forgot Apple ID after restoring iphone
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Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$ $6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$ I have been playing around with camera tracking and I'm happy enough with the tracking and alignment of the markers with the footage when viewed through the camera.    The problem is, when I am not looking through the camera I can see that the grid isn't aligned to the camera.    How do you correctly align the grid to this tracked camera? I have set a floor and two points for scale, also clicked setup tracking scene, but this just added cube and plane which were on the grid. How can I make a peer-to-peer multiplayer game? How can I make a p2p multiplayer game? I would like to have a server-less multiplayer game. But then, how all the clients know each other?  Why the p2p-protocol is so famous in file transfer but not in multiplayer games? How to evaluate the integral $\int \sqrt{1+\sin(x)} dx$ To find:  $$\int \sqrt{1+\sin(x)} dx$$  What I  tried:  I put $\tan(\frac{x}{2}) = t$, using which I got it to:  $$I = 2\int \dfrac{1+t}{(1+t^2)^{\frac{3}{2}}}dt$$  Now I am badly stuck. There seems no way to approach this one. Please give a hint. Also, can we initially to some manipulations on the original integral to make it easy? Thank you. How to know whether Lagrange multipliers gives maximum or minimum? Problem with the header/ footer width I have recently started using the geometry package to format the margins of my documents. Although, I've noticed that the width of the header/ footer remains the same. How can I correct this?    Here's a MWE:  \documentclass{article}  \usepackage{geometry} \usepackage{fancyhdr}     \pagestyle{fancy} \usepackage{blindtext}  \lhead{} \chead{Header} \rhead{} \lfoot{} \cfoot{Footer} \rfoot{\thepage} \renewcommand{\headrulewidth}{1pt} \renewcommand{\footrulewidth}{1pt}  \begin{document}  \newgeometry{margin=0.5in, bottom=1in, top=1in} \Blinddocument  \end{document} load a file and read the information I want to open an Excel file through an Apex dialog box, then browse the information in my file line and display it with visualforce. I show you my code  public class ImportExcel {       public String fileName{get; set;}     public Blob contentFile{get;set;}     public String[] csvFileLines{get;set;}     public List&lt;String&gt; acclist{get;set;}     public String[] data{get;set;}     public ImportExcel(){         csvFileLines = new String[]{};         acclist = New List&lt;String&gt;();      } public void readFile(){         try         {             fileName=contentFile.toString();         }catch(Exception e){         ApexPages.Message myMsg = new ApexPages.Message(ApexPages.Severity.FATAL,'Please upload a valid CSV document');         ApexPages.addMessage(myMsg);              return ;          }         csvFileLines=fileName.split('\n');          system.debug(csvFileLines);         for(Integer i=0;i&lt;csvFileLines.size();i++){             data=csvFileLines[i].split(',');             acclist.add(data[i]);         }     } }   Once I execute my code, it puts me this error:     13:52:13:012 VARIABLE_ASSIGNMENT   [15]|e|"common.apex.runtime.impl.ExecutionException: BLOB is not a   valid UTF-8 string"|0x4e4728 Can a virtualized machine have the CPU and RAM resources of multiple underlying physical machines? How can Innodb ibdata1 file grows by 5X even with innodb_file_per_table set? I have innodb_file_per_table set and just today my ibdata1 file jumped from 59M to 323M after I made several changes to an 800M table to reduce it to about 600M. That particular table's .ibd file was reduced but the server's ibdata1 file went crazy. Any ideas? In blender cycles render engine, how do I put a movie clip on a plane so it displays the video? I want the video to be on the plane if there is a way. Suppose we have a natural number $N$ with decimal representation $A_kA_{k-1}\ldots A_0$. How do I prove that if the $\sum\limits_{i=0}^kA_i$ is divisible by $9$ then $N$ is divisible by $9$ too? I try to get rounded corners on a UIImage, what I read so far, the easiest way is to use a mask images. For this I used code from TheElements iPhone Example and some image resize code I found. My problem is that resizedImage is always nil and I don't find the error...  - (UIImage *)imageByScalingProportionallyToSize:(CGSize)targetSize {     CGSize imageSize = [self size];     float width = imageSize.width;     float height = imageSize.height;      // scaleFactor will be the fraction that we'll     // use to adjust the size. For example, if we shrink     // an image by half, scaleFactor will be 0.5. the     // scaledWidth and scaledHeight will be the original,     // multiplied by the scaleFactor.     //     // IMPORTANT: the "targetHeight" is the size of the space     // we're drawing into. The "scaledHeight" is the height that     // the image actually is drawn at, once we take into     // account the ideal of maintaining proportions      float scaleFactor = 0.0;      float scaledWidth = targetSize.width;     float scaledHeight = targetSize.height;      CGPoint thumbnailPoint = CGPointMake(0,0);      // since not all images are square, we want to scale     // proportionately. To do this, we find the longest     // edge and use that as a guide.      if ( CGSizeEqualToSize(imageSize, targetSize) == NO )     {          // use the longeset edge as a guide. if the         // image is wider than tall, we'll figure out         // the scale factor by dividing it by the         // intended width. Otherwise, we'll use the         // height.          float widthFactor = targetSize.width / width;         float heightFactor = targetSize.height / height;          if ( widthFactor &lt; heightFactor )             scaleFactor = widthFactor;         else             scaleFactor = heightFactor;          // ex: 500 * 0.5 = 250 (newWidth)          scaledWidth = width * scaleFactor;         scaledHeight = height * scaleFactor;          // center the thumbnail in the frame. if         // wider than tall, we need to adjust the         // vertical drawing point (y axis)          if ( widthFactor &lt; heightFactor )             thumbnailPoint.y = (targetSize.height - scaledHeight) * 0.5;          else if ( widthFactor &gt; heightFactor )             thumbnailPoint.x = (targetSize.width - scaledWidth) * 0.5;     }       CGContextRef mainViewContentContext;     CGColorSpaceRef colorSpace;      colorSpace = CGColorSpaceCreateDeviceRGB();      // create a bitmap graphics context the size of the image     mainViewContentContext = CGBitmapContextCreate (NULL, targetSize.width, targetSize.height, 8, 0, colorSpace, kCGImageAlphaPremultipliedLast);      // free the rgb colorspace     CGColorSpaceRelease(colorSpace);          if (mainViewContentContext==NULL)         return NULL;      //CGContextSetFillColorWithColor(mainViewContentContext, [[UIColor whiteColor] CGColor]);     //CGContextFillRect(mainViewContentContext, CGRectMake(0, 0, targetSize.width, targetSize.height));      CGContextDrawImage(mainViewContentContext, CGRectMake(thumbnailPoint.x, thumbnailPoint.y, scaledWidth, scaledHeight), self.CGImage);      // Create CGImageRef of the main view bitmap content, and then     // release that bitmap context     CGImageRef mainViewContentBitmapContext = CGBitmapContextCreateImage(mainViewContentContext);     CGContextRelease(mainViewContentContext);      CGImageRef maskImage = [[UIImage imageNamed:@"Mask.png"] CGImage];      CGImageRef resizedImage = CGImageCreateWithMask(mainViewContentBitmapContext, maskImage);     CGImageRelease(mainViewContentBitmapContext);      // convert the finished resized image to a UIImage      UIImage *theImage = [UIImage imageWithCGImage:resizedImage];      // image is retained by the property setting above, so we can      // release the original     CGImageRelease(resizedImage);      // return the image     return theImage; } 3-4 old computers = general purpose cluster? Gray iTunes album tracks I noticed that a few tracks from an album appear gray.    The tracks are downloaded, I can play them if I double click them explicitly, but they don't play as part of the album. If I click the album's "play" button, they're skipped (1 gets played, then 3, then 4, etc.)  Why is this happening and how can I prevent it?    I saw a similar question, , but that's not what I'm experiencing — for me, the songs do get downloaded and everything appears to be OK, they just get skipped when playing the album. How to get the file name and a line number of a function call? How is memory allocated for an implicitly defined multidimensional array in C99? Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$. Let $X=(0,\infty)$. Define two metrics on $X$ by   $d_{1}(x,y)=|x-y|$ and   $d_{2}(x,y)=|x-y|+|\frac{1}{x}-\frac{1}{y}|$   for all $x, y \in{X}$.   Let $(x_{n})$ be a sequence in $X$ and $x\in{X}$.   Show  $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.  Note: $d_{1}$ and $d_{2}$ are then said to be equivalent metrics on $X$.  Since $d_{1}$ and $d_{2}$ are equivalent metrics, will it be sufficient to show $c*d_{2}(x,y)\leq{d_{1}(x,y)}\leq{C*d_{2}(x,y)}$?  So far I have the following: $d_{1}(x,y)=|x-y|\leq{|x-y|+|\frac{1}{x}-\frac{1}{y}|}=d_{2}(x,y)$. Therefore, $d_{1}(x,y)\leq{C*d_{2}(x,y)}$ where $C=1$. Is there a $c$ that would satisfy the left-hand side of the inequality?  Any help would be appreciated. (this is not homework) Can you show me a continuous function $f \colon \mathbb{R}^n\to\mathbb{R}^m$ that satisfies $f(a+b)=f(a)+f(b)$ but is not linear?   We have that  $$f(0)=f(0+0)=2f(0)\implies f(0)=0\\ f(x-x)=f(0)=f(x)+f(-x)=0\implies f(-x)=-f(x)\\ f(nx)=f(x+x+\dots+x)=f(x)+\dots+f(x)=nf(x)\quad \forall n \in \mathbb{N}$$ But $$ f(-nx)=-f(nx)=-nf(x) $$ So: $$ f(ax)=af(x) \quad \forall a \in \mathbb{Z} $$ Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite? Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?