Rates and variations
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RATES AND VARIATIONS RATES:- When sets or quantities of different kinds are related, we use the word rate. i.e 1. A rate of pay of 10,000/= Tsh per hour (money- time) 2. The price of juice is 700/= Tsh per litre (money -weight of juice) 3. The average speed of 80 kilometres per hour (distance- time) Therefore the rate is the constant relation between two sizes of two quantities concerned. NOTE: Rates deals with the comparison of two quantities of different kinds. Example 1. Hiring a car at a charged rate of Tsh 2,000/= per kilometer. (a) A journey of 40 kilometers will cost 40 x Tsh 2,000= Tsh 80,000/= (b) A journey of 100 kilometres, costs 100 x Tsh. 2,000= Tsh.200,000/= If we state the rate we always give two quantities concerned and the unit measurement. E.g: Average speed is written as 100 kilometres per 2 hours or 50 kilometres per one hour.
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Variation
May this presentation could help you, the pictures here is not mine I get it from YouTube videos, I upload this ppt because
most the ppt here help me a lot in my teaching mathematics. This topics is different kinds variation direct variation, inverse variation, joint variation and combined variation.
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z = kxy
z = -12
z = kxy
z = -84
z = kxy
z = -21
4.
a. Combined means together as a whole.
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May this presentation could help you, the pictures here is not mine I get it from YouTube videos, I upload this ppt because
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This document provides an overview of marketing concepts including definitions of marketing, the marketing mix, types of markets, and market structures. It defines marketing as identifying and satisfying consumer demand through a system of activities to plan, price, promote, and distribute goods and services. The marketing mix consists of the 4Ps - product, price, promotion, and place. Markets are classified by type of goods (commodity, input, financial) and structure (perfect competition, monopoly, monopolistic competition, oligopoly). Market structures differ based on the number of sellers, product differentiation, and barriers to entry.
International trade
International trade involves the importing and exporting of goods and services between countries. There are several reasons for international trade, including allowing countries to obtain goods they cannot produce themselves and sell surplus goods. Trade can occur between two countries (bilateral) or multiple countries (multilateral). The main advantages of international trade are that it enables countries to access a greater variety of goods and promotes specialization. Some disadvantages include over-reliance on one export good and the potential for imported goods to have harmful effects. Key terms involved in international trade include imports, exports, balance of trade, balance of payments, and various shipping terms that determine responsibilities for costs.
Communications
Communication involves conveying information from one person to another. There are three main methods of communication: writing and reading, talking and listening, and using signs. Factors like urgency, distance, need for details, confidentiality, need for reference, and costs determine the best communication method. Recent developments in Tanzania include the introduction of cellular phones, public pay phones, privatization of telecommunications, improved mail delivery services, internet access, and electronic mail.
Advertising
Advertising is used to inform customers about new and existing products or services. It provides information on price, quality, name, what is offered, and where to obtain the product. The main goals of advertising are to increase sales, introduce new products, promote branded goods, improve company image, gain more retail outlets, and outcompete rivals. Common forms of advertising media include television, radio, newspapers, posters, cinema, neon signs, direct mail, and trade fairs. Choosing an advertising medium depends on factors like cost, target audience, geographical coverage, and number of people reached.
Web development
This document provides information about web development and creating webpages. It discusses using software like HTML, FrontPage, and text editors to design pages with headers, navigation bars, and common layouts. The document explains how to preview pages, publish them to a server so others can access the site, and the difference between a single webpage and an entire website. Key topics covered include HTML tags, page structure, outlining a site map, and hosting a site on an internal or external server.
Mpact of information and communication technology (ict) on the society
ICT has had a significant impact on society. It has transformed education, industry, banking/business, communication, entertainment and more. However, it has also introduced some disadvantages like unemployment, privacy issues, lack of job security, and health risks. To address security issues, techniques like backups, encryption, access controls, passwords, firewalls and intrusion detection are used. Overall, ICT has changed nearly every aspect of modern life while also presenting new challenges around its use.
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Rates and variations
- 1. RATES AND VARIATIONS RATES:- When sets or quantitiesof different kinds arerelated, we use the word rate. i.e 1. A rateof pay of 10,000/=Tsh per hour (money- time) 2. The priceof juiceis 700/=Tsh per litre(money -weight of juice) 3. The average speed of 80 kilometresper hour (distance- time) Thereforethe rateis the constant relationbetweentwo sizes of two quantitiesconcerned. NOTE: Rates deals with the comparisonoftwo quantitiesof different kinds. Example 1. Hiring a car at a charged rateof Tsh 2,000/=per kilometer. (a) A journey of 40 kilometerswill cost 40 x Tsh 2,000=Tsh 80,000/= (b) A journey of 100 kilometres, costs 100 x Tsh. 2,000=Tsh.200,000/= If we statethe ratewe always give two quantitiesconcerned and theunit measurement. E.g: Averagespeed is writtenas100 kilometresper 2 hours or 50 kilometresper one hour. Rates canalso writtenin a ratiosform.
- 2. Rate of Exchange People in any countryexpect to pay and be paid in currencyof their own country. It is necessary to exchangethecurrencyof the first countryfor that of thesecond, when money is moved from one country to another. i.e: The rateof exchangelinked together variouscurrenciesofthe world, which enable transfer of money and payment for goods to take place betweencountries. Consider tablebelow shows the exchangeratesas supplied by the CRDB bankeffective on May 17, 2007. COUNTRY CURRENCY EQUIVALENT SHILLINGS United states Europe Japan Britain Switzerland Canada Australia Kenya Uganda South Africa Soud Arabia India 1 Dollar 1 Euro 1 Yen 1 Pound stg 1 Franc 1 Dollar 1 Dollar 1 Shilling 1 Shilling 1 Rand 1 Rial 1 Rupee 1272.50 1720.33 10.02 2513.68 1038.76 1152.48 1049.54 18.525 0.745 181.60 338.695 31.105
- 3. Sweden Zambia Mozambique Botswana 1 Kronor 1 Kwacha 1 Meticais 1 Pula 186.42 0.317 0.0535 209.85 Examples 1. 1. A tourist from Sweden wishes to exchange1,000 Kronorsinto Tanzanianshillings. How much does she receive? Soln. From the tableabove 1kron =Tsh. 186.42 1,000Kronor=? =T shs. 186420 The tourist will receiveTsh. 186420 2. 2. How much 20,600 Tanzaniashillingsworth in IndianRupees? Soln. 1 Rupee = Tsh. 31.105 ? = Tsh. 20,600 = 662.273Rupees
- 4. Variations Direct Variation The two variablesx and y aresaid to vary directlyof the ratioisconstant. The real number K is called the constant of variation. And relationship maybewrittenas which readsas “y is proportional to x” If y variesdirectlyas the squareof x, then =Constant. And canbe writtenas and the algebraic relationisy=kx2 When having pairsof different corresponding values of x and y, this equationhold true. Therefore, we say that x and y vary directlyif the ratiosof the values of y to the values of x areproportional. NOTE: If x and y represent variablessuch that , theny=kx, The form of this equationy=kx is similar toy=mx. The graph of y=mx is a straight linepassing through theorigin, M being thegradient sameto the equationy=kx, The graph is a straightlinepassing through the originand gradient isk.
- 5. A sketch is like Examples If x variesdirectlyas the squareof y, and x=4 where y=2, find the value of x when y=8. Solution Let x1 =4 , y1 = 2, y2 = 8, x2 is required But Inverse variation
- 7. NOTE: The graph does not touch the axisbecausedivisionby 0 (zero) is impossible. Example 1 If x variesinversely as y, and x=2, when y=3 Find the value of y when x=18. Solution.
- 8. Example 2 3 tailorsare sewing 15 clothesin 5 days. How long would it take for 5 tailorsto sew 20 clothes? Solution - Let t = tailors, d = days c= clothes. A number of tailorsis inversely proportionaltothe number of days. - The number of tailorsin directlyproportionaltothe number of clothes.
- 9. When t = 5, c= 20, d can be found as It takes4days for to tailorsto sew 20 clothes JOINT VARIATION If a quantityisequalto a constant timestheproduct of the twoother quantities, thenwe say that the first quantifyvariesjointlyas the other two quantities. If x = k y z where k is a fixed real number then x variesjointly as y and z. Similarlyifx1 y1 z1 and x2 y2 z2 arecorresponding valuesof the variablesx, y and z, then x1 =k × (y1 z1 ) and x2 = k × (y2 × z2) From these we get
- 10. Examples 1 1. If x varies directlyas y and inversely proportionalasz and x = 8, when y= 12 and z = 6. Find the value of x when y = 16 and z =4 Solution Example 2
- 11. 9 workers working 8 hours a day to completea pieceof work in 52 days. How long will it takes13 workers to completethe samejob by working 6 hours a day. Solution Let w= workers h=hours d=days It is a joint variationproblem and canbe writtenas