Grocery List - Common Geometric Series Examples

Grocery List - Common Geometric Series ExamplesA great example of a 'well-known' group of numbers is the geometric series, which is also known as the infinite series. To put it briefly, this series shows the relationship between certain specific numbers and other specific numbers. For example, for any particular number x and any given number a the geometric series has an upper bound: The sum of the two numbers is itself the same number that were first multiplied by the second number, and so on.If you are not aware of what the geometric series is, here is a definition: The geometric series of numbers is the collection of all the number patterns. For example, the first number in the geometric series is the number that would be the first prime number. It is also called the real line of prime numbers.A second example is the circle. A circle is a particularly intriguing example because it shows the relationship between a number, known as a radius, and another number, known as a circumfere nce. The shape of a circle is formed by the reciprocal of the diameter, and this reciprocal is called the diameter. So, if you multiply out the second number (the circumference) by the diameter, you will get the original circle that was formed by this relationship.So far we have looked at the geometric series and the circle, but there are many other examples of the geometric series, which makes it a good example of the series. The number of geometric series that exist is therefore enormous. In fact, the largest geometric series is the Harmonic series.Another geometric series is the Fibonacci series, which shows the sequence of numbers in a line, where the order of the lines does not matter. This series is very similar to the classic algorithm for making any numbers out of a set.The harmonic series, or the 'harmonic family,' is a group of natural numbers that form a well-known family of numbers. The names that are associated with this series are important. These names are all related to sound, and many times the numbers are called the Harmonic keys or the Harmonic tones.The numbers are the four-tone name for the tones that are created when you rub the fingernail of your left hand with the right number. When you hear a harmonic tone, you don't recognize it as such because it doesn't seem like music.An interesting note about the simple geometric series is that it shows the relationship between a specific number and its next higher number. This gives the collection of all numbers its upper bound.

What Does it Mean if a Singer is Classically Trained

What Does it Mean if a Singer is Classically Trained Suzy S. What do you think of when you see the words classical singing? Perhaps opera comes to mind? Here, vocal instructor  Molly R.  explains  what being classically trained really means and how it can be applied to any genre of singing Suppose you’re a rock or pop singer looking for a voice teacher   while some teachers may stress that theyre all about rocking or teaching a certain vocal method in their bios, many of them mention being classically trained.  With that said, what does it mean to be a classically-trained singer? Will it help you achieve the sound you want? Im a classically-trained singer. I received my degree in vocal performance after studying a healthy diet of art songs, oratorios, and opera arias. Now that Im a voice teacher, I find myself counting the number of my classical singing students on just one hand! The rest of my students sing commercial music styles metal, pop, RB, and others. The bottom line is that in order to sing healthfully, you should  use the classical technique. Although, this is a different ballgame from  classical STYLE. Classical Technique vs. Classical Style Classical technique is a lot less complicated than it sounds. To learn this technique, a few things must happen. First, we must breathe and support very low on our bodies this is coupled with proper balance and posture. Next, we must sing clear, round vowels with an open throat. These are the principles I was most focused on as a young classical singer,  tackling songs from the greats like Puccini, Schubert, Barber, and more.  Any singing style or genre could surely benefit from these practices, right? Thats exactly  right! Classical style comes from artistic choices you make when you sing. For example, you may choose to be a little breathy in a  lower register for a sultry jazz tune, or you may make the sound sassier, brighter, and more “in your face” (literally!) if you’re belting a Broadway song. In rock, we don’t sing the words out nearly as full as we do in an aria it’s much more conversational. (Editors Note: For more on different styles, check out our Ultimate Guide to Singing Styles and Genres!) Use a  Healthy Mix Putting together the classical technique with your preferred style is where it’s at, as far as I am concerned! A healthy singing technique and a rockin style are  the best of both worlds. Don’t assume that all classically-trained teachers won’t welcome other genres, because many of us do! In fact, rock was my first love. Sharing what I know from the classical world has helped my rocker students feel a lot more confident in their abilities. Theyve mentioned an increase in stamina after long rehearsals and gigs because they breathe and support just like the opera singers do (and those singers have a lot of singing to do talk about vocal athletes!). They realize they need not scream or push to  produce a lot of good sound. Classical vocal training also stresses the importance of a good warm-up and being mindful of proper vocal hygiene. Although, I wouldn’t suggest sticking to a regimen of solely vocal exercises in lessons. Do spend time doing exercises that cover a variety of vocal skills, including flexibility, diction, breath control, and dynamics. All of these things can and should be applied to your songs, whether theyre classical Mozart arias or metal Judas Priest covers! Apply it to Any Genre I hope  these facts will ease your fears about your classically-trained teacher “turning you into an opera singer. Good teachers are respectful of  your preferred styles of music and should  never consider turning you into someone youre not. Quality voice teachers want the best for all of their students and want to ensure many years of healthy singing. The classical technique can do that for you, regardless of the styles you choose to sing. As an  example of a legendary rock star who was classically trained, check out  Pat Benatar. She’s still rockin’ and sounding great in her sixties because she was taught solid classical technique on Brahms art songs long before she was a Heartbreaker! Classically-Trained Pop and Rock Singers A few pop and rock singers have studied the classical technique, believe it or not! In addition to Pat Benatar, Madonna (after she made it big) worked with a teacher on the “24 Italian Songs” to prepare for her role in “Evita. Lady Gaga worked on classical technique every day for six  months to prepare for her big “Sound of Music” medley at the Oscars. Contrary to popular belief, metal singer extraordinaire Ronnie James Dio did NOT take vocal lessons, but he did say he was greatly influenced by the singing style of tenor and  great singer Mario Lanza! I can safely say that my classical training has improved my singing across every genre Ive attempted. Its the perfect starting point for anyone wanting to learn a healthy and correct singing technique. Apply what youve learned from classical training to any genre you want and youll be unstoppable! Happy singing! Post Author:  Molly R. 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

Algebra Trigonometry

Algebra Trigonometry Trigonometry is the branch of algebra II. Algebra trigonometry deals with all of the trigonometric ratios and these trigonometric ratios are very much useful when you are dealing with the triangles and the unit circles. There are three main trigonometric ratios which exist in trigonometry and they are sin, cos and tan. The other three ratios are the reciprocal of the main ratios which are csc, sec and cot. They are outlined below: - Cot x = 1/ tanx Sec x = 1/cos x Csc x = 1/ sinx There are few basic angle values that is needed to be remembered, they are 0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees. We have various trigonometric identities that are required to solve many of the trigonometric equations. We can see many examples of trigonometry in our day to day life. Following are the few examples which are based on the algebra trigonometry. Example 1: Find the value of tan 225 degrees. Solution : Given: - tan 225 degrees = tan (180 + 45) degrees = tan 45 degrees = 1 Hence the value of tan 225 degrees is 1. Example: Prove that (sinx + cosx)^2 = 1 + sin 2x Solution : - Given the left hand side as (sinx + cosx)^2 After expanding, we get sin^2 x + cos^2 x + 2sinx cos x = 1 + 2 sinx cosx [ sin^2 x + cos ^2 x = 1] = 1 + sin 2x [sin 2x = 2 sin x cos x]

My Experience at Columbia University

My Experience at Columbia University The tutors behind Varsity Tutors are not just here to teachtheyre sharing their college experiences as well. Benjamin is a Brooklyn tutor and 2015 graduate of Columbia University. He holds a Bachelors degree in Linguistics and tutors several subjects, including algebra tutoring, computer science tutoring, and writing tutoring. Check out what Benjamin had to say about his time at Columbia University: Describe the campus setting and transportation options. Benjamin: Columbia University has a decidedly urban campusafter all, its extended name is Columbia University in the City of New York. Public transit in Manhattan is fantastic and inexpensive, and with it, you should be able to get anywhere you need to without a car or a bike (although we do have a free bike-share program). The school has intra- and inter-campus shuttles, but the campus is so compact and walkable that I never needed to use any of them. Columbia Universitys campus and the surrounding neighborhood (Morningside Heights) always felt safe to me. Both are well lit, and students are out at all hours of the day and night, not to mention that we have a lot of late-night grocery stores and pizza places. Dorms are particularly secure, since only current students have access to them. How available are the professors, academic advisers, and teaching assistants at Columbia University? Benjamin: Professors, advisers, and teaching assistants are generally very accessible. With professors, it is important to proactively reach out if you are having a problem (or if you just want to chat), which is why it is always a good idea to go to office hours. The vast majority of them want to help you if they can, and they love it when students show an interest in what they are teaching outside of just showing up to class. How would you describe the dorm liferooms, dining options, location, socialization opportunities with other students? Benjamin: The dorms themselves vary a lot from year to year and building to building. The newer ones tend to have a lot of great amenities, such as central air conditioning, island kitchens, and big common spaces. The older dorms sometimes have these features if they have been renovated recently, and they all have a lot of character (e.g. high ceilings, ornate fireplaces, wood floors, etc.). In general, your housing options improve every year, so you will likely end up with something great for your junior and/or senior years. All the dorms are located close to classes and dining halls because the campus is so compact, and you have a good chance of having a fantastic view of the New York skyline and/or the Hudson River in almost all of the buildings. One of the biggest advantages of having such a compact and walkable campus is that you are never far from your friends (especially since the vast majority of undergraduates live on campus all four years). It is generally easy to make friends in your dorm if you make an effort, particularly as a freshman. In fact, most of my best friends lived on my freshman floor. Dining hall food in general can get very tiresome, but Columbia Universitys is pretty good as far as they goit is relatively fresh and interesting, and there are four different locations at which you can use your meal swipes. Which majors/programs are best represented and supported at Columbia University? Benjamin: Columbia Universitys American studies department has a number of superstar professors, and the computer science department is growing quickly. The political science and economics departments are also large and well funded. I studied linguistics because I had a longstanding interest in English grammar and foreign languages throughout high school. There is no linguistics department at Columbia University, so I had to make my own major. The upside of this was that I became close friends with a lot of the other linguistics majors, got to know my professors really well, and had a lot of flexibility in which courses I could take. The downside was that most linguistics classes were offered only once every two years (as opposed to every semester), and there was very little institutional/monetary support for thesis research, summer programs, etc. How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Benjamin: Its very easy to make friends! Doing one of the pre-orientation programsCOOP or CUEis a good way to meet people right off the bat, but you will have many opportunities to make friends otherwise. I made a lot of friends in my dorm, and through extracurricular activities and my major. Greek life has a growing presence on campus; it can be a big part of your life if you want to be, and if you do not, you will barely even know it exists. How helpful is the Career Center and other student support services? Benjamin: Columbia Universitys career center is accessible and helpful, particularly if you are interested in jobs in the non-profit, legal, and finance/consulting sectors. They arrange on-campus interviews for practically every large company, non-profit, and government agency you can think of, from IBM and Goldman Sachs to the FBI. How are the various study areas such as libraries, the student union, and dorm lounges at Columbia University? Benjamin: Space is generally somewhat limited at Columbia University given its location. However, the main library is open 24/7, and you can almost always find a seat in a library if you want one. There are a ton of different libraries and other study spaces, and the university is in the midst of a huge expansion that should free up some space on the main undergraduate campus. The Columbia University student center is not as user-friendly as the Barnard College student center across the street (the Diana Center), but you will have full access to that one as a Columbia University student. Describe the surrounding town. Benjamin: It is New York, which is pretty much all you need to say. You will never run out of things to do. Restaurants near Columbia University tend to be a little mediocre and overpriced, but there are a few gems. You can also find great food if you go just a few blocks outside of the neighborhood in any direction. I did not leave the neighborhood much my freshman year because everything you need to survive is within a few blocks of campus, but I would recommend getting out into the city as much as you possibly can. How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Benjamin: Columbia University is a medium-sized school, and there are between 1,000 and 1,500 students in each undergraduate class. Class sizes vary wildly depending on your majorI have had courses with over 200 students, and some with only three or four. The bigger classes are almost always large lectures, so it does not really matter how many students are in them (especially if you have a separate section). I always found teaching assistants and professorseven in the bigger classesto be responsive and accessible. Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one you regret the most. Benjamin: During the second semester of my freshman year, one of my professors invited our whole class over to his beautiful Riverside Drive apartment for dessert, and talked to us about his work at CERN on the Large Hadron Collider. It was inspiring to hear an accomplished professor talk about such important work, and to see that he took an interest in us even as a group of bewildered freshmen (not to mention that there was a lot of chocolate). Check out Benjamins tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

Online Algebra Tutor Knows The Mantra For Top Scores Via Unique Solutions

Online Algebra Tutor Knows The Mantra For Top Scores Via Unique Solutions Learning Algebra is the toughest thing for many college students due to the mental traumas they cherish from their childhood about the subject. Many kids get alarmed on seeing letters in the place of numbers with imagined ideas about their applications in the initial stage that they fail miserably when they come to the point of solving an Algebra equation or word problem at an advanced level. ‘X’ and ‘y’ are very common letters in English alphabet but when they are incorporated in Algebra sums, they take a special place in the form of unknown values. It is only right guidance that can lead to success stories in Algebra classes which mantra is known to an online Algebra tutor. How online Algebra tutor debunks myths about Algebra learning From the early start of Math classes, kids have been given the impression that Math is the territory of the gifted brains and it can be accomplished by a selected few who have that so called Math brain. This popular myth about Math expands when students start doing Algebra. Algebra is considered as the exclusive realm of those who possess key skills in numeric with an ability to analyze problems from a logical angle. How To Sort And Solve Elapsed Time Story Problems http://t.co/j3zGC5Q6m8 #algebra #backtoschool #homeschool pic.twitter.com/dzdb9M73Rl â€" Tutor Pace (@TutorPace) August 4, 2015 Even those who were found to be stupendously excellent in their numeric calculations like addition, subtraction and multiplication at primary level go down in their Algebra grades at middle and high school because they are troubled by the myth about Algebra variables, unknown values and the ways they are incorporated in Algebra sums. When they reach college level, most of them try to do away with Algebra due to their fear cherished over years. All Algebra myths should be busted only with the help of a virtual Algebra tutor who knows how to unknot the tricky mental dilemmas of students with his psychological diagnosis and counseling and thus takes steps to lead students in the right path in learning Algebra. How to Solve #Algebra Word Problems in 5 Steps http://t.co/kg6CqctO6O #backtoschool #homeschooling pic.twitter.com/wApx3S0D5R â€" Tutor Pace (@TutorPace) August 4, 2015 One on one personalized classrooms with tech support helps tutors unravel the fact that Algebra is simple to do. Even topics like Linear Functions are easy to do if college grade students assess their skills in the subject with confidence and head for difficult areas in the subject with boosted morale. Algebra homework help online- exact approach for top notch scores When learning Algebra itself is riddling, Algebra homework is certain to puzzle minds and put them in dilemmas that bring no way out. Last minute hiccups in Solving Inequalities or Solving Absolute Value Equations are tremendously tricky during homework hours. Taking Algebra homework help online from subject experts will lead them in the right path with unique methods. Online tutors in Algebra for college Grade are able to thwart any challenge posed to them in the homework topics of advanced learners in the subject and render solutions in the background of white board teaching through step by step analysis. They know how to tap the right skills from students with proper methods and help them do their homework in Algebra with custom made techniques. College Algebra assignment help gears up your grades towards the helm of success When learning Algebra and doing homework is this much a struggle for learners, it is but natural for them to get boggled by assignments in Algebra topics, that too, when they have time constraints to add to the fuel. Algebra assignment help from virtual tutoring quarters can make things easy for them with correct answers and easy solutions. It is only a matter of a few minutes as to when you approach them and what help you demand from them. The subject experts take care of the rest of the matter with their 24/7 services and get you your completed assignments for enhanced scores in Algebra assignments. How To Study For A #Math Test Without Losing Your Mind http://t.co/eZ7iCRSVvX pic.twitter.com/gtYneR2Bc2 â€" Tutor Pace (@TutorPace) September 16, 2015 Conclusion Thus learning Algebra is a matter of smart help via online tutoring resources enabling you to get hold of successful scores in the subject at all levels of learning including college grade.

Time Management Strategies for the MCAT

Time Management Strategies for the MCAT The MCAT is typically considered a fast-paced exam. Certain sections can seem harder to finish within the allotted time than others, but all the portions of the test require students to employ time management strategies in order to succeed. The Biological Sciences and Physical Sciences sections each have 52 questions that must be completed in 70 minutes, while Verbal Reasoning consists of 40 questions in a 60-minute window. Below are several key time management strategies to exercise while sitting for the exam to ensure that you do not exceed the time limit and forego points. 1. Monitor the time This simple technique may seem intuitive, but on exam day, many test-takers forget to note the time. Wear a reliable watch, and locate the clock in your exam room as soon as you sit down. Be certain you understand the pacing of the section you are working on. You have approximately one minute and twenty seconds for each question on the Physical Sciences and Biological Sciences portions. For Verbal Reasoning, you will have one minute and thirty seconds for each problem. Do not become obsessive about the time, but establish landmarks within each section to ensure you are on schedule. For example, when you have 35 minutes remaining in Physical Sciences (the half-way mark), you should be finished with at least 26 (half) of the questions. Here is some great information on how to manage your time during MCAT prepas well. 2. Move on from difficult questions Utilizing this time management strategy can seem difficult at first, because the majority of students hope to answer every single question correctly. However, recognizing your limits and moving on from a very difficult question that you cannot seem to grasp will ultimately earn you more points. By moving on, you allow yourself to answer easier questions in the section. If you still have time remaining after you have completed the remaining problems, return to those you initially omitted. These are5 strategies for MCAT practice teststhat you may finduseful. 3. Read the question line before the stem Many question stems on the MCAT consist of several lines of text. In order to quickly understand what information you must know, read the last line of the stem before the beginning. This will focus your skimming of the rest of the stem. Many times, it is not even necessary to read the remainder because you will be able to answer the question immediately. However, you should always skim the stem to ensure you understand the full problem. 4. Practice beforehand Though this is not a time management strategy you can rely upon come test day, it is crucial to complete timed practice sections and full exams to gain familiarity with the pacing of the MCAT. Practicing well in advance will also aid you in understanding the types of questions you will be asked on test day. Moreover, you can practice applying the above strategies during your sample exams to further build your time management skills. An MCAT tutorcan even guide you through each individual step. Timing is a major component of success on the MCAT. Many students struggle to earn an extra point or two simply because they do not reach the questions at the end of a section. Pacing yourself by watching the clock, moving on from difficult questions, reading the question line of the stem first, and completing practice examsbefore test day are all important strategies to help you beat the clock.

Approaches to Studying in College

Approaches to Studying in College You will often find homework, projects, and exams to be very different in the college world than they were in the high school world. This doesnt always mean harder, just different although yes, they will often be significantly harder. But the major differences that make these assignments so much more difficult include the tighter time constraints, drastic changes in environment, and lengthier tasks in question. All of this will be so brand new to you, nothing like the days when you came home at 3 p.m. to sit and work on worksheets at your kitchen table. With all the surrounding distractions, identifying a successful study atmosphere on a college campus can initially seem like a lost cause, so here are some paths you can take that will guide you in a helpful direction. Study Groups: Never, ever, ever underestimate the power of a study group. Even if youre one of those people who prefers to work independently and thinks groups slow productivity down, youd be surprised at how many more answers you can come up with just by working with other people. Whether it be in a lecture or a small discussion class, if youre having trouble understanding a concept, odds are other students are too. By coming together and literally talking through it, you have multiple minds working, reading, and brainstorming aloud. Since youve all been through the same class sessions with the same professor and are therefore on the same page with this particular curriculum, you automatically form the best team to nail down the answers to your questions. One student may have missed a bullet point that another student picked up and some students may grasp a concept where others have no idea where to begin. These groups are the ultimate way to put the pieces of the puzzle together an d find the solutions upon you when you least expect it. It really does roll back to the old clich, two heads are better than one. Libraries, Coffee Houses, and the Student Union: These are the quintessential college spots you always hear about. No matter who you are, these will be prominent parts of your college experience just by physically living on campus you cant help but find yourself in one of these buildings from time to time. Some, actually many, students go particularly out of their way to head to these places over and over again. Why? Because they make great study spots. Caffeine is readily available, you are never alone, and most importantly, they are open late. The latter cant always be applied to the coffee shops, but certainly for the libraries and most likely the Student Union. These are terrific alternatives to your noisy dorm or drafty apartment and the way their atmospheres cater to students leaves you never feeling out of place. These are environments where its acceptable to show up in sweatpants and set up camp with your laptop open, Red Bull by your side, and midnight snack in hand. This a pproach to studying culminates a key part of the collegiate experience. Professors and Office Hours: The idea of office hours is usually blown off by students right when they read it on the syllabus or first hear the professor speak of them. The reason for this is that office hours are usually held at random times in the afternoon when students either have another class or just dont want to take the time to attend. If you want to understand class material better and none of your efforts independently or with fellow students has worked, then going directly to the source should be your next step. Your professor is required to hold office hours, a time when he or she is guaranteed to be in their office and ready to answer any questions you may have, so why wouldnt you take advantage of it? If you have another commitment at this time, such as class, then email your professor to set up a different time to meet and they will almost always accommodate you. If you arent busy during this time, you must overcome the laziness and get yourself over there. Talking to your professor one on one and being able to ask follow-up questions you might have been too nervous to ask in class will do wonders for you comprehension of a lesson plan. This is the ultimate way to get a real handle on things and receive actual insider advice on how to triumph the academic challenges in front of you. It is the most personalized learning you will get. Plus, showing up in the first place will ensure you stand out positively in the professors mind for outwardly showing effort a perk that may help you when grading time comes around. The common element in all of these studying approaches is self-discipline. In college, no one is there to make sure you get all this work done on time nor are they there to wake you up and get you to these classrooms when you need to be in them. Succeeding in college relies on your ability to take full responsibility and control of what you do. Put yourself in the right places with the right surroundings and you will study well.