Inequalities Maths Compiled By : OP Gupta [+91-9650 350 480 | +91-9718 240 480] Exercise 6.1 Question 1: Solve 24x < 100‚ when (i) x is a natural number (ii) x is an integer Answer The given inequality is 24x < 100. (i) It is evident that 1‚ 2‚ 3‚ and 4 are the only natural numbers less than . Thus‚ when x is a natural number‚ the solutions of the given inequality are 1‚ 2‚ 3‚ and 4. Hence‚ in this case‚ the solution set is {1‚ 2‚ 3‚ 4}. (ii) The integers less than are …–3
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understanding. Based on geometry alone‚ many special patterns evolve‚ such as the square numbers‚ triangular numbers‚ and much more. The Stellar Numbers are mostly used in astronomy and astrology. Stellar Numbers are figurate numbers based on the number of dots that can fit into a midpoint to form a star shape. The points of the star determine the number of points plotted around the midpoint. Triangular numbers is a figurate number system that can be represented in the form of a triangular grid of points where
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health • Minimum alcohol pricing will exacerbate poverty and entrench inequality without discouraging binge drinking • Most of the costs of drinking and smoking fall on individual consumers‚ not the public. There is no economic justification for increasing taxes on smokers and drinkers. In a report released today‚ The Wages of Sin Taxes (Download PDF) by Christopher Snowdon‚ the Adam Smith Institute condemns the government’s decision to increase taxes on cigarettes and alcohol this year and to introduce
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The Egyptian number system I choose to write about the Egyptian Number system because I am familiar with the base system they use. Therefore‚ it is easy for me to explain. In this essay I will briefly talk about the history of the Egyptian number system‚ indicate their base‚ symbols‚ whether their number system is positional or not and finally explain their number system by giving examples. The Egyptians had a writing system based on hieroglyphs from around 3000 BC. Hieroglyphs was found
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Apple Inc. is a successful developer of both computers and consumer electronics. The company’s most popular products include Macintosh computers‚ iPod mp3 players‚ iPhone smartphones and most recently the iPad‚ which is a hybrid of a tablet computer‚ and an eReader. Apple’s Macintosh computers‚ iPods‚ iPhones‚ and iPads all share characteristics that make them part of the general information technology industry. However‚ since they are very different products each belongs to a more specific industry
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concern on the minds of the drivers. Many people die every year due to reckless or careless driving. Driving safe is not a choice it is the law‚ but the law is broken and people suffer the affects of it. Driving drunk and texting while driving is the number one killer while in a vehicle. My perspective before turning sixteen was to drive with out any worries‚ but now because of the incident with my mother I realize driving safe is the right thing to do. She was a strong independent woman since her
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count the number of shirts in your closet. The second way to quantify or measure matter is to determine its mass. For example‚ you can buy bananas by the pound. The third and last way to quantify or measure matter is to determine its volume. For example‚ people by gasoline by the gallon. Chemists use a unit that is a certain number of particles. This unit is known as the mole. A mole is the quantity of anything that has the same number of particles found in 12.000 grams of carbon-12. That number of particles
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pose a number of health hazards including metallic (lead‚ manganese)‚ aromatic (e.g.‚ benzene)‚ and oxygenated additives in both industrialized and developing countries”(1997‚270). When approaching the matter of weather or not to double taxes‚ the easy answer is yes. The government doubles taxes and gasoline users are discouraged to fuel their pollutant producing vehicles. However‚ the repercussions of this tax extend far and beyond such an appearance of an easy remedy. There are a number of factors
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Mobile Number Portability What is MNP? Mobile Number Portability (MNP) allows the Mobile service subscribers to retain their existing mobile number when they move from one Service Provider to another Service Provider with in a same licensed service area. In other words‚ the Mobile Service Subscriber can switch from one operator to other operator with in telecom circle while keeping the same mobile number. MNP has often been considered as a tool to effect increased competition and improve
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I chose to analyze Beethoven’s Piano Sonata number 15. Sonata number 15 is opus/work number 28. There are 4 movements in the work‚ but I chose to analyze the first movement. Beethoven was born on December 16‚ 1770 into a family of musicians ("Classical Net - Basic Repertoire List - Beethoven" pars. 1-2). Beethoven began writing music at a young age ("Classical Net - Basic Repertoire List - Beethoven" par. 4). He composed his first original Sonata in 1797 ("Classical Net - Basic Repertoire List -
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