Composite Function

Composite Function Composite Functions is the application of one function to the results of another function. Composition functions will not be commutative. This commutatively is attained only by particular functions and in special circumstances. Derivatives of compositions that involve differentiable functions can be found using the chain rule. Suppose result of 1st function f (x) is applied into the 2nd function g (x), this composite function is written as g(f(x)) or (g?f) (x). Composite functions are combination of 2 or more functions. We can say that it is a function that is expressed in terms of one or more functions. It may be noted that, (f?g)(x) (g?f)(x). Example 1: Simplify by Composite function f(x) = 2x + 3 Solution: First we will apply f and then apply f to that result = (f?f)(x) = f(f(x)) = (f ? f) (x) = 2 (2x + 3) + 3 = 4x + 9 = f ( f (x) ) = f (2x + 3) = 2 (2x + 3) + 3 = 4x + 9 Example 2: If f(x) = 2x and g(x) = 2^x, then what is (f ? g) (x)? Solution: The given problem we have = F(x) = 2x and g (x) = 2^x = When we do composite function (f ? g) (x) we get = (f ? g) (x) = f ( g ( x ) ) = f (2^x) = And f (2^x) = 2 . 2^x = 2^ (x + 1) = Answer: (f ? g) (x) = 2^ (x + 1)

How To Solve Polynomial Equations Online Tutoring

How To Solve Polynomial Equations Online Tutoring When P (x) = 0 (1) Where P (x) is a polynomial expression then the equation (1) is known as a polynomial equation with variable x of highest power n where n = 0, 1, 2, 3, , n. Examples of polynomial expression: - x^2 + 8 x + 16 = 0 (x 1) ( x^3 6 x^2 + 9 x) = 0 x^2 x = 0 x^5 + 6 x^4 + 4 x^2 4 x + 8 = 0 Question 1: - Solve the following polynomial equation and find the value of x. Solution: - i) Factorize the L.H.S. polynomial expression X^2 + 8 x + 16 = x^2 + 2 * x * 4 + (4)^2 = (x + 4) ^2 ii) Now write the L.H.S. expression equal to zero then solve and find the value of x. (x + 4) ^2 = 0 X + 4 = 0 X = - 4 Therefore x = - 4 Question 2: - If (x 1) ( x^3 6 x^2 + 9 x) = 0, find x. Solution: - (x 1) (x^3 6 x^2 + 9 x) = 0 (x 1) {x (x ^2 6 x + 9)} = 0 X (x 1) (x ^2 2 * x * 3 + 3 ^2) = 0 X (x 1) (x ^2 3) ^2 = 0 Therefore x = 0 X 1 = 0, hence x = 1 (x ^2 3) ^2 = 0, or, x 3 = 0, hence x = 3 Answer: - Therefore x = 0, 1, 3, 3

Learning More About AutoCAD software

Learning More About AutoCAD software A Beginners Guide to AutoCAD Software   ChaptersHow to Effectively Set Up an AutoCAD AccountBasic AutoCAD ToolsWhere to Find AutoCAD Software  â€œCompanies in every industry need to assume that a software revolution is coming.” -Marc Andreessen?  We are currently living in an age of software.  Therefore, the software revolution is not coming; instead, it has arrived.  Software such as Dropbox, Microsoft Office, Google Drive, Skype for Business, and Slack are among the most popular used in modern-day offices.?  In today’s article,  Superprof  is focusing on the?revolutionary computer-aided design software known as AutoCAD. We will discuss how to effectively?set up an AutoCAD account?to use the software,?essential AutoCAD tools?that need to be mastered in the beginning, and?where to find AutoCAD software.    Many drafters in architecture, graphic design, and engineering  fields  use software such as AutoCAD to create 2D or 3D blueprints and sketches for buildings, engineering parts, or computer  chips.?  The various step s required to successfully set-up an AutoCAD account and choose a correct subscription is featured in this link.Basic AutoCAD ToolsWith the AutoCAD software, older methods of drafting or drawing have become easier. (Source: Unsplash)It is not a secret that the AutoCAD software is challenging to  learn.  However,  many experts, developers, and long-time users have provided helpful tips and tricks for beginners on websites, on blogs, and  in  books.  Many experienced professionals suggest that beginners should  work hard to assimilate the functions of  AutoCAD  by spending a whole day  experimenting  with the software  before starting an intense work assignment.?  Remember, practice makes perfect!?  Autodesk  has  developed a guide  called  Autodesk’s Hitchhiker’s Guide to the AutoCAD Basics  to  help  beginners  learn?AutoCAD’s tools.?  In today’s article,  Superprof  will also discuss some?essential tools  to  master  drawing and modifying in  AutoCAD.  Basic Drawing Tools   Drawing is an essential aspect of the AutoCAD software?for drafters and designers. The following are some of the most basic drawing tools along with their definitions:  Point:?used by drafters to create a symbol on the drawing that is tied to another specific spot or location on the draft. In the AutoCAD software, points are defined by the coordinates (x,y,z).  Polygon:?multisided shapes such as pentagons or hexagons can be frequently used on the AutoCAD software by all users. To create the desired polygon wanted by the user the software asks the user number of sides and final shape. “Closed polygons” can be edited using the command PEDIT.  Spline:?a spline is a curve that is defined by specific mathematical equations. The user can decide how many  verticles  they wish and  AutoCAD  will release a spline curve that incorporates  all of  these points. The program shortcut to create a spline is “spl.”  Hatch:?commonly known as space fillers, they can be made of a solid  colour  or a more specific pattern that was previously designed by the user.  Other essential drawing tools include  the  polyline, arc, circle, ellipse, and text  tools.  For visual learners wanting to become more familiar with  the  drawing tools,  Youtube  also has several  tutorials  to help  first-time users through the beginning stages.  Basic Modifying Tools  The following are the necessary modifying tools to learn from the get-go:  Erase:?everyone needs to erase mistakes once and awhile. Therefore, the erase tool saves the day for many drafters. Users select the item they wish to eliminate and press the erase tool.  Copy:?to move a selected object from one place to another, the copy tool is used. To successfully copy an item, the user selects two points, and the object is copied using two positions at base point. The shortcut for this modifying tool is “cp/co.”  Array:?there are two types of arrays used: polar and grid. To make a polar grid the AutoCAD system asks the user how many copies they wish to include in their draft. To create a  grid  array the user is requested by the software how many columns and rows are needed to complete the task at hand.    Like  the  drawing tools, there are many Youtube  tutorials that can  help beginners grasp?the concepts of using modifying tools.  Where to Find AutoCAD Software  Where to buy AutoCAD software at a reasonable price?It is important to mention that AutoCAD software can be  downloaded on any PC or Mac from the Autodesk site. The following points feature official websites to purchase AutoCAD:Autodesk  (UK):?Click here to purchase AutoCAD.    Autodesk (Australia):  Click here to purchase AutoCAD.At  Superprof  we make it our goal to help people grasp essential information from a variety of topics; therefore, we hope that?our article about AutoCAD?has personally helped you better understand this software system, how to create an Autodesk account, and where to purchase and download AutoCAD.  Experienced users of  AutoCAD  design software?know the benefits and if you are on edge, don’t hesitate, do it; you won’t regret it after  realising  how efficiently this CAD software works!    Also, it would be extremely wise to consider hiring a private Superprof tutor who is familiar with the AutoCAD functions.

Why Learn Dutch Here Are 10 Great Reasons

Why Learn Dutch Here Are 10 Great Reasons 10 Great Reasons to Learn Dutch ChaptersThe Dutch Language has an Amusing VocabularyLearning Dutch is Relatively EasyGo Travelling!What About Studying Abroad?Understand Linguistic QuirksWatch Dutch Movies!Speak English BetterGive Your Brain a BoostLearn Dutch to Get PromotedExplore Dutch CuisineWhen avid minds contemplate language learning, overwhelmingly, Romance languages leap to to the forefront.They seek out French courses or they want to learn Spanish, giving little thought to any Germanic language including the German language itself - which is really odd, seeing as English is considered Germanic in spite of more than a quarter of our vocabulary originating from French.What about you? Are you actively thinking of learning a new language but haven’t yet decided on one?How about learning Dutch?Superprof now provides you with 10 great reasons to learn this language that is spoken by more than 28 million people around the world.derogatory intent.It seems the Dutch settlers of New Amsterdam (now New York) did no t care for their Connecticut neighbours, leading them to call those English settlers by all sorts of demeaning names. Undaunted by the ridicule, those New World patriots even went so far as to include it in patriotic songs.Might that be one of society’s earliest instances of reverse psychology?The study of this word’s etymology proves that Yankees were indeed British subjects whose descendants became American over a century later.Today, nobody on British soil considers themselves a Yank and Americans glory in the title.Other amusing words that come from Dutch include:blunderbuss â€" from donder meaning thunder and bus originally meaning boxdapper, meaning bold or sturdy â€" vastly different from today’s interpretation!geek: from gek, meaning fool (again, a wild divergence from its modern meaning)knapsack originally represented a snack bagPoppycock: from pappekak, meaning soft dungquack: literally somebody who dabbles in ointments (original word kwaksalver)slim, in Dutch: bad, sly or crookedAnd from the long list of English words originating from Dutch, one last, most interesting term: (military) tattoo.To get soldiers back to the barracks in time â€" before they could become completely inebriated, military drummers would make the rounds at the appropriate hour, signalling innkeepers to doe den tap toe or turn off the taps.The practice has since evolved into the pageantry and precision we are treated to every year, so far from its bawdy roots...Indeed, the Dutch language has made our own tongue so rich, especially if you consider how some of our words came about!Learning Dutch is Relatively EasyBecause the Dutch language peppers our vocabulary so liberally, students of the Dutch language are constantly surprised to discover just how many Dutch words they already know.Besides, Dutch is our mother tongue’s closest relative, meaning that many native speakers of English have a much easier time learning the language of the Netherlands than they would should they endeavour to learn Italian or Portuguese.It is true that this new language you propose to learn has some sounds that don’t exist in English, such as the trilled R and the dorsal fricative â€" the ch sound, but they are pretty easy to learn.One difficulty many Dutch learners report is in article usage.English has one article, the, to represent German’s three articles: der, die and das (masculine, feminine and neutral) Dutch falls smack in the middle, calling for only two: de and het.The challenge lies in memorizing which article goes with which noun, as they are not guided by grammatical gender rules like German articles are, nor are they generic as the English article is.Go Travelling!It is true the Netherlands is overwhelmingly English-friendly, with a reported 86% of the people capable of conversing in English.Don’t let that be the reason you shy away from this delicious-sounding language!The fact is that Dutch is not spoken only in the Netherlands but in neighbouring B elgium, as well as Aruba, Sin Maarten, Curaçao and Suriname.Fancy a winter holiday in the sunny Caribbean?Learning to speak a host country’s language shows your interest in and respect for the country, the culture and the people so, even if you learn just enough Dutch phrases to get by on your next holiday, your efforts would be sincerely appreciated.But don't stop there! If you're going to learn a new language, you should learn more than just a few expressions you can use on holiday!Besides, to certify your Dutch language skills, you would have to go to the Netherlands!How about surprising your hosts by speaking Dutch on your next Aruba holiday? Source: Pixabay Credit: TampaflgalWhat About Studying Abroad?Even though the Netherlands has approximately 1,700 mostly graduate-level programs that are taught in English, you may participate in Dutch language classes offered to foreign students which, in turn, will give you insight into Dutch culture.Just think of all of the events you will be able to enjoy more thoroughly when you speak the language!words and phrases that, unless you are familiar with the language, would sail right past you.The Dutch so love their bicycles that they have built an entire lexicon of slang phrases that incorporate bikes â€" fiets, (pronounced feets... no one is really sure why).If you wanted to indicate you suddenly get what the other person is saying, you would exclaim ‘On that bicycle!’ - a phrase whose meaning would completely escape you if you weren’t in tune with the language and culture.As you learn to speak Dutch, you might be perplexed at their use of acronyms in everyday conversation: zgn, aub and ipv, just to name a few.You could think of their use as similar to texting: brb for be right back, for example, or idk for I don’t know.Dutch people, in general, are an efficient lot; a sterling example of the less is more principle,  reflected in their conversation. They certainly do not mean to confuse the hapless foreig ner.Watch Dutch Movies!Granted, the Dutch movie industry is not widely renown but some of their BNs â€" famous people are, Rutger Hauer and Famke Janssen among them.In fact, Dutch cinema has a long history and its Documentary School is known worldwide. But, for all that the Dutch film industry has been the butt of many jokes, some of their films are definitely worthy of praise.As a language learner, you might try taking in Turkish Delight or Amsterdamned with the original soundtrack playing so that you can get some listening practice in.After those two selections, you might go for a bit of comedy with Flodder... after which you may delve into their wide selection of family movies.Although Dutch cinema doesn’t make a big splash on the international scene, there certainly are plenty of titles to choose from on Amazon and elsewhere!And what a great learning experience it would be, hearing native speakers discourse!Speak English BetterThis benefit of language learning applies to any l anguage, not just Dutch.You can never understand one language until you understand at least two â€" Geoffrey WillansGranted, much of our native language is rooted in Dutch, but that factors little in the nugget of wisdom quoted above.Rather, it is the idea that you are stepping outside your own circle of linguistic experience to absorb the vernacular of a completely independent culture â€" kind of like how we never know how lovely home is until we return to it.Learning Dutch will give you a new appreciation for the English language: its subtleties and nuances, its grammar and its fluency.Now aren't you keen to go find resources to improve your Dutch?Learning Dutch can give your brain a boost! Source:Pixabat Credit: Elisa RivaGive Your Brain a BoostThe overall brain-boosting benefits of learning a second language are well-documented: your memory improves, you get better at multitasking and even your ability to conceptualise increases dramatically.Did you know that learning languages can help stave off dementia?Now, in the run-up to the biggest shopping event, you might find that language acquisition can even help you make more rational decisions amid all of the Black Friday sales adverts.Might you gift yourself and your family language lessons this year?The brains of people who speak more than one language actually work differently, studies show. Such a linguist arrives at solutions faster and tends to be more decisive.Aren’t those qualities you might need to advance at work?Learn Dutch to Get PromotedRecent analysis shows that companies prefer to hire and develop employees who can speak more than one language, in part because of the cognitive advantages such workers bring, but also because our society is becoming more diverse.Even if that company does not yet operate on the global commerce stage, surely there are still local clients and customers who might not speak English.Another benefit of hiring people with proficiency in more than one language is that s uch workers expand the company’s horizons: perhaps there is currently no trading with Holland but those connections might soon be in the works!As for you who are intent on learning a foreign language, you may consider the possibility of a pay hike a good incentive to sign up for language courses...Explore Dutch CuisineJust as you don’t have to learn Mandarin to appreciate Chinese food, you don’t actually need any language training to enjoy traditional foods from the Netherlands.However, food being integral to a country’s culture, learning how to speak Dutch may give you the incentive to try out a few traditional recipes.Especially in these cold months, you might want to try stamppot: mashed mixed with veg, served with smoked sausage. Or you could enjoy bitterballen with your evening pint.Those consist of a savoury beef mixture coated in breadcrumbs and fried golden brown. Sounds delish, doesn’t it?Learning a language is surely not a prerequisite to enjoying tasty foods â€" after all, you don’t need to learn French to eat a baguette, but acquiring language skills yields so many benefits including cultural comprehension that we understand perfectly why you endeavour to learn a foreign language.And now, you have ten good reasons to sign up for that Dutch language course you’ve long been considering!

Critical Reasoning Question 22 Manufacturing - Private Tutoring

Critical Reasoning Question 22 Manufacturing BobbiM Mar 25, 2014 Smith Products fabricates machine tools that are essentially identical to those produced by Jackson Manufacturing.   For both companies, raw materials represent about two-thirds of the cost of manufacturing the machine tools.   To gain an edge over Jackson Manufacturing, Smith Products should purchase its raw materials from a new supplier advertising much lower prices. Which of the following, if true, would most weaken the argument above? A.           Smith Products spends more on employees’ wages than Jackson Manufacturing does. B.           Smith’s current supplier provides raw materials of exceeding high quality. C.           The market for machine tools has been declining for several years. D.           The new supplier’s materials are of low quality and would reduce the lifespan of Smith machine tools by half, causing sales to decline. E.             The plant manager for Smith Products is planning to increase the plant’s efficiency. Think you know the answer? The correct answer is D. The conclusion that Smith Products could gain an advantage by purchasing lower-cost raw materials is based on the evidence that raw materials represent the largest proportion of costs for both Smith and Jackson.   For the conclusion to hold, Smith must assume the new raw materials will not have any other negative effects on its business.   So, to weaken the argument, look for a choice that casts doubt on this assumption.   (D) does so by stating that the low quality of the new materials will cause a drop in sales.   If that occurs, using the new supplier will not create an advantage for Smith Products, and so (D) is the answer.   (A) and (E) indicate other ways that Smith might gain an advantage, but they don’t have any bearing on whether changing suppliers would create an advantage.   (B) is similarly irrelevant; even if true, it doesn’t provide any reason Smith should not use the new supplier.   (C) is out of the scope of the argument.

Linking Knowledge

Linking Knowledge “Supertutor” Mark Maclaine is Tutorfair's Co-founder and Director of Learning.  Mark is currently working on his new book which is based on a series of real life clients and the experiences he has gained over his many years of tutoring. The second snippet of this series looks at how tutors can  link a student's pre-existing knowledge to the knowledge the already possess and gives some examples of how linking knowledge can help enhance their learning.   Linking knowledge The ranking systems of online search engines like Google are partly based on how many other websites link to a particular site. Similarly, memories that are linked to many others are more robust, and less likely to be forgotten, than those out on a limb. As a tutor, try and link what you’re teaching to as much pre-existing knowledge as possible, preferably deeply ingrained knowledge. One teacher I interviewed for this book, Alf Erevall, who’d been teaching for forty years, told me simply “your teaching is only as good as your analogies.” Analogies are not only fun, they contribute to the robustness of memories, because they require students to link ideas. Interestingly, they actually work because they are imperfect. As Malcolm Gladwell puts it, “You want the analogy to be a little bit odd because that's what attracts people's attention. And that's what makes them want to talk about it.” The link is analogical not logical, and as my Google example goes to show, needn’t be perfect! In general, the more links you help your student make, the better. This is especially true when you’re introducing a new topic. Ask yourself: are there ways I can link this to what they already know or things they find important? It can be useful when you connect these to topics you’ve previously covered together. Even small links can create connections in the brain that not only reinforce new learnings but also the old ones too. Here is an example: Top tips on how to link topics as a tutor   Here are some ideas for linking topics so they appear more relevant to a student’s life: Introduce topics in a way that has some relevance to their everyday lives. First find out what interests them. If they love horses, calculate how much a horse should be eating, or write a letter to mum to convince her to buy one. Teach topics using topics students find interesting: “if YouTube paid your favourite star £2 per 1000 views, let’s work out how much she made from her last ten videos.” Sometimes using topics that are a little gross, or funny, can peak interest: “You know how your dentist tells you to look after your dental health, now we’re going to see some pictures of what happens if you don’t.” Rewrite topic questions using names of the student’s friends or celebrities they admire Demonstrate maths topics, from addition to compound interest, using items they may indeed want to buy, like computer games. Or try calculating the number of points needed to win the league. If you don’t know much about a sport let them teach you! Have them write persuasive writing pieces on topics they genuinely care about, or by writing letters to people they admire. Get up and move: when demonstrating the relationship between angles in triangles, and their opposite sides, create models or stand up and demonstrate these with pieces of string. With a little creativity almost any topic can be linked to another.

Sarh Al Jaameah Private School

Sarh Al Jaameah Private School Sarh Al Jaameah Private School Sarh Al Jaameah Private School (SAPS), in Muscat, Oman, openedin September 2019. The school currently serves students in grades 1 through 3, expanding each year afterwards, up to grade 12.The school was born out of the vision of the Sultan Qaboos University and promises to be a beacon in the private school community. SAPS is an extension of the university, and it will have access to many supports, including faculty from colleges of diverse disciplines. As international educators, youll join a richly diverse team of professionals with vast experiences that will translate into service learning, real-world application, subjects and content of interest for students to explore and experiment in and the opportunity to leave your indelible mark as the founding teachers. You will be part of a brand new school, which will welcome your gifts and talents. There is ample room for professional growth and opportunities to be creative and flexible in approaches to learning. This is a very exciting project, which encourages the innovative juices to flow and impact children and the school community.

Benesse BE studio Inc.

Benesse BE studio Inc. Benesse BE studio Inc. Benesse BE studio provides exciting English learning programs for children. We currently operate over 1700 schools across Japan, employing2,000+ teachers, and are looking to expand further. Our students demographic exemplifies BE studios unique positioning, where the youngest student is9 month, and the student majority is under the age of 6-7. BE studio was selected as theoverall best schoolandschool with great teachersin the young learners division of the iid Award 2019. Teachers at BE studio enjoy the fun and interactive, activity based lessons just as much as the students. We also have abilingual lesson partner to support the teacher with classroom management and parent communication to ensure a fun, safe, and productive environment. Combined with our small class size, of up to 8 students, BE studio creates a highly engaging communicative environment for young learners, to be expose to and exercise authentic English communication skills. BE studios brand concept symbolizes such key features, as we pay great respect to, and encourage each students originality and character. We aim for our students to be able to collaborate across cultures, and create new value through heartfelt communication. As part of the Benesse group, the leading education company in Japan, BE studio continues to bring impact to support with the development of English communication skills for young learners. There are also opportunities, in collaboration with the Benesse group, to expand your teaching experience and develop your career. If youre passionate about teaching children, and would like to pursue careerin the education industry, BE studio is agreat match!We look forward to meeing the next BE studio teachers! View our Brochure