matched and written to the second file.  What is the correct regular expression or way to do what i want to do, using powergrep?  -AD. What did the public at large know about the assassination attempt on Palpatine and how he survived it? Jackknife vs. LOOCV How to solve a system of PDEs with zip condition? At what time will the upcoming Ubuntu release be made available? Every six months a new Ubuntu version will be released. Does anyone know at which time this will be? What command can I type into the Terminal so that I can delete all .svn folders within a folder (and from all subdirectories) but not delete anything else? A clock in freefall Time dilation  using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$  For such a non rotating spherical body, what would the time dilation of a clock in vacuum free-falling from infinity be?  (If the answer is non-trivial; a high level outline of the calculation would suffice / be appreciated)  Edit: I am currently working on an iOS app that is trying to model the mechanism underpinning relativity.  So, far the mechanism that I have created is shockingly simple and shockingly good at conforming to Relativity.  However, I am trying to break it.  I am trying to find any possible areas where the two may diverge.  I have noted that using my model a clock in freefall will experience no time dilation, i.e. $t_0=t_f$ and I want to make sure Relativity agrees.  I have noted the gravitational component of time dilation above.  Since my clock is moving one might also expect a kinematic time dilation.  I can calculate the velocity of my clock: $$E_k=\frac{1}{2}mv^2$$ $$E_p=\frac{-GMm}{r}$$ $$v=\sqrt{\frac{2GM}{r}}$$ Plugging this velocity into the kinematic time dilation equation: $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$ $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{2GM}{rc^2}}}$$  At this point one might make the observation that the kinematic dilation is the inverse of the gravitational dilation and therefore conclude that: $$t_0=t_f$$ How did Newton discover his second law? I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to his studies of the motion of the moon and earth? Was he able to analyze this data to see that the masses were inversely related to the acceleration, if we assume that the force the moon on the earth is equal to the force the earth exerts on the moon?   According to , the  reads:     Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.   Translated as:      Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.   My question is how did Newton come to this conclusion? I get that he knew from  the idea of inertia, but this doesn't instantly tell us that the change in momentum must be proportional to the net force. Did Newton just assume this, or was there some experiment he performed to tell him this? Can the relative pronoun "whose" be used for animals, things and countries? When I was a student of English as a foreign language, more years ago than I care to count, I was taught that the relative pronoun “whose” could only be used for human beings, i.e., when someone possesses something.   My teachers were native speakers from England, then.   Since that time, I’ve seen “whose”, as a relative pronoun, used in several contexts where no human beings are mentioned, e.g. with animals, objects, countries, abstract nouns, etc, in American newspapers and magazines. Unfortunately, I can’t remember any of the sentences and cannot give examples.  What is acceptable in written and spoken English, and what isn’t, concerning the use of “whose” ? Exactly what the name entails. The function $2^n-1$ I see largely tends to generate primes when $n$ is prime. However, a week ago I heard that this was horribly false. Please show me a disproof. "Answerer" and "asker" Error in Obj-C : Expected identifier or '(' Is the Playstation 4 backwards-compatible? Does the PS4 have backwards compatibility of some form? The majority of forums/sites suggest not, or posters are adamant it doesn't yet. Others imply that some form of backwards compatibility will include a cloud service and PS3 titles? I've even heard on some forums that PS4 does actually play PS3 games but those posts seem to be a minority compared to those that say it's not... How can I get distribution name and version number in a simple shell script? File l3backend-pdfmode.def not found when loading expl3 I updated my TeXlive distribution a couple times in the past week, and now I get this error when I include package expl3 (or any other package that includes it, such as fontspec). Before the updates it was working fine. Am I missing any package that should be installed? I tried searching for l3backend-pdfmode.def, but I found no results.  \documentclass{article} \usepackage{expl3} \begin{document} Hi \end{document}   λ lualatex a This is LuaTeX, Version 1.10.0 (TeX Live 2019)   restricted system commands enabled. (./a.tex LaTeX2e &lt;2018-12-01&gt;  luaotfload | main : initialization completed in 0.042 seconds (/opt/texlive/2019/texmf-dist/tex/latex/base/article.cls Document Class: article 2018/09/03 v1.4i Standard LaTeX document class (/opt/texlive/2019/texmf-dist/tex/latex/base/size10.clo)) (/opt/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3.sty (/opt/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3-code.tex)  ! LaTeX Error: File `l3backend-pdfmode.def' not found.  Type X to quit or &lt;RETURN&gt; to proceed, or enter new name. (Default extension: def)  Enter file name:  ! Emergency stop. &lt;read *&gt;   l.282   }   379 words of node memory still in use:    2 hlist, 1 rule, 1 dir, 3 kern, 1 glyph, 4 attribute, 48 glue_spec, 4 attrib ute_list, 1 write nodes    avail lists: 2:9,3:3,4:1,5:2,7:2,9:2 !  ==&gt; Fatal error occurred, no output PDF file produced! Transcript written on a.log.