C intersects the X-axis at the points A and B. You can be asked to find the coordinates of the points of intersection of a circle with the x-axis.Įxample: C is a circle with centre (0,3) and radius of 5Īnswer: Label (0,3) with h and k. (You could also draw a sketch of the circle on the x and y axis, plot the given point and the centre point, use a ruler to join the point to the centre and continue from the centre to the edge of the circle where you will find (8,-1).) INTERSECTION OF CIRCLES add 5 onto 3 = 8, and ADD the y coordinates i.e. Now ADD the x coordinate of the translation onto the x coordinate of the centre i.e. How far is it from the y coordinate of the point to the y coordinate of the centre i.e. How far is it from the x coordinate of the point to the x coordinate of the centre i.e. What we are doing is finding how far it is from the point to the centre, then going the same distance from the centre to this new point.Įxample: ( -2, 5 ) is a point on the circle (x-3) 2 + (y-2) 2 = 34Īnswer: The centre of the circle is (3 ,2) However, if the centre is not (0,0) and we are asked the same question, then we use a translation to find another point. Putting the point of a compass on the origin (0,0), as this is the centre, stretch the compass to 3 and draw a circle.Įxample: The point (-4,3) is on the circle x 2 + y 2 = 25Īnswer: The centre of this circle is (0,0) ( there are no numbers after the x and y)Īny point with the numbers 4 and 3 in it will be on thecircle. This circle has a radius of 3 ( square root of 9)ĭraw an x and y axis, marking to 3 on each axis, How to draw a given circle:Įxample: Draw the circle with equation x 2 + y 2 = 9 If your figure on the left is greater than that on the right, then the point would be outside the circle. (-2-3) 2 + (6-4) 2 = 36 (put all figures on left into calculator)Ģ9 < 36 therefore the point is inside the circle. To show whether a point is inside, outside or on a circle: Label the given point and sub into the equation of the given circle.Įxample 1: Show that the point (2,-3) is on the circle x 2 + y 2 = 16Īnswer: Labelling the point x and y we see that x=2 and y=-3ġ6 = 16 therefore (2,-3) is ON the circleĮxample 2: Show that the point (-2, 6) is inside the circle Write down the centre and radius of this circle.Īnswer : The centre is (0,0) (as no numbers after the x and y) and as r 2 = 25 then the radius will be 5 which is the square root of 25.Įxample 4: Given the equation of a circle is (x-5) 2 + (y+3) 2 = 49Īnswer: The centre is (5,-3) (The sign is the opposite to what it was insideĪnd the radius is 7 which is the square root of 49. Our Equation is therefore, (x-3) 2 + (y-4) 2 = 6 2įinish by squaring the 6, so our answer is (x-3) 2 + (y-4) 2 = 36Įxample 3: Given the equation of a circle is x 2 + y 2 = 25 We label the centre (h,k) so h=3 and k=4 and sub into the Formula. This circle has numbers at its centre, therefore we use Formula 2. We simply write Formula 1 and replace r 2 with 4 2Įxample 2: A circle with centre at (3,4) and a radius of 6: write its equation. This circle has centre (0,0) so we use Formula 1. There are 2 types of question you can be asked: one in which you are given the centre and radius and asked to write the equation of the circle and another where you are given the equation and asked to write down the centre and radius of the given equation.Įxample 1: A circle with centre (0,0) and a radius of 4: write its equation. What does it mean then, if your quadratic that you end up with has 2 solutions? or 1 solution? or no solutions?Well, it would mean that the line goes straight through the circle, or just touches it (is a tangent), or doesn't intersect it at all.FORMULA 1 : Used for a circle which has a centre of (0,0) and a given radius.įORMULA 2 : Used for a circle which has a centre of (h,k) (which means it has numbers, not zeros) and a given radius. When you solve these simultaneously algebraically, you are really finding where the graphs intersect!So, if you were to solve them simultaneously you would end up with a quadratic (either in terms of x or y depending on what you substitute) - but hang-on. It is the part under the square root sign, in other words it can't be negative or there are no real solutions to your quadratic equation.We also know that if it equals 0 there is 1 repeated solution, and if it is greater than 0 then there are 2 distinct solutions.So how does this all relate to coordinate geometry?Well, remember how you can talk about solving equations as the intersection of curves/lines? For example solving 2x = 3x+ 4 could be interpreted as finding the intersection of the line y = 2x and the line y = 3x + 4.So now say you had a circle and a line. Where does the discriminant come from? It is from the quadratic formula.
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However, when it comes to simple operations, they are usually done mentally.ĭo not miss this collection of more than 20 arithmetic books in PDF format, we are sure you will find them very useful and you will be able to achieve your goal of study and research. Nowadays, arithmetic calculations are made easier with the help of calculators. It also delves into some more complex ones such as nth root -an archaic term for the operation of taking nth roots is radication- (finding the n root of a number), exponentiation (raising one quantity to the power of another) and logarithm (the inverse function to exponentiation). In its etymology one can clearly see its definition.īut the basic operations are not the only ones that arithmetic deals with. 35 31 27 23 Write down an expression, in terms of n, for the nth term of the sequence. 18 Here are the first four terms of an arithmetic sequence. 21 27 33 39 45 Write down an expression, in terms of n, for the nth term of the sequence. The word arithmetic is a compound word that comes from the Greek “arithmos” meaning “numbers” and “tiké” meaning “art” or “craft”. 19 Here are the first five terms of an arithmetic sequence. Since we know that you recognize that value, we can’t help but recommend that you take a look at our arithmetic books.Īrithmetic is the area of mathematics that studies numbers and basic operations, such as addition, subtraction, multiplication and division. Since then, the contribution of this branch of mathematics has been unparalleled. Euclid (also known as the father of geometry) and Nicomachus of Gerasa, classified as neopythagorean, are considered great exponents of arithmetic at that time. In that historical period mathematics regained a new relevance, awakening more and more interest in its study. Understanding this, we have created a collection of arithmetic books in PDF format, so that you have access to the wonderful world of numbers and can expand, refresh or teach this knowledge to others.Īrithmetic has its origins in ancient Greece. Everyone, in one way or another, must master the basic operations to have an accurate understanding of countless everyday aspects. The 7 Habits of Highly Effective People is a comprehensive program based on developing an awareness of how perceptions and assumptions hinder success-in business. If you enjoyed books like The 7 Habits of Highly Effective People, The 52 Lists Project, or The High Performance Planner , you’ll love The 7 Habits of Highly Effective People Guided Journal. Other books he wrote include 'First Things First', 'Principle-Centered Leadership', and 'The Seven Habits of Highly Effective Families'. Featuring thought-provoking prompts, worksheets, and self-development quotes that teach you how to achieve your goals, this is the ultimate guided self-growth journal. The 7 Habits of Highly Effective Families: Creating a Nurturing Family in a Turbulent World Paperback Import, 15 September 1998 by Stephen R. Covey presents a holistic, integrated, principle-centered approach for solving personal and professional problems. In The 7 Habits of Highly Effective People, author Stephen R. (19,262) Only 1 left in stock - order soon. Each habit is broken down into a weekly format inspiring both beginners and seasoned 7 Habits readers to get motivated, build confidence, and boost inspiration and personal growth.Ĭultivate success, skill, and self-growth. There is a newer edition of this item: 7 Habits of Highly Effective People: Powerful Lessons in Personal Change. Its concise format is accessible and easy to stick with. Now, this companion journal gives readers a chance to craft inspiration into action. Covey’s time-tested principles in a whole new way. In his first major work since The 7 Habits of Highly Effective People, Stephen R. When The 7 Habits of Highly Effective People was released as a card deck, audiences approached Stephen R. How do you manage your time and stay organized? Whether you’re struggling to stay motivated or are looking for new high-performance habits, The 7 Habits of Highly Effective People Guided Journal offers journal prompts, worksheets, and exercises to help you accomplish all your short and long term goals. The 7 Habits of Highly Effective Families’ workshop is an engaging, family-strengthening programbased on Stephen R. #1 New Release in Strategic Business Planning Without any doubt, we are all fully aware of the turbulent times we live in. 1 Bestsellers The 7 Habits of Highly Effective People and The 7 Habits of Highly Effective Families. “If you follow this simple process, I promise that you will see positive changes in your relationships and find a higher level of personal satisfaction in your life.” ― Sean Covey, author of The 7 Habits of Highly Effective Teens The 7 Habits of Highly Effective Families’ workshop is an engaging, family-strengthening programbased on Stephen R. Once Hercules completed every one of the labors, Apollo declared, he would be absolved of his guilt and achieve immortality. He ordered Hercules to perform 12 labors for the Mycenaen king Eurystheus. Guilty and heartbroken, Hercules tracked down Apollo, the god of truth and healing (and another of Zeus’ sons), and begged to be punished for what he had done.Īpollo understood that Hercules’ crime had not been his fault-Hera’s vengeful actions were no secret-but still he insisted that the young man make amends. When her stepson was a young adult, she cast a kind of spell on him that drove him temporarily insane and caused him to murder his beloved wife and their two children. The infant Hercules was unusually strong and fearless, however, and he strangled the snakes before they could strangle him.īut Hera kept up her dirty tricks. Then, after Hercules was born, Hera sent two snakes to kill him in his crib. (Perseus, who was also said to be one of Zeus’ sons, famously beheaded the snake-haired Gorgon Medusa.)ĭid you know? The constellation Hercules is the fifth-largest one in the sky. According to legend, his father was Zeus, ruler of all the Greek gods on Mount Olympus and all the mortals on earth, and his mother was Alcmene, the granddaughter of the hero Perseus. That dung in the Augean stables is symbolic of the foulness of humanity – something Jonathan Swift, if his fourth book of Gulliver’s Travels is anything to go by, would probably agree with.Hercules was not a god but was born a mortal, although, like many mythic heroes, he had a complicated family tree. Heraclitus argued that each of the labours represents some aspect of man: the Erymanthian boar is man’s ‘incontinence’ or intemperance, the Nemean lion represents man’s determination to rush towards the wrong goals in the pursuit of something, the hind of Ceryneia represents cowardice, and so on. At many points in the twelve labours, he looks set to fail, be thwarted, or even be killed, but – like Odysseus making his way home from the Trojan Wars – he always manages to succeed, despite the problems he faces in a particular quest.īut did the Labours of Hercules hold a deeper symbolism? They have been subjected to allegorical interpretation and analysis, perhaps most famously by Heraclitus the Grammarian, a first-century thinker who wrote a commentary on Homer, among other things. Heracles is a classic example of the hero who triumphs against the odds. Some of the voyages take him months to undertake, and it’s only the main details which we remember from the labours but the early compilers of the myths describe the specific details of Hercules’ numerous journeys across land and sea as well as the apple-stealing and lion-slaying. Hercules (or Heracles in the original) is the consummate Greek hero: strong, fearless, cunning (perhaps it’s only Odysseus who outdoes him for wit and wiles), and a man of action who manages to complete every single one of his twelve labours, despite the various hardships and setbacks he faces. In some accounts, however, Hercules didn’t require Atlas’ help and slew the dragon and made off with the golden apples himself. Atlas, clearly not the brightest of Titans, agreed, whereupon Heracles strolled off with the apples Atlas had retrieved for him. He tricked Atlas by initially agreeing to the request, but asking that Atlas take the heavens back onto his shoulders for just a moment while Heracles adjusted his cloak (or added a cushion behind his head). When Atlas came back, he declined to take back the heavens onto his own shoulders, but Hercules was having none of this. Hercules tricked Atlas into retrieving some of the golden apples for him, while he offered to help shoulder Atlas’ burden (shouldering the heavens). The Garden of the Hesperides belonged to Hera, who put them under guard, the guard being a fearsome dragon with a hundred heads (yet another monster that was one of Echidna’s offspring). The last of Hercules’ twelve labours is also one of the more famous, even though it sounds essentially like the ancient Greek version of scrumping apples (or oranges, as the case may well have been). Stealing the Golden Apples of the Hesperides. After he had shown Cerberus to Eurystheus to prove he had completed the task, he returned the dog to Pluto. Hercules eventually managed this, and brought the dog back up to the land of the living with him. Pluto, the god of the Underworld, agreed to give Cerberus to Hercules, if he could train the dog without using a weapon. For his next labour, Hercules had to travel there to find Cerberus, the three-headed dog. No epic adventure story from classical antiquity would be complete without a descent into the Underworld. Fetching the dog Cerberus from the Underworld. Now, CyberLink has announced the latest and most sophisticated version, PowerDirector 12 Ultra that features more than 100 video editing tools and 400 built-in effectsĬyberLink PowerDirector 12 Ultra includes the innovative features to create studio-quality videos that are found only in highly priced top-notch video editing applications. It is simple, easy to use, economical and powerful software packed with stunning features and effects. It is one of the most acclaimed video editing platforms available today. Here, the CyberLink has been helping the enthusiasts with their award-winning software, the CyberLink PowerDirector to create, edit and produce professional quality videos. 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