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Unit 21 Formula Presentation 1 Using Formula Presentation 2 Constructing Formulae Presentation 3 Negative Numbers Presentation 4 Temperature Differences Presentation 5 Substitutions into Formulae Presentation 6 More Complex Formulae Presentation 7 Changing the Subject Presentation 8 Pendulums Unit 21 Formula 21.1 Using Formula 4cm w 8l cm Question The perimeter length, P, and area, A, of a rectangle Solution Solution are given by the formulae ? (b) are? the? perimeter What and ? length and area if (a) ? ? ? ? where l is the length and w the width of the rectangle. ? Unit 21 Formula 21.2 Constructing Formula When repairing air conditioning systems, an emergency engineer charges a basic fee of J$3000 plus J$1200 per hour. Question What Find adoes formula the for engineer calculating charge theinengineer's total if the charge repair takes for repair 6 hours? work which takes n hours. Solution ? ? Let C = J$3000 Charge + J$1200 ×6 So C = J$3000 fixed?charge + J$7200 + ?hourly charge × no. of hours ? ?? + J$1200 C = J$10200 J$3000 × n? ? C = J$3000 + J$1200n Unit 21 Formula 21.3 Negative Numbers Rules to remember + + x x x x + + = + = = = + + + ÷ ÷ ÷ ÷ + + = + = = = + Calculate ? 4 + (−10) = −6 ? −4 − 5 = −9 ? (−40) ÷ (5) = −8 (−40) ÷ (−5) = 8? −6 + 8 = 2? ? −6 + (−7) = −13 ? (−24) ÷ (3) = −8 (−6) × 7 = −42 ? Unit 21 Formula 21.4 Temperature Differences What is the difference Use information given in ontemperature the above tobetween answer these questions. Kingston and Singapore Kingston and Vancouver London and Sydney Oslo and Kingston 4? ? 29 ? 26 ? 30 Kingston and London London and New York Lima and Kingston Moscow and Kingston ? 25 3? 0? ? 34 Unit 21 Formula 21.5 Substitution in Formula l = (40 + 0.02T) cm The length of a metal rod changes with temperature according Question to formula is when the temperature in ˚C What is theabove; lengthwhere of the T rod (a) T = 50˚C (b) T = −10˚C Solution (a) (b) ?? cm 50) l = (40 + 0.02 x −10) cm = = (40 (40 + + ?−0.2) 1)?cm cm = 39.8cm ?? 41cm Unit 21 Formula 21.6 More Complex Formula The formula gives the focal length f for a lens Question What is the value of f, if u = 10cm and v = 8cm Solution Hence ? ? ? ? ? ? Unit 21 Formula 21.7 Changing the Subject The formula that connects ˚Celsius (C) and ˚Fahrenheit (F) is Question Rewrite the formula in the form C = ...... Solution Take 32 from both sides of the formula So ? Multiply by 5 throughout Divide by 9 throughout ? ? Unit 21 Formula 21.8 Pendulums The period of revolution, T, of a pendulum of length l is given by the formula when G is a constant. Solution Problem Divide sides by give Make lboth the subject of this to equation. ? Square both sides ? Multiply both sides by G to give ? ?