Metric in Mathematics - Tangent Space of a Monomde

Metric in Mathematics - Tangent Space of a MonomdeMany students can easily learn about using a metric. The benefits of learning about metric are often overlooked by students who would rather learn about a different concept than one that will help them understand the tangent space of a manifold. One thing that may be easily overlooked is the importance of the use of a metric in science. Metric systems and their uses will help students learn about the properties of manifolds.Metric is the use of real numbers that can be interpreted as a measurement in a manifold or set of sets. There are many types of metric systems, including non-metric. Metric systems are useful for different applications in geometry, but it can also be used in other areas as well.There are many ways to represent a metric on a graph. A non-metric system usually consists of vertical lines on a graph with few points in between. A metric system is a set of lines with many points on the graph. The spacing between the lin es may be slight.A metric can be used to represent geometry. For example, if a metric representation of a circle is used on a graph, then students can see the distance from any point on the circle to the circumference of the circle. This metric may be defined by creating a graph of points along the circle's circumference. Different points on the circle may be plotted along different horizontal axes.A metric system can be used to compare two manifolds. There are two basic ways to define manifolds. The first is by setting each manifold to a common metric, which is the most popular metric. The second way is to create two points on a manifold that are separated by a metric line.The use of a metric can help students understand both definitions. Two geometrically similar manifolds may be compared by looking at the distances between the points on either manifold. One way to compare manifolds that are of the same shape is to create two parallel lines, which is the most common way to compare manifolds that are of different shapes. It is not the distance between the points that make the comparison, but rather the difference in the sizes of the points that determines the comparison.Parallel metric systems may be used to see what is similar and what is different between two manifolds. A parallel metric system consists of horizontal lines that parallel each other. The systems are parallel if they cross each other horizontally. A parallel system is usually used to find the similarity between two manifolds.The metric may also be used to find similarities between manifolds. The system must have two parallel lines, which is the most common case of a parallel metric system. Another possible comparison is to make a point that is half-way between two parallel lines. Using a metric system is essential to the understanding of the tangent space of a manifold.

How to Become a Professional Tutor

How to Become a Professional TutorA professional tutor is one of the most sought after and well-paying tutors in the world. With its immense popularity, it is worth understanding what makes a good tutor and to help you become one yourself.This is a tutor that has experience in the profession, has received sufficient education and is well-known in the teaching and learning community for his/her standard teaching experience and credentials. They are highly skilled in their field. Good teachers know how to listen to their students, see their needs and give all they can give.Good tutors also care about their students. They always try to meet their students' needs. They have the ability to analyze and understand what the student is trying to achieve and why. They know how to relate with the students to make them feel important.If you want to become a professional tutor, you need to follow a few pointers. You should be willing to meet deadlines set by your employer. You should be committed to a system and expect from yourself that you will put in the effort to finish the course work.It is always better to get proper training in your field before choosing to teach. This ensures that you can also apply the learned skills to other areas of your life. And a good way to learn is by getting coaching from a professional tutor. You can take courses online or get an actual instructor to show you through a seminar.Another way to become a professional tutor is to join a college that offers tote helping classes. You can enroll yourself and start earning. Or you can join a tutoring club or tutoring service provider to earn at the same time.Experience, education and expertise are important factors that have to be considered before you decide to become a professional tutor. As you will soon find out, being a professional tutor is not an easy task.

More About Ketone Organic Chemistry

More About Ketone Organic ChemistryMost of us have heard about the benefits of ketone organic chemistry and that has made us all curious to know more. This is a practice where your body is able to burn off fat in the liver, heart and other fat tissues. There are also some people who say that they don't want to be on the traditional type of medicine because they think it is not effective enough. Ketone organic chemistry is definitely one of those products which helps people reduce their body fat by as much as 25%.Because ketone organic chemistry is derived from natural sources, the benefits are even greater than those of the conventional medicines. This is because there are no harmful side effects or toxins that are involved. So you don't have to worry about the side effects and your health as well.The use of this organic chemistry is very easy, you only need to apply it regularly to your skin and it will help your skin to look better and you will also see that you are reducing your w eight. Of course, this can be used every day and it will help you feel better.Ketone organic chemistry can also be used as a supplement for every person's daily diet. It will help you to prevent other diseases, improve your health and to be more energetic. Since you are losing weight, you will also feel great and you won't feel hungry anymore.When you take the supplement, you will see that your body starts to function like a normal size because your hormones will start functioning properly. You will get healthy results in no time and you will notice how you look better too. You will find yourself looking like a younger version of yourself.So if you want to reduce your weight and prevent any diseases, you should definitely use ketone organic chemistry. This is also a good alternative for other fat loss products because it has many benefits.You don't have to feel stressed because you are getting results at different stages. This product is definitely a wonderful one to try.

5 Blues Guitar Secrets That Will Make You a Better Player

5 Blues Guitar Secrets That Will Make You a Better Player Sign up successful Play the note you are going to bend to first, get the sound of the note in your ear, then bend up to it, and try to get it to be the same exact note. Plug in to a tuner, and practice bending from one in-tune note to another, either a half step or a whole step away. Practice unison bends. Unison bends involve playing two notes, the note you are bending and the note you are bending to, on two adjacent strings. When doing this, take special care, and make sure that they are exactly the same two notes. To get started, practice the examples below: Be sure to practice this all over the neck of your guitar, since it will take different amounts of strength to bend in tune in various parts of the neck. We want to train our muscles and our ears to be in tune no matter where we are on the neck. 2. Learn Entire Solos A lot of players tend to overlook this aspect of learning, and just end up digging into individual licks they enjoy. The importance of having a lot of licks and ideas available to you cannot be overstated, but there is a lot to be gained from learning the entirety of a solo. Learning an entire solo gives you a chance to see how the soloist paced themselves, and how they built their solo from the beginning to the end. It also gives you a chance to see how the soloist utilized space. When we  look  at  just  individual licks, we dont get to see what led up to them, and what came after them. Its these aspects of a solo that really make you stand out from the rest. 3. Serve the Song Typically, a solo should serve the song it is within, and should be viewed as your turn to speak and convey how you feel. What you choose to say in your playing should serve the song in some way. For example, if its a slow song, it may not be the time to unleash your fastest licks, back-to-back. In other instances, a song may need all of your fastest licks. Keep your ears open, and think about what it is that you are trying to express. Does it add to the song, or are you simply letting your fingers speak? Dont forget that the song has a melody. You can quote it in your solos, or simply just use the rhythm of the melody to relate your idea back to the melody. Leave space. Sing along with your playing. 4. Repetition Repetition can be viewed in a few ways: repeating your idea verbatim, repeating the rhythm but changing the notes, or playing variations on your original idea and allowing them to morph into new ideas. This is such a crucial tool for crafting a good solo. If we think about it, do lyrics typically have a bunch of unrelated ideas through the duration of the song, or are the lyrics all along a central theme? Typically we will find the lyrics are all around one idea, but when a lot of people go to take a solo, they tend to play a bunch of unrelated ideas stringing them together one after another. Sometimes it works; a lot of times it doesnt. Wouldnt it make more sense if instead of playing 100 ideas or guitar  licks in a solo, we played three or four, and got as much out of them as we could? Here are some ideas on how to practice this: Play the lick, and have a different ending each time. Vary the rhythm a few different ways. Keep the rhythm the same but change the notes. Play an idea, then respond to it (call and response). 5. Listen to the Greats This probably doesnt need to be said, but always be listening to guitar players (and other instrumentalists) who you enjoy, and learn from them. If you havent already, youve got to check out these great blues guitar players: B.B. King Freddie King Albert King Stevie Ray Vaughan Everyone that ever played in the Allman Brothers Band Eric Clapton Mike Bloomfield Muddy Waters Robert Johnson Robben Ford Larry Carlton Charlie Christian Tinsley Ellis Albert Collins There are many, many more tips worth mentioning, but this should get you started as you continue to learn blues guitar. Hopefully there are a few names here that you dont yet know. Keep practicing! Mike B. teaches acoustic guitar, blues guitar, and guitar  in Arcadia, CA.  He received his Bachelor’s Degree in Guitar Performance from  University of Redlands, as well as his  Master’s Degree in Studio and Jazz Guitar from  University of Southern California.  Mike divides his time between performing live, doing recordings, and being an educator.  He has been teaching students since 2004.  Learn more about Mike B. here! Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher Photo by  Soumyadeep Paul

4 Things NOT to Let Slide During Senior Year

4 Things NOT to Let Slide During Senior Year The following is a guest post written by Anna Carapellotti of Admissionado, a premier college admissions consulting company focused on helping students get into their dream schools. Seniors, youre in the homestretch (well, almost!). As we rapidly approach the Early Decision / Early Action deadlines, knowing that the Regular Decision deadlines are just around the corner, were here to remind you that now is not the time to lose motivation. In order to sail through senior year with success, its important that you keep your grades up, stay involved, and keep your eye on the prize (the acceptance letter, that is). So, with that in mind, here is a list of four ways to ensure a strong finish to your high school career: Grades Raise your hand if youre busy calculating the absolute minimum that you have to achieve this year in order to keep a competitive GPA. Hopefully no ones hand went up, but if yours did, consider this: What if you dont get into the school of your dreams and decide to transfer? What if you decide to apply for a scholarship, fellowship, etc. sophomore year of college and they request your high school transcript? It certainly wont look great if you dont have either a steadily improving or consistent GPA. For one, a significant drop in your GPA shows a lack of motivation and maturity. Why should anyone assume youre willing to work hard now if you werent willing to work hard then? Second, you might actually be missing out on material that will be useful to you in college. And finally, you will risk jeopardizing your relationships with your high school teachers, counselors, and administrators, who might otherwise be able to support you in your ambitions. Which brings us to Relationships Whether or not you have plans to return to your hometown, its important to continue to build relationships at your high school through senior year (and we dont just mean with your friends). As you grow older, you will learn that the connections you make truly matter. So if nothing else, continuing to work hard and make a good impression will simply be good practice for the future. At the same time, you never know when you might need to call upon a former teacher, your principal, or another adult at your school for a letter of recommendation or a reference. However, at the same time, were certainly not suggesting that you build relationships with the sole goal of getting something out of them. Were simply encouraging you to continue to work hard, do well in your classes, and remain involved in extracurricular activities in such a way that people are impressed with your effort. If you do so, these connections will form naturally and you will have a solid network to build upon in the future. Extracurricular activities While you certainly need to set aside some extra time to spend with your friends and family, work on your college applications, and perhaps even visit some college campuses, senior year is not the time to let your extracurricular activities and community involvement slide. These activities will help you continue to build a strong foundation for success with skills surrounding time management, teamwork, and leadership, in addition to helping you discover where your strengths and passions lie. Moreover, staying involved, whether it be in a sport, art, or volunteer effort, will help you continue to strengthen the relationships referenced above. College application essays Last but not least: your application essays. Chances are you already have a solid draft of your Common Application essay (we hope!), but some (if not all) of those school supplements may remain unchecked on your to-do list. We have three words for you: Dont. Burn. Out. With many of you applying to six or mores schools, you might find it difficult to remain motivated until the very end. But its important that you do, and heres why even if youre considering a gap year, feel like youre a shoo-in at a certain school, or think youll ultimately transfer, youll still want to make sure youve put your best foot forward. First of all, this will give you more options. Depending on where youre applying, even the brightest of students arent necessarily guaranteed admission. And a great, truly personal application essay can help tip the scale in your favor. Second, youll simply feel better waiting for those admissions letters if you know you tried your hardest. So write, rewrite, rewrite again, and be sure to proofread for clarity and errors. The end product should be something that youre proud of. If you keep working hard, stay involved, and put forward an application that reflects your best effort, then you should feel confident that you have set yourself up for admission and success. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

Your Guide to Kickboxing

Your Guide to Kickboxing Starting Kickboxing? Here are the Essentials ChaptersA Guide to Kickboxing RulesThe Essential Kickboxing EquipmentKickboxing, Muay Thai, or Savate?Some of the Kickboxing World ChampionsWhy Try Kickboxing? The Health BenefitsSo, you’re thinking of starting with kickboxing.Maybe, you’ve looked into kickboxing classes, enthusiastic about throwing a roundhouse kick. Maybe, your pals have told you about the thrills of the kickboxing workout, with its aerobic and cardio workout. Maybe, you’ve seen a kickboxing champion or two perform on the tv â€" and feel inspired to give it a go yourself.Whatever the reason for your interest in this combat sport, you’re in for something really special when you get yourself into the gyms and can finally call yourself a kickboxer. It’s a wonderful sport: high intensity, full contact, and supremely elegant at the same time.And if you are going all the way with it, you’re not letting yourself in for just an exceptional fitness program, but you’re going to building incredible balance and e xcellent self-defense skills too.There’s hardly a downside â€" unless you consider receiving punches in the face a downside. The point, however, is a different one. Whilst, as a martial art, kickboxing receives either sneering dismissals as ‘too violent’ or responses that are just based on fear, if you are not too fussy about a few bruises, kickboxing is a great sport in so many ways.So, don’t listen to the haters, and don’t fear too much about the fists you’ll receive (you’ll be wearing protection). Just enjoy it â€" and get in shape whilst you’re doing it. AndreyBoxing Teacher 5.00 (1) £35/h1st lesson free!Discover all our tutors KostiaBoxing Teacher 5.00 (1) £17/h1st lesson free!Discover all our tutors LeeBoxing Teacher £17/h1st lesson free!Discover all our tutors SajBoxing Teacher 5.00 (1) £20/h1st lesson free!Discover all our tutors KaranBoxing Teacher £15/h1st lesson free!Discover all our tutors ThomasBoxing Teacher £20/h1st lesson free!Discover all ou r tutors HaileyBoxing Teacher 4.50 (2) £50/h1st lesson free!Discover all our tutors DavidBoxing Teacher £20/h1st lesson free!Discover all our tutorsA Guide to Kickboxing RulesAs with any sport â€" literally any sport from the combat sports or the mixed martial arts to football and tennis â€" there is little you can do in kickboxing without knowing the rules.So, let’s start here with a brief run down of them â€" but note that you can find more information on this in our guide to kickboxing rules.The aim of a kickboxing match is to win. And, to do that, you have a number of options. Firstly, you’re aiming to knock the other person out â€" either literally or through what is known as a ‘technical knock out’, in which either the ref, the doctor, or your opponent himself deems themselves unfit to continue.The second way is through points. If neither of you have knocked the other out, then this is what is going to happen. At the end of the match, the three or five judges will r eveal the scores that they have taken at the end of each round. These will either be ’10-10’, ’10-9’, ’10-8’, or ’10-7’, depending on the strength of the win (including the number of takedowns and the effectiveness of the respective boxers’ display).That’s pretty much it. But watch out, because there are plenty of things that you can’t do, depending on what type of kickboxing you are doing. Whilst in Muay Thai, elbows are allowed, they ain’t in other forms â€" in which you can’t clinch or grapple either. Kickboxing can be a pretty brutal sport.The Essential Kickboxing EquipmentAlthough the fundamental principles of kickboxing are fairly straightforward, the kit required can run to a pretty long list.As you can expect, the majority of this is protective gear, covering all the different parts of your body. And whilst it immediately might seem like it’s all a bit over the top, it really isn’t â€" and you’ll agree soon enough.The majority of this equipment is mandatory â€" meaning that you can’t participate in any bouts without them. Which is something well worth taking into consideration. Meanwhile, whilst your boxing gym may well provide boxing gloves and mitts, consider the smell: it’s just better to have your own.Here are a few that you might need.Boxing Gloves â€" You won’t be allowed in any bout without them. Often fighters put hand wraps beneath their gloves too, for extra protection.Body Armour â€" That means headgear, shin pads, a gumshield and groin protection. You ain’t gonna last long in the ring without them.Clothing â€" Obviously, this one is a given. But you need to have specific length shorts and the right shoes to be able to kickbox.Find out what other gear you might need in our article on kickboxing equipment. Make sure to invest in the right kickboxing gear AndreyBoxing Teacher 5.00 (1) £35/h1st lesson free!Discover all our tutors KostiaBoxing Teacher 5.00 (1) £17/h1st lesson free!Discover all our tutors LeeBoxing Teacher £17/h1st lesson free!Discover all our tutors SajBoxing Teacher 5.00 (1) £20/h1st lesson free!Discover all our tutors KaranBoxing Teacher £15/h1st lesson free!Discover all our tutors ThomasBoxing Teacher £20/h1st lesson free!Discover all our tutors HaileyBoxing Teacher 4.50 (2) £50/h1st lesson free!Discover all our tutors DavidBoxing Teacher £20/h1st lesson free!Discover all our tutorsKickboxing, Muay Thai, or Savate?Kickboxing, really, has a long and complex history, drawing its inspiration, rules, and movements from Muay Thai kickboxing, Brazilian Jiu Jitsu, full contact karate, taekwondo, English boxing, and French savate.Really, it’s a mixture of styles from across the world â€" and this is both its beauty and its complexity for beginners.Because where a re you supposed to start if, at the gym, you see classes for savate, Muay Thai, Glory kickboxing, or oriental rules. These things should come with an explainer which, unfortunately, they rarely ever do.But let’s take these three â€" Muay Thai, Savate, and kickboxing â€" in a bit of detail here. Their particular styles and histories are pretty different.Check out more on the different styles of kickboxing.Muay ThaiLike other styles of boxing from east Asia â€" ‘Burmese’ boxing or lethwei from Myanmar and the Malaysian Tomoi â€" Muay Thai is ancient, dating back hundreds of years, and potentially even further. It simply means ‘Thai boxing’.What’s striking about Muay Thai is that, unlike other forms of kickboxing, it uses ‘eight limbs’ â€" or elbows and knees as well as hands and feet â€" as well as grappling and clinching.It remains fairly ferocious: full contact and risky, but completely exhilarating to watch and be part of.KickboxingIn the fifties, in Japan, professi onal fighters started to look elsewhere for inspiration. Karate was publicly displayed all over the place, yet, at the time, it was very rare that anyone would actually make full contact.This changed when kickboxers started to fuse elements of Muay Thai into their karate style. It was here that kickboxing was born â€" and it soon spread across the world, picking up elements from different combat sports as it went.These days, kickboxing remains a generic term for combat sports that allow the punch and kick. So, whilst there are many varieties and lots of different rulebooks, it is a heterogenous discipline.SavateDeveloping from the shipyards and street fighting techniques in France in the nineteenth century, savate is often thought of as fencing without weapons. It is elegant, eloquent, and composed, with mesmerising shapes and movements.The main weapon is savate is your feet â€" and you have to wear particular shoes for this. It, like Muay Thai boxing, get’s pretty brutal too. Kickboxing is really excellent exerciseSome of the Kickboxing World ChampionsUnless you’re into the sport, there is little chance that you will have heard of the big names in kickboxing. In mainstream discourse, hardly even the world championships and the world champion get much attention â€" in the UK at least.Yet, the great names in the sport are icons â€" and formidable athletes at the same time. And if you are starting out in kickboxing, you should look to these guys and girls for inspiration.We have a larger list of kickboxing world champions and heroes, yet here we’ll just focus on a few â€" to whet your appetite.Giorgio PetrosyanOne of the current heroes of kickboxing, Giorgio Petrosyan is known for his defense techniques and his lightning fast counters.His record is a massive 101 wins to two losses and two draws â€" and he is hoping to continue on such form for a long time to come.Cris ‘Cyborg’One of the legends of the female game, Cris Cyborg is a record-breaker in h er field. Her specialty is in MMA â€" mixed martial arts â€" yet her kickboxing is incredible too.Having won female fighter of the year more times than pretty much anyone else, she will remain a hero of the sport forever.Sittichai SitsongpeenongCompletely at the top of his game right now, Sittichai Sitsongpeenong is a Thai fighter and lightweight hero. It seems to be fairly unanimous that he is the best lightweight fighter in the world right now.If you’re looking for what contemporary kickboxing can be, he is your man.Why Try Kickboxing? The Health BenefitsKickboxing is a real physical workout. Like, a total body workout. If you have fitness goals towards which you are aiming â€" whether that’s to get fit, to reduce stress, or just to get your heart pumping a bit more often â€" then kickboxing can work wonders for you.With the combination of fat-burning cardio and intense muscle toning, kickboxing really is, more than anything, just excellent exercise.This is why it has become s o popular in recent years, with gyms offering fitness kickboxing, fitness programs using parts of the kickboxing repertoire, and training of all the muscle groups.And the beauty of exercise is that it does so many more things that we take for granted. Sure, you burn calories, enable fat loss, and develop your cardiovascular endurance. But you also build self-confidence and develop your self-esteem, concentration, and mental health too.Follow the link for more information on the health benefits of kickboxing.

How to play the digital piano

How to play the digital piano Learn to play the digital piano ChaptersCan the digital piano replace the acoustic piano?Different ways to learn to play the digital pianoLearn to play the digital piano with private lessonsWith their fingers moving quickly across the keys, showcasing an unfathomable suppleness and dexterity, the virtuoso pianist leaves their mark on the listeners of any performance.Ray Charles, Nina Simone, and Stevie Wonder have all left their mark on the world of music, and their melodies have provided a backdrop to generations of fans. The way they play keys, press the pedals, and that expression on their face as they play all seem to exude a certain enigmatic sensuality. But does a musician’s performance depend on whether they’re playing a piano keyboard or an electric piano?A 2010 study by the chamber of instrument sellers in France found that the total market for musical instruments came to about $300 million per year.Out of this total however, it’s interesting to note that the total cost of acoustic pianos being sold was slightly less than money from digital piano and keyboard sales, making up 15% and 16% respectively.Keyboards and digital pianos are now an integral part of the music market today, especially given the amazing success of different Japanese and Korean brands.The Japanese Casio and Yamaha brands, for example, have become synonymous with children's first piano lessons. They specialize in models like the Clavinova or the Silent system, and make up a whopping 15-20% of total revenue from instruments sold in 2010.There are many reasons the professional pianists and amateur piano players alike would choose to play digital pianos instead of the heavy, expensive, and bulky acoustic piano models. Are acoustic pianos perhaps destined to become extinct, relegated to public gardens and middle school music classes in favor of Yamaha arias and Casio privia?It’s another good reason to consider learning to play the digital piano and how to take advantage of all its features in order to become a modern, 21st century, piano virtuoso.SaveSave

What Are The Different Hindi Dialects Spoken in India and Which Should I Learn

What Are The Different Hindi Dialects Spoken in India and Which Should I Learn Which of the Hindi Dialects of India Should You Learn? ChaptersWhat is the Hindi Belt?Hindi and Urdu: One Language, Two Languages or Two Dialects?Learning Hindi: Hindi Dialects in IndiaIndian Hindi Creoles and PidginsHindi Dialects Outside of the Indian SubcontinentWhich Hindi Dialect Should You Learn?It’s hard enough to try and figure out which language of India you should learn - Sindhi, Telugu, or Tamil? Or maybe Punjabi? Is it easier to learn an Indo-European language or will you dare to try one from the Dravidian language family?But once you have decided on Hindustani as the language in India with the most speakers and as being the most universally understood, you still find yourself confronted with the question:Is there only one dialect of Hindi? If not, which should you learn?Superprof is here to help! if not, or if you already speak and read Arabic and don’t want to learn another new alphabet, Urdu is the way to go. You’ll be understood on either side of the border anyway.However, if you are more interested on an academic l evel, you will notice greater differences in the language of poetry and literature, and you will have to consider whether you prefer Muslim literature or Hindu literature. However, if you find yourself in a bind and can’t decide - and don’t mind studying on the other side of the Pond - the University of Texas offers combined Hindi-Urdu language programs.Hindi is written using the Devanagar script. Photo credit: basicshit.org on VisualHuntIf you choose Hindi, it’s probably best to stick with the standardised version. Everyone in the Hindi Belt and much of North India will understand standardised Hindi, and if you are moving to India you will soon pick up the local dialect - it’s easier to find Hindi lessons near you than a teacher who speaks Awadhi or Bundeli.However, if you are moving to Fiji or the Andaman Islands, finding a tutor who can teach you the local Creole is the way to go - maybe you can find Fiji Hindi class online to help you out.Whichever you choose, when learn ing Hindi, make certain that your teacher or language coach speaks Hindi as his or her mother tongue. Many Indians understand Hindi (Bollywood again) but didn’t grow up speaking it. They might have a good grasp of Hindi vocabulary, maybe even speak it relatively fluently, but they won’t know the finer points of grammar and idiom the way a native speaker would.

Online Proportion Formula Tutors

Online Proportion Formula Tutors Proportion is a fixed ratio between two substances. Proportion always maintains a fixed ratio between two fractions. For example, a / b = c / d. It can be written as a : b = c : d. This can also be called as the proportion formula. Proportion in math is defined as the similarity while comparison between two quantities or substances. Proportion is also used between two geometric objects where their dimensions can be compared. Example 1: Find the x in the proportion 2 : y = 10 : 3. Solution: Here the given proportion is 2 : y = 10 : 3. It can be expressed as a fraction in the form. 2 / y = 10 / 3 Now multiply both sides of the equation by y. This gives 2 = 10 y /3. Now multiply both sides of the equation by 3. This gives 10 y = 6. Now divide both sides of the equation by 10. So y = 6 / 10. Hence the value of y for the given proportion = 3 / 5. Example 2: Find the x in the proportion x : 5 = 1 : 15. Solution: Here the given proportion is x : 5 = 1 :15. It can be expressed as a fraction in the form. This gives, x / 5 = 1 / 15 Now multiply both sides of the equation by 5. This gives 5(x/ 5) = (1 / 15) (5). x = 1 / 3. Hence the value of x for the given proportion is= 1/3.