Hi everybody it's Sam at Mixed Up Craft, thank you for watching my tutorial today. I'm going to be showing you how to make a cute little gift bag which I'm going to show you in a minute but I just thought I would share some bits and pieces with you first. I've just had my parents stay with me for three weeks which has been amazing and I shared a photo, it must have been about three weeks ago now, over on my Facebook page of the huge craft stash that my mum brought over from the UK for me. And this is just some of it here and I just thought I'd talk through a little bit. So in the UK we have the pound shops and we've got one that's called Poundland and they have slowly that I've noticed over the last 18 months been expanding their craft department. They had sometimes it was like discontinued branded stuff and just little things like embellishments, foam adhesive, some cardstocks and things like that but recently they have launched this new collection Love to Craft which is their craft range here. And my mum saw it in the shop and she showed me a picture and she said do you like this and I said yeah go for it. So everything here is a pound each and they really are good so you get, so this is called Papallon and you've got bows, you've got resin flowers, I mean she literally just raided the store, I don't think there was anything left after my mum had been there. Buttons, pegs, sequins, adhesive pearls, paper doilies, some more buttons, some little wooden frames and then the paper pack. Now from what I know there's only six by six paper packs and also every pound shop is or pound land sorry is different some are very big stores but some are very small some may only stock just that for example and like a lot of them once it's gone it's gone you have to be quick with these things so I was really fortunate for my mum to see all of this when she did and that's why she kind of just just grabbed it so it all matches really really lovely and then I'll just show you a close-up here of the papers so you've got butterflies, birdcage, peas, roses and just nice patterns and stuff so six by six eight designs 24 sheets 120 gsm it's very thin it's just like origami paper so don't you know go running in there thinking you're going to get this all in cardstock because it's not but that doesn't mean to say that they won't eventually I'm sure they're probably already evolving this and making more stuff and it's also acid and lingon free so yeah I've not got anything bad to say about it I think it's really really really nice so that's the papalom then they also have this let's celebrate so again you've got the buttons you've got the bows you've got these little sentiments here you've got all these more pearl embellishments I've got two paper packs here and some resin roses there the one thing I will say is they do not go so these are the sequence you can see the sequence of the papalom match really lovely and then these ones they've just randomly given you some like teally green and a really really kind of I guess deep pink but that's not in this the colors are what's in the the kind of balloons there but they they don't match at all so I'm not quite sure what's happened there but you can see it really does stick out but again here's the paper pack really really is lovely balloons I love the bunches of balloons there now dare I say this is very very similar to trim craft when they do their collections so I again I don't know I haven't been asked to do this or anything but they may have something to do with this I don't know but if I was trim craft dovecraft it's all under the same umbrella first edition I would be a little bit miffed if I wasn't included in this because it is even packaged the same and trim craft do buttons they do the pearl embellishments they do the resin they do even tag sentiment toppers just like this so yeah I don't know please comment anybody just kind of educate me a bit more if I'm getting this completely wrong but as a consumer and someone who shops both brands this is very very very similar even like doilies and the pegs they always do pegs with their collections so I don't know anyway so everything here is a pound a piece the button I don't think there's anything that's not really these are a pound same it's the same price and same ones that you get in the range a lot of this is you know comes from factories and then the company's just brand them so you will see very very similar like that so yeah so that's the little kind of hall there of just this stuff that my mum brought over for me and I'll share other bits and pieces so let me just get rid of all of this okay so this is the project I'm going to show you today so it's just this little kind of handbag little treat bag and it's got a really nice little fasten in so you basically just slide this out and then it just opens up like so okay so you could put some little cellophane chocolates in there or even chocolates in a cellophane bag because cellophane chocolates sound disgusting but you know what I mean and I've done it as one long piece of ribbon I've just put a knot there just so you can kind of open and close it easily and then you just slide this piece back in like so and it keeps it all nice and shut and I think it's a really cute nice little treat bag so yeah it doesn't fall completely flat but it's pretty narrow anyway so it's easy to store away and yeah they're relatively quick to kind of knock up so that's using the papillom so that's one of the papers there and that's using one of the bows this is from my own stash just a broken piece from a piece of jewellery and they're the little pearl um adhesive pearls there as well from the um collection so yeah okay so this is what you're going to need so let's come on down there we go so you need one piece of 11 by 8 and a quarter okay so we're using the whole piece and I'll go through all these other pieces as we go through the video so first of all scoring along the 11 inch side you want to score at four and three quarters and six and a quarter then you're going to rotate it onto the eight and a quarter inch side and you're going to score at two inches and six and a quarter then you're going to go back again along the 11 inch side and you're then going to score at four and three eighths just down to that first score line and then at six and five eighths again just down to that first score line so you're creating a little three eighths of an inch kind of um tab on each side of this square here that we've done then just flip your card and do that again so four and three eighths just down to the first score line and six and five eighths just down to the first score line okay these are going to be cut lines we're going to cut down there and we're going to cut up here so we're going to remove all of this then just go back and again along the eight and a quarter inch side just with the thinner point of my stylus here I'm just going to put a little notch so just a little kind of indent into the card at two and three quarters and at five and a half and again flip the card and do that two and three quarters and five and a half then the last thing to do is again go back along the 11 inch side and at five and a half which is your center point just do a score line down to that first score line again okay and then rotate this time don't flip it because you do want it that way again five and a half just down to that first score line and that will allow us to be able to just squeeze in the sides there okay so that is what you should have so up here you can see that's your your um this is your base here these two long score lines so this is our base of our card you've got the square here with the halfway five and a half inch score line and you've got these two little three eighths of an inch tabs each side okay just bring that one up a bit more right that's where you should be um then you're going to need two pieces of pattern paper which is four by four and a half okay and we are going to create this shape and that is going to be our main decoration our main mat on the front and the backs then to make the kind of flap over the top you need a piece of one and a half by four and along the four inch side you want to score it one inch okay now you can round off the edges if you want which is what I did there this time I'm going to leave this one square because I just want to see how it looks and I'm going to actually mat and layer a few more colors because this one I've done in white um which I like but I've obviously done pink with this one so I'm using a white tab and then using them a pink colored mat which is one and a quarter by two and three quarters and that's going to go on top okay and now that's all I've done for this one here but I just rounded off the edges but I'm now going to put my pattern paper on top of that one so I'm adding this extra piece which is one by two and a half and that is going to go on top like so I'm just creating a slightly different um kind of pattern I guess with this one um then this is the little kind of um lock that we're going to slide that tab in and the white piece is two and a half by three oh by half an inch yeah just under but half an inch will be fine and then I've literally just freehand cut this strip to go on top which I've already stuck down which is a quarter of an inch by two and a quarter okay and that's just already stuck on top because I just didn't want to lose it and then I've got my ribbon already here which is roughly oh gosh it's going off 22 because I'm going to knot it and it obviously goes all the way around so it's 22 by sorry 22 you're looking at 32 inches but just hold fire before you cut that until I go to put mine together okay so that's all the scoring done let's just get rid of the board and then come back in with our card here so what you want to do is just burnish all of your main score lines so the two longer ones then your base okay and then all you'll be left with is these center ones here and these ones so all the ones that you only scored to these score lines here that's what you'll be left with that you can't burnish right now so let me grab my sorry if you can hear my squeaky squeaky chair I think I need to um need to get that sorted yeah look that's really bad I'm going to try not to move now okay so what we want to do first of all is I think it's going to be easiest if we just cut down the outer so where the tabs are outside of the main square okay so you can see the ones have cut down so this is going to be our little tabs which we're going to stick inside so this is this bit here that we're doing okay so I'm just cutting down them and then I'm going to cut all the way down here now when you see me doing this there will be a quicker way but I'm doing it in this step by step just to you know so that everybody can do it I don't want to always try and keep them as simple as I can so just go and cut these squares out and the reason I'm doing it this way as well is it gives you nice pieces of scrap okay so they're ready now to go away in your scrap drawer and then again I'm just going to cut another one and that one okay so you'll have four nice pieces now you can put them away in your scrap drawer then you'll be left with this kind of shape so now we need to create that kind of sloped side that almost triangular look so where we done those little kind of notches those little indents you can see just here and here just grab your ruler and a pencil okay so from the little notched part you're going to draw a pencil line down to this corner here okay so from the little notch down to there and then again on that other side like so and again on this side now we're going to cut down those these ones you need to be really really neat because this is all going to be exposed I'm cutting away my pencil mark but if there is any pencil then you can obviously just rub that out so you know you can do the pencil mark and then cut that whole piece out so this piece is still attached to the scrap but then you'd have to cut that bit off anyway because I don't know if anybody else is like me but I like my scrap pieces to all be straight and nice and neat I wouldn't put that in like that into my scrap drawer it drives me nuts there's a little bit of a an OCD there with that anyway so now I'm going to cut down this one so again I'm just just slightly removing the pencil mark there so okay I just realized I've actually done the pencil down to the wrong corner so you actually need to do your pencil mark it's fine it's not causing me any problems but your pencil mark you don't want to do it to this corner you want to do it to here so if I for example just cut that away like you just cut down there you want to do your pencil mark down to your actual score line this baseline here so it literally doesn't really make too much of a difference it just give you a nicer finish on the front so you can see there so that's where I did my pencil mark to when that was in now we're coming down to that one there okay so you're doing it down to this this your base score line okay hopefully I've not made that more confusing it needs to be and then just again just cut very nicely all the way down and then what you can do is take a little wedge off of your tab like so see what I've done so from that notch there I've gone all the way down to this piece that corner we're going to keep this so again with this side here so I'm going to cut a little wedge there and then I'm just going to go and just very slightly I won't edit this out you can see if you have just done what I did you were crafting along all you've got to do is just redo that pencil line okay so we're going right down there so I'm just going to again very carefully kind of stagger it I'm going to come down a little bit further so so just goes to show you know we all make little errors and stuff but most of the time they are easily rectified so now I'm going to just grab my rubber here and just just take off any few bits there you can see on the side you can see I'm really concentrating and I've got a bit more here there we go so then you can just burnish those over again and you can see the shape that you should have and then these ones here you want to just create a kind of a valley fold just slightly just so it kind of bends in like that there we go so then you will have these two pieces here so I've already done one and that is going to fit inside like so and you can see it gives me a nice border so to get that one what you need is this is a piece of four by four and a half along the four inch side okay the four and a half is your length this is the width the four so this is going yeah this way um this would be the top so if you've got directional paper what I'm doing now you want to do at the top okay so that you've got your pattern facing the right way basically you just want to come in three quarters of an inch and put a little pencil mark and so in this case I'm coming in at three quarters of an inch and then three and a quarter okay and then the same way that we just cut on the bag we're then going to do a pencil mark from that to pencil mark down to the bottom corners there so the left and right hand side okay so that's what you will have and then you just want to nice nicely cut those don't matter about the pencil marks obviously this is on the back so you're not going to see it make sure it's nice and neat so so I've already done my other ones you only need two pieces like that and then this one we'll sit nicely in there okay so go and get those two all stuck down then you want to start to stick your edges so I'm just going to pop a little bit of my wet glue just on the tab there like so come up a little bit higher there actually there we go and then you're going to bring it in here and you're going to line it up so it's got that nice sloped side so you want it to just marry up nicely with the edge there just turn that on its side okay you can see what I've done there so again with this side bring that one in and up and just bring it right across until you get it nice and lined up so that's how it should look so again just repeat that with the back okay and then you can just you can see there when you squeeze it it will come in along that score line that we made there okay so there we've got that coming along really nicely so next we just need to finish these bits here so with the tab here where you scored along that side at one inch just burnish that one over make sure it's nice and lined up which mine isn't do that one again there we go and then I'm going to pop all these mats and layers so this is the first one so and then choose what's the front or your back you may have different paper you may have one side that's maybe a little bit wonky like we do I know I'm always slightly off on one side sometimes so then I'm going to pop that oh I know I've got to do as well we've got a nice little piece of patterned see on the back there I've put a little piece just in that so we need to do one for there as well so I'll go through that in a minute but first of all just pop some glue on the inside okay and then you want to make sure line the top up with the score line bring it over just make sure you've got equal sides here and then at the same time bring this all over so you can make sure it's all nicely lined up with the front which it is you can see now when that comes down how that looks okay and then this piece is going to be like I said I kind of like lock which is going to go over the top like that and I'm going to obviously get that all decorated so just pop a little blob of glue on each end and I would say you want to come up um I've come up about an inch from the bottom again I'm just eyeballing it so make sure it's all lined up it's entirely up to you if you want to go higher you can but I think that's about right and again just make sure you've got even distance from the left and the right hand side there because that will all add to your finished look and you can see there how that's going to come together it looks really really nice so now I'm going to see what decoration I want to use so I'm going to use some of the lighter colored pearls here um I've got that drawer of bits and pieces here I've got my heat gun on um and I have I have got one more of them I don't know whether to do the same again I guess I should because they're nice and matching so I'm going to stick let's check that it's nice and hot so just pop this one a little bead of glue there and you're only sticking the decoration on that strip there do not stick it on the piece underneath so again I'm just making sure it's all nicely lined up like so and then I will add my bows so again sorry about the rustling so I know that can be quite annoying in videos don't know whether to do the light or the dark let's have a little look because it has got a darker oh no I don't like that one let's try this one yeah I think that one will work fine so I'm actually going to end up doing the same design that I did on that one with this one here so again just pop a bead of glue on the back of the bow and that's going to stick on top what I might do actually now as well I think the bow the center of the bow needs a little something so I'm going to put another one of these beads on there as well so let's do tiny tiny ones and then let's do this bigger one in the center of there I probably need to put some hot glue with that as well you can see so let's just add bigger one on this one I think it just kind of finishes it there we go it looks much better and now we need to do so you can keep it like that and then what you could do is add some card handles if you wanted to but that looks nice just as it is but I'm now going to add my little eyelets and the ribbon again I like that metal work and it just kind of works well with this metal decoration that I've got here so again I've got my eyelets so I'm just bringing out four of the silver ones which I'm running out of I'm not using the gold at all so maybe I need to start working the gold colors in because all I seem to be going to is the silver but I've got those I've got my pliers so all I did was just to take that out and just find the I just kind of kept it about a quarter quarter inch down from the top and in from the side just be careful it does crinkle up ever so slightly because you are working with the corner but you can get away with it and that one by the time you put the pliers in it does kind of flatten itself back out again like so and then just get them all stuck down so I'm just going to feed these through and squash them all in okay so that's my eyelets done and then again I'm going to let me just see roughly what length I did use I think it was that because by the time you do the knot yes there's not much in it so the length I gave you is about right but you can obviously make it shorter or longer it's entirely up to you and then you're just going to feed it through the front into the back back around in through the back and then leave it there and then this other front this one here sorry the other end you're going to take through the other side of the front and then get them together let's just cut off the excess there the knot will stay in the middle so just play around until they're nice and even and then this piece here I mean you can what I should do with that one is just kind of curl it a little bit just because it helps slide it in each time because I've got two layers of card on this one I'm just going to move it a little bit more and you can see that just slides in nicely like so that knot should be inside there we go I think that's super cute I might need to make that knot a bit smaller I don't like it like that there we go it's hidden but how cute I think they are so lovely you can see there closer up so that's that one and there's the other ones two really cute little treat bags these are going to be given to some friends with some chocolates in and yeah I love them I think they're really cute I love the shape and the papers yeah I just wanted to kind of show you those and have a play around with them and I think they are really really cute so this is the papillon papers from Poundland yeah Poundworld's closed down Poundland gotta remember we've got so many of them anyway there you go hope you've enjoyed it and you can get ahold of some of those supplies please give me a thumbs up if you've enjoyed today's tutorial and subscribe to my channel to see more thanks for watching bye


Alright guys, I haven't done a video in a long time because I've just been procrastinating too much and Yeah, I just I don't know. I was kind of relaxing in summer. Anyway, today. We're gonna go over another leecho problem for Google This is called step-by-step directions from a binary tree node tree node to another so you're given a binary tree right and they represent numbers from one end Okay, and then You're also given the start value and the end value, which is the destination value, okay? So we have a destination start and an end Now we what we need to do is we need to find the shortest path Starting from node s and and then and ending at node t. So what that means is that yeah So we're giving it. We're giving the starting node and the ending node and we need to find the shortest path. Okay, so We also want to generate the step-by-step directions When we're going through the path. So what this means is that L r and u are the letters that we want to generate for our step-by-step directions So l means to go from a node to the left child r means to go to the right child and u means to go to the parent So if we're gonna go look at this Let's actually copy this image and go to paint so in this situation So here our start node if I for some reason this is not connecting up. Whoops My bad Some difficulties here. So if our start node here is three So they said our start is three and our end is six. So there's our start and then our end is six So we're starting at three here and then we want to end at six. So you want to end up here, okay? so As you can see here, like the shortest path would be like going this way. So if we look at three What what do we have to do to get to six well since they said we only could use every step there's L R and you right go left go right or go up. So in for three In order to get to six, right? We have to go up. So we went up once right went up and we went up again From one to five and then here from five we have to go to the right because For five to the right to go from five to two we're going to the right So we're gonna go R and then from two to six. We're going to the left. So that's L so our answer here would be you you are L, okay and And yeah, you you are L. So that's the shortest path here for the output okay, and Now the second example is pretty much very similar If we just go from here to In order to go from two to one We the only way to do this is go to the left right because there's nothing to the right and there's nothing Down nothing up. So to go from two to one is left. So the answer would just be L So yeah, so the two is the starting nodes to start and this is the ending node destination, okay, so how do you do this problem? One way is to actually do lowest common ancestor so what that means is that We want to find the ancestor that is like they both shared like the smallest ancestor that they both share So if we go back to the original problem here the original test case so If I find the lowest common so the lowest common ancestor lowest common ancestor LCA right lowest common ancestor. It just means is that what is like the smallest parent that both of them share? right, so in this case this six and six and three they both share Five as like the lowest common ancestor as a parent, right? because if we were to just like Try to find the parent that they both share five is the one that Is shared by three and six and what I mean parent. I mean like the one that is above it So like if this six wasn't here if this six wasn't actually here and said it was like Oh crap So let's say the six was not here, but the six was like right here Then the lowest common ancestor would be one Okay, because they both share the common ancestor of a parent of one But that's not the case in this case. Okay Yeah, so what's good about it is that if you define the lowest common ancestor if you find five All you have to do is just go up like from three to five My bad. So we find five and then we just have to find the values of both like six and three So we just have to go down To whatever values to three and then whatever value six So so here the algorithm would be like lowest common ancestor fine of Of three and six which would give us five and then now we just have to go from five and go down to Three are starting node and then we have to go five and go down to six ending node Okay, so starting node and ending node Then um Going from five to three since we know that this is like always on the left side For the lowest common ancestor on the left we could just always Append up for that right because it's always gonna go up like it from three to five It's never gonna go down or go right or go left So the only way you could do is just go up So once we find the lowest common ancestor and go from five to three We could just like as we travel from five to three. We could just every time I go left or Right, we just replace the values with up So in this case going from five to three If I go five to three I'll go like left left and then I go three right. I assume I go five to three So this would go a left left three LL and then We get to three so then what I would do is I just replace these with ups because to go from three to five No matter what happens, whatever whatever, whatever I do. I have to go up, right? So this one you just replace these with ups, so that'll be you you right so three to five We'll just always go up So this would be you and you and then yeah, we place these with you you and then if I go from Five to six it would just go right and then go left right left So they'll be right and then left right because if I use it do a tree traversal from five to six The only way is to go like right and left right You could use any type of tree traversal as long as you are able to like get down to your children But yeah, this would be right and left And then once you have that all you have to do is just append both of these together So we have you you and are you L and we just append you you and are L and that would be our answer, okay? So yeah, just find lowest common ancestor between the three The dear two nodes which will give you your parent and from there I just traverse downwards from that to the start node and that to the end node Replace all the values of left with up right because that's just that's where you go up, right? And then yeah, then a pen near to Append your two strings together and just return. So yeah, that's basically it just the algorithm I can show you guys I can make a whole video on lowest common ancestor but here's Like the algorithm how lowest common ancestor would work. So anyway, let's just Let's just start here So here's a code get direction and we have the root the start node destination So what I do is here is I'm just going to replace the root to you equal the lowest common ancestor Which is LCA of root start value and destination value and I have the two strings of F and S F and S just represents like Represents the the directions that we're going as we go downwards, right? So this would be like F and this would be like S, right or two straight Okay So I'll be going from Yeah, going from here then um, we're gonna get path from Our start value and From a root to our start value right and then we're gonna get path from root to destination value and each time We're gonna suspend it every time we go down. We're gonna append it to our string For F and S for our path, right our path Then what we're gonna do is we're going to replace all the values of F with up Right, like I said before early in this video because no matter what You're gonna have to go up on your left node, right for the left node The left side to get to your parent you have to go up like there's no way you could go right or down So yeah here We just replace the the path for the for F of the left node to be always up and then I just return The the two strings combine together so F plus S can coordinate together Okay, so yeah F and S represents the paths for both of the string representing each of the paths from our root of lowest common answer to the starting value and Root from lowest common answers or to Destination value, okay, so that's what F and S mean Okay, so now let's think about how to get path Yeah, so this is this is how to get to the path Let's actually go look at lowest common ancestor first because that's I think that's the hard part of this about this problem Okay, so to get the lowest common ancestor Here's what you do So here if the root is knowledge just return all right the first case So if our root is equal to our start value, right? That means that we're kind of done So like if you look at this Yeah So to get lowest common instead of being three and six Yeah, so whoa Well, I kind of like assuming in too much Okay, so if I want to get three to six right So I'm gonna go from Yeah, okay, so currently in my root is at five right so what I'm gonna do is I'm just gonna Go to the left and go to the right Okay and Yeah, and then I'm gonna recursively call Keep searching on the left node in the right now So if my root node is equal to the start value, I'm just gonna return the root Otherwise, I'm gonna return Otherwise if they're my root value is equal to destination value I'm gonna I'm gonna return the root the reason why we do this is that we want to check like Which node that we're on if that makes sense so So here five is equal five is our root node, right? So we're trying to get lowest common answer three and six So our new root node is always like the starting value of five. So this is our root and What we're gonna do is we're gonna go just Check is equal to our start value So five is not equal to our start value. So we do nothing then we're gonna check it does equal to our destination value So our destination value is six Right, so so remember three is our start Six is our destination Okay, so this is lowest common answer So but the five is not equal to any of three or six Right five is not equal to three or six so what we're gonna do is we're gonna go to the left of five and We're gonna get So we're gonna go to left of five left five is one and three to the left of five is one, okay So here I'll just I'll show you guys what I mean. So let's do So now now what we're now we did it was we call it on the left side of Function call five is one right? This is all the left side five. So yeah, so now we have one We're gonna go to the top Is one equal to our star value? No is one. No, no as one equal to our destination value No, so then then we're gonna go To the left of one also. So we'll go to three. So here it's gonna call three now Okay, so now that we go through three Three, okay, so that's this part. So it's three equal to our start value Yeah, it is so then we're gonna return three so this is gonna return three It's gonna return three and then so once this return three It's gonna Go to the right of one right. Remember the right of one. So one's right is gonna be No, one's right is gonna be no so one's right is no They'll come back to the top here and it's gonna return all so then we have three and then no So three is gonna be on our left side and null is gonna be in our right side So here it's saying that if the left side is not equal to null and the right side is not equal to null Then we're gonna return the current root value the current know that we're on But here our left side is not equal to null. So we're just gonna return the left side So this is gonna return three, right? So yeah, the common answer three is just three So then this is gonna return three Okay, so returns three so now now that that this returns three We need to go to the right side of One. Yeah, so yeah, so that returned that so the whole thing returns three to the top And then we have to do the right side of five, which is two So what is two? LCA of two so this is like another recursive call Okay, and at two is two equal to our Star value or a destination value. Nope, right two is not equal to that So then it's gonna call on two's left and two's right So two's left is six and two's right is four. So it's gonna do LCA on six and then LCA on four Okay, six goes to here six is equal to our destination value. So we return six. So this is gonna return six Then yeah, then four Four is not equal to our Any of these so it's gonna recursively call four with both nulls and then if they're both nulls, it's gonna return No, no, so they're both the both these are null The left is not equal to no, so this is not it'll return right so this would just return null So that's it's four is return nulls. So four returns no, so then it's gonna go to no So then we have six and no Six and no if it's six and null, it's not even you return all so here six is not equal to no So then it returns six this whole thing returns six So then here we have three and six. Okay, so then our left side is three and the right side is six So both of them are not no Right, both of these are not null. So then it's gonna return Five Because five was the root when three and six were called when we're traversing Okay So, yeah Yeah, that's pretty a really fast approach of me going through lowest common ancestor I'll probably make another whole video about it later on About lowest common ancestor because that's a pretty That's an algorithm that is pretty important. Okay All right, so now that we got the lowest common ancestor Let's just go over how to get the path from our lowest common ancestor of a root to our start value and our destination value Okay, so here I pass in our lowest common ancestor of five. So Yeah, so here now that we have this we just need to Pass in five to each of this so So we have our lowest common ancestor five and then we have three and then we have six. Okay, so we have start and then destination So here from five to three now now what we're doing is we're gonna go from five to three. Okay So here start value search fries three. Okay, so is five equal to three? No is five equal to null. No So we're gonna recursively go on the left So it's gonna go down to the left So it's gonna go left down here and then what it's doing is it's gonna append L to the path So our path is now gonna have L Okay, so we went down here Yeah, so it goes back to the top now is one equal to no. No is one equal to our Three. Yeah, our search value is three. So one is not equal to three. So this does nothing also So then we're gonna go to left again. So and During that time we add an L to our path path plus equal to L so add an L So then this goes down again. So now we're at three We go to the back to the top Is three no, nope is three equal to our search value. Yep, three is equal to three So we return true. So then this goes back to here and then this is true Okay, so this returns true Returns true true. All right three is equal to three returns true now is Is our did we find it on the left side? So if we found it, let's just return true. Okay, so at this point, I just returned true for that So this is gonna equal just return true So we found it. So then at this point we do nothing because we already found it. Okay So yeah, now we found so we found three going through it Now let's go to the right side Not right side. Now we're gonna try to find six Okay, so Here so this one LL and return true. So this was going from five to three and it returned true L Okay, well we guys get what I'm saying All right. Now we're gonna do another thing We're gonna go from Five to six now because six was our destination. So let's actually get rid of the picture again I should go over topics like how to search through trees Okay, so now we're gonna go from five to six. Okay, so how do we go from five to six? Yeah, so it calls back here is Five equal to no nope is five equal to six. Nope. So we're gonna go through the left side So here it's gonna go to the left side So here right it's gonna go left side And add the now so adds path is gonna equal to L. Okay is So we're going to the left side here one L All right is one equal to six. Nope is one equal to null. Nope. So we're gonna go to left side again And we pass in L again, okay, so now our path is L Now we're at three. Okay is three equal to six. Nope is three equal to No, nope, we're gonna add go through the left side again passing L and the left side is null Okay, so now we're at down here. So this is that null All right is is null equal to null. Yes. So we're here at this point to return to false So this whole thing returned false which means we did not find out left side So now is found one equal to false is fine one equal to true. Nope. So we're done that now at this point We're just gonna pop back Pop back our path. So what that means is I'm not gonna go to the left side now from three I'm gonna go to the right side. So From this we pop this back from LL and then I'm gonna go to the right side So here we're gonna search through the right side of three. So here right side of three is null also So we go back here is null equal to null. Yes, so equals returns false So by the way, this is the right side three. So it would have been LLR So this is also false, which means we did not find it and then here would return False so here did we find out on the right side of three? Nope. So we're gonna pop back it again So we're gonna remove R again, and then we're gonna return false. So this is gonna return false again. So false so now we have both false's and this point at this point Yeah, it returns false so we come back up here I think it was on the note of one now because we went through the left side of three and we went through the right Side of three. So it's gonna go to one After it popped back again. So I think uh wait LL Hold up. Yeah, okay. I think it's gonna go to the right side now so at one it's gonna go to the right side and it's gonna return false again because There's nothing on the right side. It's also null. So then this whole thing it's gonna return null on LL. So here Going through the left side It's gonna pop back them twice again So because it's gonna keep going returning all so then at this point after every goes null like multiple times here It's gonna go to the right side of five because after searching through this many times popping back It's gonna go to the right side of five So when it goes to the right side of five, it's gonna go to the right and we're gonna add R to the right side of the path So now Let's just copy this It's gonna go to the right side of path. So here's right side of five, which is gonna go to R here and then from here We're gonna go to Did we find it? Nope Not yet, right? So then it's gonna go here. So it's two equal to Two equal to null. Nope is two equal to six. Nope. So now we're gonna go to the left side So here at from two so we're at this point. We're at two right because we went to the right side So it's two equal to null. Nope is two equal to six. Nope. So we're gonna go to left side so it's gonna go to left side here and Then from here it adds To the left side of the path here. So it's gonna add L here and it goes to the six So now at six is six equal to null. Nope is six equal to six. Yep So then from here It just returns true. So now that we have this the path is gonna be RL and returns true If it didn't return true, let's say assume that it didn't return true, right? It would have I would go to the right side of two again. So yeah, basically what it's doing It's it's going to the left and the right and left and the right until we actually find the node that we want We are searching for So that's that's basically what it's doing Yeah Okay, so once this is done it returns true. So now we have R and L for this part. So here get path of Of the first path of F is gonna be The first path that F is LL and then the second path of the path is RL so now we have F is gonna equal to LL and S is gonna equal to RL right F of F and S are like the paths of For five to three and five to six All right, so now that we're at here What I do is I just replace all the values of our path to be up because for the left side you have to go up right from left side you must go up because I mean to go from left to the Ancestor there's no way to go down or go right or so you have to go up So you go up and then it's what here what we're doing here is we're just replacing all the values From our F to be up. So it's gonna replace this with up and up and then now We just return F plus S which is gonna be up up RL. So up up RL and it returns that okay And after that, that's the answer and this code actually works it runs And yeah, that's basically the gist of how to do this problem. I hope you guys understand this video It's it was this is kind of kind of a long video to go over. But yeah, Raycom subscribe I'll check you guys later. It was a pleasure for this one But yeah, I'll probably go over lowest common ancestor next time. But yeah peace


Namaste, Myself, Mr. Biraj Dar Bala Sahib, Assistant Professor, Department of Humanities and Science, Walchand Institute of Technology, Solapur. In this session, we will discuss linear differential equation of higher order with constant coefficients part 4. Learning outcome. At the end of this session, students will be able to write particular integral of higher order linear differential equation f of d into y is equal to x of x when x of x is equal to e to power a into x. Let us pause the video for a while and write answer to the question. Question is write complementary function of differential equation d minus 2 bracket cube into y equal to 0. Come back. I hope you have written answer to this question. Let us see the solution. This is the differential equation of the type f of d into y equal to 0. Here f of d is equal to d minus 2 bracket cube. Now, to get auxiliary equation, equate this f of d equal to 0. Therefore, we get d minus 2 bracket cube equal to 0. That is, we can write as d minus 2 into d minus 2 into d minus 2 is equal to 0, which gives d minus 2 equal to 0, d minus 2 equal to 0 and d minus 2 equal to 0. From this, we get d equal to 2, d equal to 2, d equal to 2. Here root 2 is real and repeated 3 times. And we know that when 3 roots are equal and real, m 1 equal to m 2 equal to m 3, then the complementary function c f can be written as in bracket c 1 plus c 2 into x plus c 3 into x square bracket close e 2 power m 1 into x. Here root is 2, which is repeated 3 times. Therefore, the complementary function c f equal to in bracket c 1 plus c 2 into x plus c 3 into x square bracket close e 2 power 2 into x, where x is independent variable. So, this is the required answer to the given differential equation. Now, let us start with a particular integral. As we know that the general solution of linear differential equation f of d into y equal to x of x is y equal to c f plus p i. C f means complementary function and we discussed this part in previous session. Now, today we can see how to find a particular integral for some standard functions. Particular integral is a part of solution of linear differential equation f of d into y equal to x of x. Here f of d is function of differential operator capital D, so that 1 upon f of d is known as inverse differential operator. Since f of d into y equal to x of x to remove f of d from the left hand side operate 1 upon f of d on both the side. Therefore, 1 upon f of d in bracket f of d into y is equal to 1 upon f of d of x of x. In the left hand side f of d gets cancelled, hence y equal to 1 upon f of d operating on x of x. The value of this y is nothing but a particular integral and it is denoted by p of y or y suffix p. Therefore, p i is equal to y suffix p is equal to 1 upon f of d operating on x of x. So, this is the formula we are using to obtaining particular integral for the given differential equation. Note that 0.1 meaning of 1 upon d operating on x of x. As we know that d means differential coefficient, so that 1 by d means inverse of differential coefficient that means integration. Therefore, 1 by d of x of x is equal to integration of x of x with respect to x. 0.2 meaning of 1 upon d minus a operating on x of x. It can be simplified as 1 upon d minus a of x of x is equal to e to power a x into integration e to power minus a x into x of x into d x. So, these are the two fundamental results are essential to find particular integral in further. Now rules to write particular integral. Rules to find particular integral depends on a nature of right hand side function x of x. Following are the standard types of functions x of x e raise to x e raise to x cos a x or sin a x x raise to m e raise to x into v and x into v. But in this session, how to find a particular integral when the function is e to power a x is discussing. Case 1, when x of x equal to e to power a x. As we know that p i equal to 1 upon f of d operating on x of x. Therefore, p i equal to 1 upon f of d, but x of x is e to power a x. Now to simplify this, we put every d equal to a in the denominator f of d. So, we get p i equal to 1 upon f of a into e to power a x if f of a not equal to 0. That means when the given function x of x is equal to an exponential function of the type e to power a x. Then to find particular integral, we put every d equal to constant coefficient a in the denominator f of d provided f of a not equal to 0. Now, case of failure. If suppose f of a equal to 0, then above step fails. In this case numerator by independent variable that is here x and differentiate denominator f of d with respect to d, we get f dash of d and then write as p i equal to x into 1 upon f dash of d and which is operating on e to power a x. That means I can put every d equal to a in the denominator f dash of d. We get p i equal to x into 1 upon f dash of a into e to power a x. This is the p i if f dash of a not equal to 0. If suppose again f dash of a equal to 0, then above step fails. Again repeat the above procedure and write as p i equal to 1 more x we have to multiply numerator. Hence x into x is x square into 1 upon differentiate f dash of d with respect to d. We get f double dash of d and into e to power a x. Now, to simplify write and said again put d equal to a in the denominator f double dash of d. We get p i equal to x square into 1 upon f double dash of a and into f double dash e to power a x. This is the particular integral if again f double dash of a not equal to 0 and so on. We may get answer in first step or in second step or may be in third step or may be in fourth step. We have to repeat this procedure till to get a answer. Note that when x of x is constant, then p i equal to 1 upon f of d operating on k which is equal to 1 upon f of d. k we can write as k into e raise to 0 x which is equal to k we can take outside the operator and to operate 1 upon f of d on e raise to 0 x. We put d equal to 0 by case 1. Hence we get p i equal to k into 1 upon f of 0 into e raise to 0 x if f of 0 not equal to 0. So, this is we can write as p i equal to 1 upon f of d operating on k is nothing but write k as it is simply put d equal to 0 in the denominator. We get k upon f of 0 if f of 0 not equal to 0. That means for function x of x which is equal to constant, then to find particular integral put every d equal to 0 in f of d provided f of 0 not equal to 0. Now, let us consider one example. So, all the differential equation d square minus 2 d plus 1 into y is equal to e raise to 3 x plus 8. This differential equation is belongs to type f of d into y equal to x of x. So, here f of d equal to d square minus 2 d plus 1 and x of x equal to e raise to 3 x plus 8. Now, to find complementary function we write auxiliary equation by equating f of d equal to 0. Therefore, d square minus 2 d plus 1 equal to 0 is auxiliary equation. Now, solve it by factorizing its factors are d minus 1 into d minus 1 which is equal to 0 which gives d minus 1 equal to 0 and d minus 1 equal to 0. Therefore, d equal to 1 and d equal to 1. Roots are real and equal. Therefore, by formula when 2 roots are equal m 1 equal to m 2 c f equal to c 1 plus c 2 into x bracket close e raise to m 1 x. Using this formula we can write c f equal to in bracket c 1 plus c 2 into x bracket close e to power 1 x that is e raise to x. This is the complementary function. Now, to find particular integral we have the formula p i equal to 1 upon f of d operating on x of x.  Now, separate into two terms in the right hand side.  Now, using case 1 when the function is of type e raise to a x put d equal to a and when the function is a constant then put d equal to 0. Therefore, in first term function is e raise to 3 x a is 3 that is why put d equal to 3 and in the second term the function is 8 which is constant. Therefore, we put d equal to 0 hence p i equal to 1 upon 3 square minus 2 into 3 plus 1 into e raise to 3 x plus 1 upon 0 square minus 0 plus 1 into 8. After simplification we get p i equal to 1 upon 4 into e raise to 3 x plus 8 by 1 that is 8. Hence, general solution is dependent variable here it is y is equal to c a plus p i. Therefore, y equal to c f is c 1 plus c 2 into x bracket close into e raise to x plus p i is 1 upon 4 into e raise to 3 x plus 8. So, this is the required general solution for the given equation. To prepare this video session I refer this book as a reference. Thank you.


This study investigates the potential of a novel slow release fertilizer, SRF, based on polymeric materials to improve the yield and quality of tomatoes. Three types of polymeric materials were synthesized and tested against conventional fertilizers. The results showed that the SRFs had better yields and quality than conventional fertilizers. Furthermore, the SRFs had lower nitrate content in the fruits, indicating reduced environmental pollution. This article was authored by Elahav Motamedi, Marzia Safari, and Mary Salimi.


Creating a website using Canva. Canva is an online graphic design tool. It can be used for creating many different multimedia projects, including one-page websites. Canva is a freemium tool, which means it includes both free-to-use and paid-to-use content. Using Canva for free means that you'll be limited to using the platform's free graphics, templates, and features. Canva is known for a large collection of templates that you can easily customize with design elements and tools. Then you can publish your site within their free domain, or an existing one you already own. Creating websites in Canva is relatively simple, no matter your previous experience with the tool. In this video, we'll cover the basics of using Canva to create a beautiful website. The first step to creating a compelling website is to write the content and collect any supplementary images or logos you'll be using. Canva has a great multimedia library, but you won't always be able to find the perfect image for free, so it's better to be prepared. Once your content is nailed down, it's time to begin creating in Canva. The first step is to log in to your account. Go to www.canva.com and press Login if you already have an account. If not, you'll need to create one. To do this, click the Sign Up button. Now that you have access to the site, it's time to begin crafting your webpage. Search for or click on Websites on the homepage. Then you need to decide whether you want to start your project from scratch or if you would like to use a pre-populated template. Starting from scratch will give you more freedom with the design, but as mentioned previously, Canva is well known for their templates. You can find templates in various themes, styles, and purposes, such as a business website, portfolio website, event website, or education website. Make sure the template you choose is labeled as free. Pay-to-use content can be identified by a crown or dollar sign icon beside the resource or feature of the site. If you're not sure whether a picture, graphic, or template is free to use, bring it into your website and then tap on the Publish Website button. If you have used any paid content, you will see a cost to download your project. Some templates may not have a paid resource icon, but may still have paid for images embedded within the design. Once you've chosen a template, you're free to begin customizing it. Canva sites are made of multiple sections of pages, combined into a one-page scrollable website. When you click on any page, a small menu will appear on the left. This has options to add notes, which is the text that only you can see, lock page to prevent any more edits, duplicate page, which simplifies creating multiple sections in the same style, delete page and add page, which will add a blank page under your current page. To change the order of the website sections, click on the square with a number in the bottom menu bar. It should be beside the Zoom slider. Here, you can drag your pages around to change the order, add new blank pages, hide pages, as well as change the title of each page. Creating page titles will come in handy later if you want your site to have a navigation bar. You can change your template at any time by clicking on the Design tab in the left menu bar and searching for a new template. You can choose to replace all your current content by clicking Apply All Pages, just one page by dragging the chosen template design onto your site, or to just replace this style by clicking Template Style, then Apply Style to All Pages. To explore just the different style options that Canva has to offer, navigate back to the Design tab and click Styles, right under the search bar. Here, you can explore different font and color combinations and even shuffle how the colors are used on your site. The key to making your website look professional and cohesive is consistency. Be sure to maintain the same colors, logos, and fonts across all the pages of your website. You can preview what your website will look like to the public at any time by clicking Preview in the top menu bar. Everything on your page is editable. If you want to edit a specific text entry, you can double-click on the text block and use the Edit menu that appears above your page to edit the specific text size, color, alignment, font, and more. Choose from the fonts and colors included in your theme or something entirely different. You are also able to modify your page background. Look for the Background button on the left-hand side of the screen. Here, you can decide if you want a solid color, a pattern, or image as a background. Because your website is scrollable, you'll also be able to resize the individual sections by clicking on a page and dragging the little bubble that appears on the bottom. The media possibilities on Canva are almost endless. You can use photos, videos, audio, graphics, charts, graphs, or tables. It can, at times, be difficult to find the perfect, free picture or resource for your website. If you're not able to find something within Canva, an alternative is to create your own or find a Creative Commons resource online. Canva accepts both PNG and JPEG image files. To upload an image or graphic into Canva, tap Uploads, Upload an image or video. Now locate the media you wish to upload on your computer. Do not forget to cite any content that is not yours. To add elements directly from Canva, tap on the elements button to add lines, shapes, graphics, photos, and more. Use the search feature to help narrow your options. Once you find a resource you would like to use, click on the resource to import it into your website or simply drag it onto the page. If you use any frames or grids, you can place these on your page, then drag any media into the placeholder. If you want to visualize any data, find the format you would like to use, such as a chart or graph, then you will be able to input the appropriate information. Play around with the layout and design of your website's presentation until you have something you're happy with. Once the content is settled, you can make the site itself more dynamic by adding animations. To animate an element, first right-click on it, then choose Animate from the menu bar, then Preview and select your preferred animation. There are different animations available depending on what kind of element you can click on. You can animate text and graphics individually, or if you click on a whole page, there are animation combinations that apply to everything on each specific section of your site. Another way to make your site more dynamic is to add to hyperlinks. These will allow you to link internally to other pages of your site. Say if you want to have a next button, or externally to any other site on the web. Simply right-click on the element and click Link. Here you can choose to link to other Canva websites or a page within your site or paste a URL. Once you've completed your website's presentation and have carefully reviewed it, it's time to publish. Click Publish Website in the top menu bar. Here you'll be able to make some selections. First, whether or not you want your website to resize on mobile devices. This will just change the layout to optimize for a smaller screen size. Then you can choose to add navigation. This is a handy feature that we recommend you include. Make sure to name all your pages. Then once your site is published, your users will be able to easily access the content they want without having to scroll through your whole site. Then you can choose to publish to a free domain. You can also purchase a new domain or publish using an existing domain. But both of these options either require a Canva Pro subscription or a yearly domain payment. Canva will allow each user to have up to five free domains published at one time. Under this, you may see a price listed. As we mentioned earlier, this is probably because your template came with premium images. Simply go back to edit your page and remove the images listed here or replace them with something free. Once you're satisfied, click Continue. Now you'll be able to type in your chosen domain or subdomain name. The only difference with free domains is that they will include My Canva site in the URL. Type in your chosen domain and Canva will tell you if it's available. You're able to edit your domain name at any time through your Canva account setting. Click on Continue again and here you will preview your URL, your browser tab, and write a website description. You'll be able to make changes to your URL if desired and change how the name and icon of your site will appear on a browser tab. You're also given the chance to create a website description up to 160 characters. This is what will appear below the page title and URL in search results. Finally, there are two checkboxes. One to make your site password protected. This will only allow access to those who you're given a password to and one to hide your site from coming up in search engine results. The last thing to do is click Publish and your site will be published to the world. You can share your finished website using the link with the domain you just created. You now have a fully functioning website that you can continue to edit and improve on.


Good afternoon, Pastor David. Hey, John. Welcome, everybody, to an Unfiltered with Pastor David, a random moment. Recently, we've been speaking off camera regarding the role of the title, Pastor. And I was sharing with you that sometimes in certain circles when, for me, at least my own thing, when people don't reference you as Pastor David, it bothers me. But then, taking it a step further, I wanted to spend a little bit more time on this, is when people will reference somebody as my pastor, and then later on may decide to leave or go and then come back and attend somewhere else, has that role, that title, my pastor, lost its potency, in a sense? I think that the term my pastor is just a general term people use. A pastor, the word pastor, speaks of one who is going to tenderly care for and feed the sheep. The shepherd is to do that. And so a pastor, elder, a pastor leader, is one who has an affectionate relationship with people in the church, primarily. So it's possible to be a member of a church that is pastored by an individual, and perhaps because the church is so large, never really even have a personal time or name basis with the man who is shepherding the church. And that's just today, that's reality. So from my perspective, there are people who use the term pastor as a title. It's something that they use to define what that person does in the church. Excuse me, and a number of people do that. I was sharing with you and with the men recently that it takes a while for somebody to actually be a shepherd to somebody. So they're going to use the title pastor, as they do here in this church. They approach me and they'll say pastor David. But that doesn't mean that I actually have that position. That simply means that's the title that I have here in this church. Over time though, there are those who may regard me in a more tender way, in a more personal way. And it becomes what they know me as, as their pastor. I had one pastor, and that was Chuck Smith. There was another in my life that I loved very much and it considered an interim type pastor. As a matter of fact, he was dear to me in that fashion, but that was a short-lived relationship. Ultimately, when Pastor Chuck and I became more acquainted when he and I actually developed something beyond a high health, how are you, how is it going, hello, that kind of thing. When it got beyond that, I realized that this is the man who shepherded me. This is the man who feeds my soul. This is the man that I'll go to for advice or correction when necessary. He's the one that I'll ask for prayer. I remember on a couple of particular occurrences that I had told him. I've been baptized in the Holy Spirit, Chuck, but I've never asked you to pray for me that the Lord would fill me. And that was a special moment with me and my pastor. We went through some pain. My wife and I, and I went to see him, sat in his office and shared my heart and received his prayer. When my father went to be with Jesus, Marie gave him a call at home, and I spoke to him, and he comforted me over the phone. He was more than just the man who stood in that pulpit or the man who led the Calvary Chapel movement. He was my shepherd, and I had love for him. And so there's a difference. So some guys will, some people will say, Pastor David, and that's just the title. Other people will say, this is my shepherd, and there's a different relationship. I mean, even when you're just sharing that with Pastor Chuck, he was there for you when his father passed away. I think of own life. And when my dad passed away, that you were the way you called me in and poured your heart out to me. You know, but again, I hear people will reference pastors as just their pastor. But like for myself and a lot of the guys, when they sit, when they referenced to you as my pastor, there's a lot there. And I don't know if today that is thrown around so loosely that it's kind of lost significance of just a title. For me at least, it's something that you've earned and God has anointed you with. And it goes beyond that in the role that you've played in my life and a lot of the guys' life and a lot of the family's life here where you're truly our pastor. And grateful for that, and for all that you've done. But today, I just kind of see a lot of past, that's my pastor, but then they're quit to go somewhere else or they're quit too. Well, they don't have relationship with that person. You know, a shepherd can't always, again, in a church as large as many churches today in the United States, it's very difficult for that one person to really maintain that many relationships. And so you have to give him room, you have to. And yet on the other hand, sometimes the churches are packed because the person who is leading it isn't really a shepherd at all. He's more of, we'll say a communicator or something like that. So the church fills up with people, but the problem is, is the sheep become like the shepherd. So the things that the shepherd believes to be important that he feeds constantly to the sheep, these are the things that some embrace and it changes their lives, you know, and then some guys are feeding things to their church that aren't necessarily even spiritual in the sense of it being scriptural. We're going through the word of God. These are the things. Sometimes there are just current events or sometimes whatever is on their heart that day.   And it's so impersonal that he becomes kind of like a celebrity on the stage who becomes their personal news broadcaster. And then he has other people around him to do the work of ministry that he is not qualified or called to do because in his mind what he's doing is shepherding them. And if you spoke to him and said, but you don't have any relationship, you don't have ministry for people in your church. Why? Well, he wouldn't have an answer.  We see that, you see that, that's part of what's going on in the church today. So we with intent want to be ministers to those that God has entrusted to us and we want to. That doesn't mean that I am, that doesn't mean I'm that good at it because God knows I'm not, but I do the best I can in him. And that's the way it works. And so I think everybody has their own gifting, their own things at the Lord's place on their heart, John. And in the church, you have people who will sit in one place and go to another. I remember someone who was speaking to a friend of mine who said, well, my Sunday morning church is this church. My Sunday night church is this church. My Wednesday night church is this church. Three different churches that they were going to. Not one of those churches was that person giving his gifts to. Not one of those churches was he using his spiritual gifts in. He was just a consumer because a lot of churches are like that. We have a product, a product is consumed. The people come and eat and then they leave. And so there's no connection. But the sheep know the shepherd and the shepherd knows him. And there's that relationship. And they follow him, they know his voice and he feeds and tenderly cares for them. And he has character qualifications. And he's somebody that, that God has entrusted the souls of people to and a true shepherd really, really is aware of that. So there are a lot of hirelings. There are a lot of public speakers or a lot of great communicators or a lot of people who can get you jumping in that aisle and excited and all of that. And well, it's not, it's not how high you jump. It's how straight you walk. And if you're not getting, when you land and it's, if you're not getting fed, you're being hyped. And that's just the way it is. So I believe that, yeah, there are a lot of people who's well, they come up and call me pastor, but that's just the title to them. Over time, it may become a reality. I may have more of a connection in their life. I may have more of that place, but I don't tell people what to call me, you know, they call me a lot of things and sometimes they call me pastor, but that's the general truth of that. Amen. Well, thank you pastor for sharing that. And again, we're so thankful as a church family on behalf of the men's ministry, I know I can speak and for a lot of people here, thankful to have a pastor such as you that lead us weekend and week out through the word of God, something that's so needed today. Oh, thank you. With that pastor, I wanna invite our church family come on out Wednesday evening, tomorrow evening, at 7 p.m. as you're talking about the boots that are shot at, boot. Having your feet shot with preparation. I'm gonna start reading my Bible. You better, because I don't see any boots in that verse. Okay, these boots are made for walking, John, all right. Yes, it's not even a weapon, it's more of a protection. And I will give some insight into that.  Our Israel trip's coming up in March. Great opportunity to go with pastor David and Marie or the church family to Israel. I mean, it's a life changer. And even if you're not part of this church family, we would welcome you. Yes, and you can actually go on our website, calvaryccv.org, go to the events tab, and under the events tab, you will see the Israel trip there. We'd love to have you come out and join. And thank you again, pastor David. God bless you guys, and we look forward to seeing you.


Taking better photos made simple. These are Mary and Paul. They're looking forward to their vacation. But what cameras should they take on their trip? Mary knows that many modern cameras are so good that they usually take great pictures in automatic mode. But some of her photos still don't turn out well. What can Mary do better? Photography literally means painting with light. Why? Because everything around us reflects the rays of light in the environment. A camera lens captures those rays. That's what forms a picture in the camera. The light, and therefore the photo's quantity, is controlled by several determining factors. The most important ones are aperture, exposure time, and light sensitivity. Imagine the aperture as a pair of curtains. It controls the amount of light entering the lens. When it's dark, Mary wants to capture as much light as possible. To do that, she needs to open the aperture wider. If it's very bright, Mary draws the aperture curtains closer together. Otherwise, her picture will be overexposed. The F number, or focal ratio, specifies up to how far the curtains can be opened. At F2, only halfway. At F4, only a quarter of the way. So, the lower the number, the more light can pass through a particular lens. But those aperture curtains don't always stay open. They only open for a split second. That length of time is called the exposure time, or shutter speed. The longer the exposure time, the more light enters the photo. That's fantastic if Mary wants to take a photo at twilight, for example. But if a car drives through the photo, it will reflect the light from different positions, so it just appears blurry in the picture. The same thing will happen if Mary moves slightly while taking the photo. That's why when using long exposure times, the camera should always be resting on a steady surface. But when it's bright out, Mary only needs to briefly expose her photo. So the car comes out nice and sharp. No tripod needed. Mary still isn't quite satisfied. Despite using a wide open aperture and a long exposure time, the result is still too dark. That's where light sensitivity, or ISO, comes into play. It's more or less the photo's skin type, and determines how sensitively the camera reacts to the light. High sensitivity can quickly lead to a sunburn. Then the photo has something called noise. Mary is overwhelmed. Fortunately, she doesn't have to do everything manually to take pretty pictures. In semi-automatic mode, Mary specifies just one value. The camera figures out the rest. Even so, the perfect setting for all situations just doesn't exist. A good photographer reacts to prevailing light conditions, uses average values, and accepts a compromise now and then. It's almost like a healthy relationship.