Using the Expression Calculator Algebra Help

Using the Expression Calculator Algebra HelpExpressions are one of the most fundamental and useful tools in mathematics. They allow us to express mathematical concepts in ways that are not impossible for humans to understand. These ideas include sums, roots, differences, formulas, and other important ideas that are used in mathematics. These are also the ideas that most people fail to understand when they begin their study of calculus, analysis, and so on.Expression calculators allow us to express and evaluate an expression in just a few seconds. It takes only a few seconds to do this. This feature is very useful when we have to write the expression and evaluate it. It is useful in many other situations too.There are many ways in which to use the expression calculator algebra help. Many of these uses are common to everyone, but there are also special ways to use it. We can use it in a similar way to how we use a calculator. When we use an algebra calculator to evaluate our expression s, we can enter the equations we want to solve, and then click the relevant button to see the results.This way, we can use the expression calculator algebra help to create a result or to find the value of the expression. By doing this, we can evaluate any expression. The calculator will do this for us.We can use the expression calculator algebra help in algebra, geometry, calculus, statistics, economics, and many other subjects. With the help of the expression calculator algebra help, we can solve a problem with ease.We can use the expression calculator algebra help to create a graph, solve a problem, and many other things. This is the idea behind the concept of expressions. It allows us to find the solutions to problems, evaluate and solve many other equations, or graph things to show their relationships.Expressions are one of the most important concepts in the world of mathematics. There are many ways to use the expression calculator algebra help to solve a problem, or to create a n expression, and many other things.

Standard Form Math - Online Math Tutoring

Standard Form Math - Online Math Tutoring Standard form in math is the way to represent the decimal number, expression, linear equation, quadratic equation, polynomials, conic sections etc in a standard form by using an expression or an equation. We can easily identify the figures or curve with the help of standard form. Few examples of standard form in math: - Standard form of decimal number Example: -Find the standard form of 1235600000000000000. Solution: - Standard form of 1235600000000000000 is 1.2356 x 10 ^ 18 Standard form of a linear equation is ax+ by =c. Example: - Represent this equation into a standard form of a line. 2(x-3) + 4(y+1)- 8=0 Solution: - 2(x-3) + 4(y+1)- 8=0 Or, 2x- 6 + 4y +4 8 =0 Or, 2x + 4y -10 = 0 Or, 2x+ 4y = 10 Therefore the standard form of the given equation is 2x+ 4y = 10 Where a= 2, b= 4 and c=10 Standard form of a quadratic equation is ax^2 + bx + c = 0 Example: - Represent the following equation in standard form. (x - 1) ^2 + 5(2x + 5) =100 Solution: - (x - 1) ^2 + 5(2x + 5) =100 Or, x^2 - 2x +1 + 10x +25 = 100 Or, x^2 + 8x +26 =100 Or, x^2 +8x + 26 100 =0 x^2 + 8x 74 = 0 Standard form of the given equation isx^2 + 8x 74 = 0 Where a= 1, b = 8, c = -74

How to Learn Japanese Through Textbooks

How to Learn Japanese Through Textbooks What Are the Best Books to Learn the Japanese Language? ChaptersLearn Japanese with the 'Japanese Manual'Japanese in 40 LessonsJapanese for Busy PeopleJapanese For Dummies1001 Japanese ExpressionsIf you want to speak Japanese, you will first of all need  to define your own Japanese language learning project.How to learn Japanese is therefore a key question that you need to answer. There are a number of different methods for learning Japanese, but one of the most popular ways to learn basic Japanese is to get hold of a textbook.But before you dive straight into buying a book from Amazon, you need to know why you want to learn Japanese.Indeed, there is not much of a point getting into a 500-page manual if you just want to go to Tokyo for a few days, and only need to know some greetings and how to introduce yourself. For this, Japanese learning tools such as mobile or iPad applications (or a Japanese course) may be enough!You may not want to leaf through a Japanese beginner's manual if you already have a solid foundation in Japanese and your goal is to work in the land of the rising sun.But if you want to take the Japanese Language Proficiency Test (JLPT), you will need to learn the intricacies of Japanese grammar, and not just have a conversational level. In such a case, you will need a more substantial textbook to help you as you learn to speak Japanese.As you will have understood, your profile and your expectations dictate which method and manual will be best for you.This article will help you to understand the different methods of learning Japanese.Many people who have learned Japanese using these manuals point out that despite the fairly high price, the book is of exceptional quality and will allow you to make great strides in learning the Japanese language.  This is important for all beginners because Japanese writing is very complex for English speakers.Japanese in 40 LessonsTake the 40 Japanese Lessons Book with you everywhere--it's as light as a manga!Just as learning Japanese via an app  will focus on nihongo , books for studying Japanese will do the same. You will still be able to communicate with a native speaker, but nihongo is generally the form of Japanese learnt by any new learner as a second language, and therefore differs slightly from what Japanese people learn at school.This book has the advantage of being a paperback book and is much more transportable than some other options. It is for those who want to learn this new language on their own.And let's not forget why you may be wanting to learn Japanese to begin with!  Japanese cultural exports are exploding.  From anime to sushi bars, karaoke to manga, bonsai to origami, Japanese culture has become part of international culture.A knowledge of the language will give you direct access to Genki video games,  Japanese film, animations, and comic books.  Speaking Japanese will set you apart from the crowd. The majority of people who learn a foreign language choose a European language like Spanish, French, German, or Italian. Choosin g a less commonly learned language will pop out on your resume and differentiate you from the crowd.Also, Japanese is a stepping stone to learning other Asian languages, such as Korean or Mandarin. Like other Southeast Asian languages, Japanese is a highly analytical language, relying heavily on function words rather than extensive systems of inflection to denote linguistic properties.These languages also share a similar subject-predicate sentence structure. Though Southeast Asian languages are distinctly different among themselves, as a group they are clearly different from geographically more distant language families, such as Indo-European and Afro-Asiatic languages.From an organizational point of view, each of the 40 lessons is separated into four sections. For each lesson, you will also find themed exercises and  pages on civilization, Japanese culture, and  the history of Japan with beautiful texts on the Emperor, the Second World War, or the samurai.This is a very useful book if you are  preparing a trip to Japan and want to go further than just learning the basics as you can simultaneously study the language and culture.The grammar you will find in the book is relatively simple, so that you can use it in conversation and concrete examples.It is the same for the vocabulary and additional lessons, where you will learn Japanese words and Japanese phrases.Concerning writing Japanese and the Japanese alphabet, you will have access to 20 lessons in order to learn each kana:10 lessons to master basic hiragana and their variations10 lessons to learn basic katakana and their variationsBonus detailed Japanese lessons.The other 20 lessons will serve as an introduction to learning the different kanjis.The box-set, consisting of the book and two CDs with audio recordings, allows you to work on your written Japanese and refine how to pronounce certain words and other types of oral expression. In doing so, your ability to hold a Japanese conversation will improve dra matically.Why not go through the 40 lessons with a Japanese tutor via webcam?Or search for an online Japanese course here.to define your priorities and your learning objectives when it comes to learning Japanese. If the idea is to go sightseeing, spend a few yen in Kyoto or in the capital, your learning method is going to be different when compared to someone looking to work or study in Japan.You can figure out what method would be best via questions such as:What basic level do I have in Japanese (beginner, intermediate, advanced)?How much time can I devote to learning?How often am I willing to invest in Japanese lessons?What is my ultimate learning goal?These questions can help you find which book to guide you to:For a beginner or intermediate, and for someone  who is not necessarily in a hurry, your best bet is going to be the two Japanese Manuals as well as the Japanese Exercise Handbook, to complete the oral part of the learning.For someone wanting to learn expressions in order to communicate before going on a trip to the country of Mount Fuji, we recommend the pocket size Japanese for Dummies, or Japanese in 40 lessons.Finally, for someone who is fluent in the language, the Japanese Handbook remains a safe bet. You can become even more fluent thanks to the 1001 Japanese Expressions textbook, which will teach you some idiomatic expressions and allow for greater immersion in the Japanese tradition and customs.

The Top 10 Keyboard Shortcuts for Windows Users

The Top 10 Keyboard Shortcuts for Windows Users Computer Courses: The Keyboard Shortcuts for Typing More Quickly ChaptersWhat’s the Point in Windows Keyboard Shortcuts?The 10 Best Windows Keyboard ShortcutsShortcuts for Managing WindowsA Few More Bonus ShortcutsIn terms of desktops in 2017, Windows had a market share of 83%, Mac OS X accounted for 13%, Linux 1%, and less than 1% used Chrome OS.While smartphones and tablets have been increasing their market share in the last decade, desktops and laptops are still regularly used in the world of business.Put simply, typing on a touchscreen keyboard on your smartphone or tablet isn’t effective enough when it comes to forging customer relations, brand communication, or even creating text for Indesign or Photoshop projects.  This means that the qwerty keyboard still remains one of your PC’s most important peripherals.Writing texts in Microsoft Office, editing images in Adobe Photoshop, developing web sites, etc. all require that you can type quickly and effectively.  In order to do this, you’ll need to learn a few important keyboard shortcuts for Windows.Are you sick of right-clicking on the mouse to open a context menu and then left-clicking to choose the option?Did you make a mistake? It only takes a second to accidentally select a load of text instead of a word and delete everything.  Don’t worry, though! Everything can be undone with a quick press of ctrl + z.Here are Superprof’s 10 best keyboard shortcuts to speed up your work on Windows.To put it simply, shortcut keys are useful because they help you to do things more quickly. This might seem obvious, but you’ll soon see how useful they can be and how much time they can save you. You've probably noticed that your keyboard layout includes a lot more than just letters, numbers, and a spacebar. Your keyboard has function keys, esc, ctrl, alt, and the Windows key (Command if you're using Mac). They're there for a reason, after all.Check out some coding courses here.If you work in IT, productivity is hugely important. (Source: Jay Kunwar)The digital revolution ha s turned workplaces on their heads. Across the channel, the French journal Sciences Humaines had this to say:“In the years to come, 42% of jobs are at risk of being transformed by digitalisation. 3 million jobs could be eradicated. Robotisation continues to deeply destabilise the [French] middle classes.”The same could happen here! Everyone will therefore be required to be familiar with computers and how to operate them effectively if they’d like to keep working. Mastering shortcuts when interacting with computers is therefore seen as a must for all users.  It’s a quick and easy way to increase your productivity.In fact, knowing the shortcuts can save valuable seconds every time you use them and, over the course of a day, drastically improve how much work you output.From simple operations like opening a window to editing texts (copying, cutting, and pasting), opening windows explorer, placing an image into a text, editing and developing websites, you can use keyboard shortcu ts to reduce the time it takes to carry out a number of different digital tasks.Another important thing about these shortcuts is that if your mouse, trackpad, touchpad, or wheel stop working, you can still operate the computer effectively without them.You can carry out most tasks on your computer using just the arrow keys, escape, enter, ctrl, alt, and the number pad.Not convinced? Here’s a quick test for you:Do the following operations by just using your mouse, then try it again using mac keyboard shortcuts. You can save around 50% of the time taken by using the latter method.Open your browser.Search something on google.Click on an article.Highlight a paragraph.Copy and paste that paragraph into Microsoft Word (or OpenOffice).Select all and change the colour of the text.Open the file explorer.Choose an image and import it into the text document.Save the file and then export it as a .pdf.Send the file by email to another computer.Not know the shortcuts for any of these? Why not st art with a few computing tutorials for beginners?Here are some of the most important keyboard shortcuts you should learn...The 10 Best Windows Keyboard ShortcutsWhile these shortcuts are incredibly simple, they’re also incredibly useful and everyone should know them.Copying and PastingInstead of right-clicking and choosing “copy” then going to a new part of the document and right-clicking again to choose “paste”, you can carry out these operations by holding down the ctrl key (the command key is used on Macs) and pressing:Crtl + cCrtl + vThis is useful for anyone who wants to edit document more quickly. When you copy or cut, the computer saves the text temporarily to the clipboard. You then just have to scroll to where you want to insert it and use the paste shortcut.Cutting and pasting is something you need to do quickly if you work with Word a lot. (Source: kaboompics.com)Cutting and PastingSo what does ctrl + x do?When you press on cntrl and x, the text or image you’v e highlighted will disappear. This isn’t used for deleting your selection, it stores your selection you can paste it elsewhere in your document by pressing “ctrl + v”.UndoHow many of you have accidentally deleted something by mistake?When you’re editing a text, if you accidentally select a whole line or paragraph instead of a word, you might end up deleting the whole thing.  A quick press of ctrl + z will undo the last step you made.Useful, isn’t it?SearchingThis is a great shortcut if you want to know how many times you’ve used a specific word, find a specific part of a text, or see if a text talks about a certain topic:In Windows, you’ll need to use the shortcut ctrl + f (for find). You can also use this function in browsers, too. Keep in mind that this isn't the same as the search you use online. This function is used solely to find exact matches within a text or browser window.Select AllRather than scrolling from the very top of a page to the very bottom while left -clicking with your mouse, you can use the keyboard shortcut ctrl + a to select everything. This is really useful for formatting an entire text if you've ended up with a lot of different fonts being used.Opening the Task ManagerDo you need to lock your computer or close a programme that’s stopped functioning?The famous shortcut ctrl + alt + del will open the dialogue that you need.  You can consider the shortcut ctrl + alt + del as your panic button for when your computer starts bugging out.Shortcuts for Managing WindowsIn this day and age, it’s very common for computer users to get lost in the various windows and tabs they have open. Finding the page you want to look at can end up like trying to find a needle in a digital haystack.We’ll save you the price of a private IT tutorial with this little tip - though you might want to consider taking programming courses if you want to delve deeper into the world of computers!Changing WindowsPressing alt + tab will quickly take you to your next active window. If you hold down alt, every time you press tab, you’ll move to another window.  This is very useful when you have a lot of windows open like your settings, a database, image editing software, webpages, etc.Before you know it, you can end up with too many windows. (Source: snapwiresnaps.tumblr.com)This can save you a lot of time against finding a stack of windows on the task bar.Minimising All Windows and Returning to the DesktopIf you want to go straight back to your desktop, you just need to press Windows + d. This will minimise all windows to the task bar and you’ll find yourself back on your desktop. Pressing Windows key + d again will maximise all the windows.  This is useful if you end up with tonnes of windows stacked on top of each other.Additionally, simply pressing the Windows button will open the start menu (which is the Windows logo in newer versions).Moving Windows AroundHere’s a shortcut that I like: especially when you’re working with multiple screens. This can be used to move windows around:  Windows + Shift + arrow keys (left or right)Create a Virtual Desktop If you’re working on a small screen, like a 10” or 13” laptop, you can create a virtual desktop.  A virtual desktop will be created to the right of your current desktop. The command is simple: Ctrl + Windows + d. This means you can juggle several desktops without any of them getting too cluttered. You can navigate between desktops as you wish and remove them when you're finished.  As you’ve probably gathered, there are plenty of different shortcuts on Windows.A Few More Bonus ShortcutsHere’s a list of other useful keyboard shortcuts:As you can imagine, we haven’t included all of them. There are literally hundreds of them...Thanks to shortcuts, you can navigate web pages as quickly as you can regular pages. (Source: Tirachard Kumtanom)Move an active window: Alt + Space Bar + l + arrow keysFullscreen mode: F11Open the file menu: Alt + fChange tab s: Ctrl + 1, 2, 3, etc.Update the page/refresh: F5Delete a file directly without sending it to the recycle bin: Caps lock + delNew tab: Ctrl + tNew file: Ctrl + nPrint: Ctrl + pClose the window: Alt + F4Bold: Ctrl + bItalics: Ctrl + iShow the properties of the selected file: Alt + returnIn the special characters window in Microsoft Word, you can also find the shortcuts for the characters you want to use. This is especially useful when typing in foreign languages as the English keyboard doesn’t tend to have accent keys.For example, if you want to put an acute accent on the letter “E” (like in the words café or cliché), you just need to type: Alt + 144 (on the touchpad).Finally, keyboard shortcuts are essential if you want to work with Photoshop and edit photos.  If you want to work effectively, keyboard shortcuts can make both Macs and PCs far quicker than a simple typewriter.Ready to find out how to type faster?

5 Good Audition Songs for Musicals by Voice Type

5 Good Audition Songs for Musicals by Voice Type Sign up successful For some initial pointers check out the video below, then keep reading as we share 20 more good audition songs for musicals. Well include selections for each voice type, representing a mix of both classic and modern shows! Good Audition Songs for Musicals Sopranos This Place is Mine from “Phantom” by Maury Yeston. Everyone sings from the OTHER “Phantom” don’t make that mistake! Funny divas can really sell this song. It’s as big as anything you’d find in the major hits from that era (and you know what they are!) but this song is hardly overdone. “To Keep My Love Alive” from “A Connecticut Yankee in King Arthur’s Court” by Rodgers and Hart. So outrageously funny! This is for the soprano who’s also a comedienne. Plus, it’s always good to have some Rodgers and Hart in your repertoire! “Unexpected Song” from “Song and Dance”. This is an absolutely beautiful ballad from Sir Andrew Lloyd Webber’s lesser-known works. You can’t go wrong with a single song in the show, in fact; it’s a one-woman show and you have a lot of great audition songs to choose from! “One More Kiss” from “Follies”. It’s not always a good idea to bring in Sondheim unless they specifically ask for it (too complicated for many accompanists), but this is a simpler tune in the style of song from an old operetta. Belters/Mezzos “How ‘Bout a Dance?”  from “ Bonnie and Clyde” by Frank Wildhorn. This is a sassy and fun song perfect for a younger actress that belts. This musical is fairly recent, but due to the fact it was not a hit well, chances are not too many other people will be walking in with this one! “Wherever He Ain’t “ from “Mack and Mabel”. What a score! This is an up-tempo, rag-timey song that is just plain fun to sing by a spunky leading lady. While “Mack and Mabel” is respected for its glorious score by Jerry Herman, this show never took off! “Home “ from “The Wiz”. This a pop-like song that builds. Memorable melody and you can really put some emotion behind it. Perfect if you’re auditioning for something like “Dreamgirls” (but again, it’s best to avoid those songs unless they specifically ask for them). “All Falls Down” from Chaplin.This song is sung by the character of Hedda Hopper in the show. It’s a real scene stealer! Another modern (2006) musical that was not a hit, but has a marvelous score (see a theme here?). “The Music That Makes Me Dance” from “Funny Girl”. We all know that Barbra owns “People” and “Don’t Rain on My Parade”, but this lesser-known ballad from the show is gorgeous and a solid choice. Tenors “A Bit of Earth” from “Secret Garden”. If you need something a little more modern that’s a moving yet simple ballad, this is a great choice. “When I’m Not Near the Girl I Love” from “Finian’s Rainbow”. This is a mid-tempo song for a tenor with charm and personality, from a more “classic” show. “Seeing is Believing” from “Aspects of Love”. Another one of Sir Andrew’s flops but what a score! This may be a better choice than “Love Changes Everything” from the same show, which many performers tend to oversing. “Shiksa Goddess” from “The Last Five Years”.  This is for a comedian! A mid-tempo number from another more modern show with very clever lyrics that will leave the audition panel rolling. “You are Beautiful” from “Flower Drum Song”. Ballad for a young lyric tenor from one of Rodgers and Hammerstein’s lesser known shows. Baritones “C’est Moi”- from “Camelot”. Need something classic? Are you a solid actor? This one’s for you. “Gonna Be Another Hot Day” from “110 in the Shade”.  Mid-tempo as well as lyrical, and could suit a variety of types. “I’ll Be Here”- from “The Wild Party”. Wonderful song from another more modern show for a baritone who is a bit more pop/jazz-like and comfortable with some vocal improvisation. “Love Sneaks In” from “Dirty Rotten Scoundrels”. Need something current that’s also a ballad? Perfect choice! “You Won’t Succeed on Broadway”- from “Spamalot”. Perfect for the man who is an “actor first, baritone second”! Very patter-like and needs a comedian to sell it but that goes without saying, doesn’t it? See Also: Best Audition Songs for Baritones [Video] Repertoire selection becomes a piece of cake once you establish who YOU are (comedian, ingenue,  baritone, belter, etc.). After knowing your type, it’s all simply a matter of two really big things: what shows are being cast (all modern? All classic? A mix of the two?), and what YOU truly enjoy performing. There is so much out there that theres no excuse for using a song you think is just okay as an audition piece. The audition panel will always be able to tell! Have fun discovering new shows and songs are one of the best parts of being a “musical theatre geek”! Want even more audition  song ideas?  Check out our list of 400+ songs to sing,  and our newest article the 50 best audition songs for musicals. Molly R. teaches online and in-person singing lessons in Hayward, CA. Her specialties include teaching beginner vocalists, shy singers, children, teens, lapsed singers, and older beginners. She joined TakeLessons in November 2013. Learn more about Molly  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 Rande Archer

How Will the AP Physics B Exam Change in May 2015

How Will the AP Physics B Exam Change in May 2015 In May 2015, the Advanced Placement (AP) Physics B exam will undergo some change. Reviewing the breakdown of these changes below will help students to ensure readiness for the new exam when it premieres. The need for change The National Research Council (NRC) recently determined that the AP Physics B course covered too wide a breadth of material so wide that students were not developing a deep enough understanding of concepts. To improve exploration of such materials, and to expand the scope of knowledge covered, the NRC made a recommendation that AP Physics B be divided into a two-year course, effectively doubling its length. Content is now divided across two years, the first of which is the equivalent of a first college semester of algebra-based physics. The class will cover: Newtonian mechanics; work, energy, and power; electronic circuits; and mechanical waves and sound, with an emphasis in inquiry labs and physics state standards. The second course will serve as a second semester college-equivalent course and will cover fluid mechanics, thermodynamics, electricity and magnetism, optics, and atomic and nuclear physics. Splitting the course into two separate entities will provide for more hands-on learning, as well as a greater overall understanding of the curriculum. These are some great tips on how to ace your AP courses. Changes in learning objectives When the AP Physics B course becomes two courses, the learning objectives will also change to reflect the new organization. These objectives will now fall under seven categories, which outline the framework of introductory physics. The learning objectives are presented as a checklist that provide exactly what a student is responsible for knowing and demonstrating in order to receive college credit. The learning objectives also define what will be on the exam; questions that do not match up with one or more objectives will not be on either test. Each objective is associated with both knowledge of physics and basic foundational science principles. Course vs. test While the AP Physics course is recommended to be taught as two courses, each lasting the duration of one year, each school is responsible for setting their own AP schedule. Students who do not take AP courses are still eligible to take AP exams. This means that the exam can be taken, no matter how you have prepared for it. While it is recommended that students and teachers follow the approved exam schedule, a student has the opportunity to try their hand at the test under any circumstances. To be more prepared for the exam, it is recommended that students take Physics over two years, on the same lines as the AP Physics course. Here are 3 questions to ask yourself before taking an AP course. The test The AP Physics exam will be offered in two exams: one for AP Physics 1 and the other for AP Physics 2. Each exam requires three hours, and both can be taken in one year. Like the previous exam, the two will require students to complete both multiple choice and free response questions. Questions on the new tests will assess how well students understand physics conceptually, which means test takers will be required to demonstrate understanding by applying science practices. This involves more writing in free response sections, though the tests will contain fewer of these questions. The free response questions will focus heavily on qualitative and quantitative explanations, reasoning, and justification of answers given. The changed tests will also include a question focusing on experimental design. This question will require students to demonstrate a full range of knowledge in order to explain the various steps of an experiment. Also, while the old test emphasized the use of mathematics to solve problems, the new test will be more cumulative in its approach, asking students to rely on a breadth of knowledge involving math, reasoning, knowledge of the scientific method, and so on. These are 3 common mistakes to avoid on AP exams. Test format The former AP Physics B exam involved 70 multiple-choice questions over a 90-minute time period and six or seven free response questions over a 90-minute time period. Now, the AP Physics 1 exam will have 50 multiple-choice questions over 90 minutes and five free response questions over 90 minutes. One free response question will deal with experimental design, another will deal with qualitative/quantitative translation, and the remaining three will take the style of short answer. The AP Physics 2 exam will follow the same format, but will limit the number of free response questions to four, cutting out the third short answer question. While these changes may seem significant, they will ultimately leave students better prepared for college physics. Working with AP Physics B tutors can be of great help in this process as well. By spreading the acquisition of knowledge over two years, students will be more knowledgeable, prepared, and confident in their abilities to perform advanced physics.

wave

wave Wave It will be amazing to know that there is not a single moment in our daily life when we do not encounter a wave. Let it be in the form of light waves, sound waves, water waves, radio waves etc, waves are always a part of our life. Considering a slinky as an example after we stretch a slinky from end to end, it naturally comes back to its original equilibrium rest position. So here we can notice that a wave passes through the slinky as a disturbance is generated due to our stretching it. This disturbance passes through the slinky and after some time gets it back to its original state of rest. What is a Wave? A wave is usually described as the disturbance that passes through a medium from one location to another location. A wave medium is a substance or material that transports the wave from one location to another location. Here it is to be noted that the medium simply carries the wave from one point to different locations, but the medium does not play any role in creating or generating a wave. For instance, we can notice the waves in an ocean. The medium through which the water waves travel in an ocean is the ocean water. For a sound wave, the medium through which the sound wave travels is the air present in the room. A single disturbance that passes through a medium from one point to another point is known as the Pulse. However, if the disturbance is continuously repeated causing it to become a periodic disturbance that moves from one location to another location, then that disturbance is described as the Wave. Interaction of Particles in a Wave: Medium is a collection of particles that have the ability to interact with each other. Due to the interactions between a particle and its adjacent particle, the disturbance travels through the medium. The constant push or pull between the neighboring particles allows the disturbance to spread across the medium. However, it is to be noted that the individual particles of the medium are only temporarily displaced from their original rest position. Eventually every particle carrying the wave return to their original position. Therefore, we can say that a wave transports energy from one location to another location but it does not transport matter. Due to this reason we can see that in an ocean waves are seen to move through the water, however the water always returns back to its rest position. Only the energy is being transported through the medium, but the water molecules are not transported. Therefore, a wave can also be described as the disturbance that travels through a medium (with the help of particle interaction) carrying energy from the source to another location, without transporting matter. Types of Waves: Waves can be classified into 2 types based on the ability to transmit their energy even in vacuum or only through a medium. i) Mechanical Waves ii) Electromagnetic Waves 1)Mechanical Waves: The waves that travel through a medium that is a solid or a liquid or a gas (at a speed which depends on the elastic properties of the medium) are known as the Mechanical waves. Based on the direction of the individual particles of the medium to the direction of the travelling wave, these mechanical waves are commonly classified into 2 types. a) Transverse Waves b) Longitudinal Waves a)Transverse Waves: The wave in which the particles of the medium move in a direction that is perpendicular to the direction in which the wave travels, is known as the Transverse wave. For instance, if the energy of the wave is transported from left to right, then the individual particles in the medium are displaced upwards and downwards in a transverse wave. Transverse waves are always characterized by the property that the particle motion is perpendicular to the wave motion. In order for the particles in a transverse wave to move perpendicular to the wave direction, they must be able to strongly exert a pull on its neighboring particle. Due to this reason, transverse waves require a rigid medium to pass through and hence these waves can usually pass through solids only. b)Longitudinal Waves: The wave in which the particles of the medium move in a direction that is parallel to the direction in which the wave moves, is known as the longitudinal wave. For instance, if the energy is transported from left to right, then the individual particles of the medium will be displaced leftwards and rightwards in a longitudinal wave. Longitudinal waves are always characterized by the property that the particle motion is parallel to the wave motion. Unlike transverse waves, longitudinal waves can pass through solids, liquids and gases. A sound wave passing through air from the speakers mouth to the listeners ear is an example of a longitudinal wave. Seismologists have discovered that during an earthquake, the waves produced were both transverse and longitudinal waves as they could pass through the solid structures of the Earth, however only longitudinal waves were able to pass through the core of the Earth. Geologists therefore believe that the core of the Earth contains a liquid (mostly molten iron). Surface Waves: These are another kind of waves that are can be either elastic or seismic waves (seismic waves are the waves generated during an earthquake or an explosion). The motion of these particles decreases as we step away from the surface. In seismology (study of earthquakes), there are different types of surface waves and they are usually either Love waves (they have transverse motion) or Rayleigh waves (they have both transverse and longitudinal motion). The waves on the surface of the oceans and seas are also examples of surface waves. 2) Electromagnetic waves: The waves that are capable of transmitting the energy even through vacuum (or empty space) are known as the Electromagnetic waves. This implies that these waves do not need a medium to transport energy from one location to another location. These waves are produced due to the oscillation of the electric and magnetic fields. It is interesting to note that we use electromagnetic waves everywhere in our daily life. From the point of listening to a radio, watching television, or cooking lunch in a microwave oven, we are using electromagnetic waves every time. The radio waves, microwaves, ultra-violet rays, X-rays etc are all examples of Electromagnetic waves. We need electromagnetic waves for our very existence as the life-giving beautiful light rays emanating from the Sun that travel all through the outer space and reach Earth are also electromagnetic waves. Crests and Troughs of a Transverse Wave: In a transverse wave, since the particle motion is perpendicular to the wave motion, we can observe the maximum displacement reached by the particles from their original position. When a string initially at rest is disturbed, then we can observe that the particles of the string vibrate upwards and downwards, reaching maximum upward/downward displacement. In a medium, the crest of a wave is the point that exhibits maximum amount of upward or positive displacement from the original rest or equilibrium position. In a medium, the trough of a wave is the point that exhibits maximum amount of downward or negative displacement from the original rest or equilibrium position. Compressions and Rarefaction of a Longitudinal Wave: In a longitudinal wave, since the particle motion is parallel to the wave motion, we can observe that there are certain regions where the particles are pressed together and other regions where the particles are spread apart. The region where the particles are pressed together in a small amount of space during the longitudinal wave motion is known as the Compression. This region is also said to have the maximum density as the particles are pressed tightly when the longitudinal wave passes through it. The region where the particles are spread apart in a small amount of space during the longitudinal wave motion is known as the Rarefaction. This region is said to have the minimum density as the particles are spread apart when the longitudinal wave passes through it. During the longitudinal wave motion, there are alternating compressions and rarefactions generated along the wave, as shown in the figure above. Properties of a Wave: A wave motion has various properties and some of the terms that describe a wave are amplitude, wavelength, frequency, time period, etc. Amplitude: The maximum amount of displacement of a particle from its rest position during a wave motion is known as the amplitude. Amplitude is measured as the distance from the rest position to a crest or the distance from the rest position to the trough. Wavelength: In a transverse wave, the wavelength is the distance between crest to its consecutive crest or from trough to its consecutive trough. In a longitudinal wave, wavelength can be referred to as the distance between consecutive compressions or consecutive rarefactions. Since a wave repeats itself periodically over time and space, hence a wave is known to have a repeating pattern. Therefore, the wavelength can also be simply measured as the distance from a point on a wave to the corresponding point on the waves next cycle. Frequency: It is the measure of the number of waves that pass through a fixed place in a given interval of time. This implies that in a given amount of time, the number of complete cycles of wave that passes through a medium at a certain point is known as the Frequency. Usually the units of frequency are given as cycles/second, vibrations/second, waves/second. However, the standard unit commonly used for frequency is Hertz denoted by the symbol Hz. 1 Hertz is equal to 1 cycle/second. Examples: If a coil of a slinky makes 5 vibrations per second, then its frequency is 5Hz. If a coil makes 12 cycles per 3seconds, then its frequency = 12cycles/3seconds = 4Hz. iv) Time Period: During the wave motion, the time taken by a particle in the medium to make one complete vibrational cycle is known as the period or the time period of a wave. Example: The period of orbit of the Earth around the Sun is approximately 365 days. Period and Frequency are related by the relationship: Frequency = 1/Period This equation can also be written as Period = 1/Frequency Example: A period of 8seconds corresponds to what frequency? Given: Period = 8 seconds Frequency = 1/8 = 0.125Hz Wave Equation: The wave equation is a mathematical equation which describes the relationship between the speed of a wave, the wave frequency and its wavelength. The Wave Equation: Speed = Frequency * Wavelength == v = f * Here, v = speed of the wave f = frequency of the wave = wavelength of the wave Example: If the speed of a wave travelling in a medium is 600m/s, then what is the wavelength of the wave if 1800 waves pass through a certain point in a minute? Given: speed of the wave, v = 600m/s Number of waves passing through a point in a minute = 2000 This implies, that the frequency of the wave = 2000 waves/minute Hence, waves per second = 1800 waves/minute * 1minute/60seconds = 30 waves/second = 30Hz Speed = Frequency * Wavelength == wavelength, = speed/frequency Hence wavelength, = 600/30 = 20m Therefore the wavelength of the given wave is 20m. Example: What is the frequency of the light whose wavelength is 600m? Given: wavelength, = 600m Speed of light, v = 3.0 * 108m/s (speed of light is a constant value) Speed = Frequency * Wavelength == frequency, f = speed/wavelength Hence frequency, f = 3.0 * 108/600 = 5.0 * 105 Hz Therefore the frequency here is 5.0 * 105 Hz Electromagnetic spectrum: The distribution of electromagnetic radiation according to the energy, depending on factors such as wavelength and frequency is known as the Electromagnetic spectrum. All the waves including the light rays that our eyes can see, the microwaves, radio waves, X-rays, gamma rays etc. all belong to the electromagnetic spectrum. The visible light of the electromagnetic spectrum consists of the colors that we usually see in the rainbow.

Happy Pi Day! Enjoy Heart Math Tutorings p Chart!

Happy Pi Day! Enjoy Heart Math Tutorings p Chart! Happy Pi Day! 3 Ways To Find p Happy Pi Day! 3 Ways To Find p March 13, 2015 For years, math fans around the world have celebrated Pi Day on March 14. You can find videos, songs and T-shirts to mark the occasion. Many also count it as a day to eat lots of pie. Why is the number Pi, denoted by the Greek letter p and pronounced “pie,” worthy of so much praise? Pi   is one of the most common constants in all of mathematics. It is the ratio of the circumference of a circle to its diameter or approximately 3.1415926. This year, the day is even more special since it’s 3-14-15. According to PiDay.org, Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits. Here are some ways to find p if you don’t have a pie or calculator: