In one sentence, describe what the following article is about: One way to think of the radius of a sphere is as the distance between the point at the center of the sphere and any point on the surface of the sphere. Because this is true, if you know the coordinates of the point at the center of the sphere and of any point on the surface, you can find the radius of the sphere simply by calculating the distance between the two points with a variant of the basic distance formula. To begin, find the coordinates of the sphere's center point. Note that because spheres are three-dimensional, this will be an (x,y,z) point rather than an (x,y) point. This process is easier to understand by following along with an example. For our purposes, let's say that we have a sphere centered around the (x,y,z) point (4, -1, 12). In the next few steps, we'll use this point to help find the radius. Next, you'll need to find the (x,y,z)  coordinates of a point on the surface of the sphere. This can be any point on the surface of the sphere. Because the points on the surface of a sphere are equidistant from the center point by definition, any point will work for determining the radius. For the purposes of our example problem, let's say that we know that the point (3, 3, 0) lies on the surface of the sphere. By calculating the distance between this point and the center point, we can find the radius. Now that you know the center of the sphere and a point on the surface, calculating the distance between the two will find the radius. Use the three-dimensional distance formula d = √((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2), where d equals distance, (x1,y1,z1) equals the coordinates of the center point, and (x2,y2,z2) equals the coordinates of the point on the surface to find the distance between the two points. In our example, we would plug in (4, -1, 12) for (x1,y1,z1) and (3, 3, 0) for (x2,y2,z2), solving as follows:  d = √((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2) d = √((3 - 4)2 + (3 - -1)2 + (0 - 12)2) d = √((-1)2 + (4)2 + (-12)2) d = √(1 + 16 + 144) d = √(161)  d = 12.69. This is the radius of our sphere. In a sphere, every point on the surface of the sphere is the same distance from the center point. If we take the three-dimensional distance formula above and replace the "d" variable with the "r" variable for radius, we get a form of the equation that can can find the radius given any center point (x1,y1,z1) and any corresponding surface point (x2,y2,z2). By squaring both sides of this equation, we get r2 = (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2. Note that this is essentially equal to the basic sphere equation r2 = x2 + y2 + z2 which assumes a center point of (0,0,0).
Summary: Find the (x,y,z) coordinates of the central point of the sphere. Find the coordinates of a point on the surface of the sphere. Find the radius with the formula d = √((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2). Know that, in general cases, r = √((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2).

In one sentence, describe what the following article is about: Whether you’re meeting her for the first time or you don’t know her well, but you have mutual friends, just be friendly and sure of yourself.  A simple “It’s very nice to meet you.” is a great opener in this situation. Remember that in this situation she’s in the same place as you. So don’t feel like you need to one-up her (or anyone else there) or act like someone you aren’t. Just be yourself. Remember that you don’t know this girl very well or at all, so reading her body language can give you a good indication of her comfort level. Trying to embrace her with a hug may be too forward if you two aren't close.  You can offer to shake her hand if she seems open to it, or even just give a friendly wave. Be polite. Like the saying goes, “You catch more flies with honey.” In this scenario you're probably making a first or second impression. Trying to show off or joking with her like you might a good friend could offend her. Don’t overdo it though by smiling too big or being too enthusiastic. Acting too eager to meet her or greet her could make her uncomfortable and make you look like you’re coming on too strong. If you’re greeting her in a group of friends, hopefully your friends will properly introduce you, but if you're not introduced, politely ask her name and offer yours.  When you learn her name repeat it back to her when you tell her yours. Making eye contact and using her name can also help you to remember it better. There’s a reason that people are drawn to comedians and funny people, as laughter can be comforting. When you greet a girl you may not know all that well, some humor will show her that you’re comfortable with yourself (even if you’re nervous) and not a rude person.  Using humor is a great approach when greeting a girl because it can ease any tension. If you’re shy or nervous you can use a little bit of self-deprecating humor to break any tension and make her feel more comfortable around you. Joke about your appearance or the situation. "I'm glad [name of mutual friend] dragged me to this, I had a pretty crazy night of Netflix binging planned, but this seems better." Sometimes the best impression is a quick one that leaves her wanting to know more about you.  If you have a hard time making small talk with people, especially when greeting a girl, keep it short and sweet. Don’t try to force any conversation. If the conversation doesn’t seem to be going anywhere, politely excuse yourself.
Summary: Introduce yourself with confidence. Read her body language. Smile at her. Learn her name. Use humor in your introduction. Don’t overstay your welcome.

In one sentence, describe what the following article is about: Tap the Chrome app icon, which resembles a red, yellow, green, and blue sphere. This will open Google Chrome. Enter https://www.luckypatchers.com/download/ into the address bar at the top of the screen to open the Lucky Patcher download site. You'll find this green button near the bottom of the page. Doing so prompts Lucky Patcher to begin downloading onto your Android's SD card or internal storage.  As of May 2018, the most recent version of Lucky Patcher is 7.2.9. You may have to confirm this decision before Chrome will allow you to download the APK. Once Lucky Patcher finishes downloading, do the following:  Open a file manager (e.g., ES File Explorer or your Android's built-in file manager). Select your Android's default storage location (e.g., Internal). Tap the Download folder. Tap the LuckyPatchers.com ZIP folder (you may have to select ES Zip Viewer from a pop-up menu before proceeding). Tap the Lucky Patcher APK file. Scroll down and tap INSTALL
Summary:
Open Google Chrome . Go to the Lucky Patcher site. Scroll down and tap DOWNLOAD LUCKY PATCHER APK. Install Lucky Patcher.