algebra sub&for - W2 algebra substitution&...

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Unformatted text preview: W2 algebra substitution & formulae IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII This unit eonsists of Boat-ts. Part 2: You are introdueed to the use of formulae. When vou have worked through Part 2, you will be able to - substitute given values in an expression or formula, and evaluate it. Substitution One of the things we often want to do in algebra is to find the value of an expression when we substitute numbers for the different letters. Examples (i) lfs:2, i=—I, ”2—2, o:3, tozeevaluate —2I+uv 35*“:- Substituting the values gives (—2)x{—1}+(—2)x3 *2_—_s 3s2—4 _6—4 oil. _ 2 =4. {ii} Using the values for t, u, v and w given in {i} find the value of 3 I W T u, v Substituting gives (— l}><{—l)>< (—1))4. 4 _ j (#2)): (-2)! 3 12 FDrmUIBE A fermula expresses a relatienship between twe er mere variables in a particular applicatien er preblem. It always includes an '1 =H sign, and se it is an equatien. [Equatiens are dealt with mere fully in a later UNIT] The variables are deneted by letters. which must be clearly defined in the centest ef the applicatien. This usually invelves stating their units tee. The fellewing are feur examples ef fermulae. 1. Simple Interest it an amtiunt [it meney F" is invested fer time T at a rate ef Elli: per annum then the interest I is given by FTR I = -—. lllll If F = 500%}, T = 3(vr) and R = 2.5 then the interest is given by 500 X 3 X 2.5 . - I -3-' ——"" '1' 65'“"'-— 23,15 lHE the lIll‘EI'E'St l5 £3?-5U 2. Temperatures en the Fahrenheit and Centigrade scales are cennected by the fermula 5 C = —{F- 32) El Where C and F denute the temperatures en the twe scales- Substituting the value F = 212 {beiling peint ef avatEr} gives the equivalent temperature en the Centigrade scale as c = gem—32) 9 :EXISU 9 = 100 If F =7 63, check that C 2 20. In seine fermulae ene er mere ef the letters ma}.F stand fer special censtants. 3. The fermula C : Ear gives the length ef the circumference ef a circle whese radius is r. E is a special number which is deneted by a letter ef the Greek alphabet {preneunced pi} and it has ne exact value- 22 Simple appres'imatiens fer a: are —- er 3.131. 7 If the circle measures 6 metres acress its diameter, then its radius is 3 metres. and the terrnula gives the circumference as v C=2X%:K3 :: 18,9 {metres} 4. The formula for the time taken for a complete swing of a pendulum of length I is H T=2ar — 3 This not only involves 1:, but also the special constant 3. This denotes the acceleration caused. by the gravitational force towards the Earth’s centre. In metric units it has a value of 9.31 nifs“. If I = 1.09 (metres) then T can be calculated approximately via ||__ T=jj§<2>§ .11? 7 9.81 : 2.1 (S) In UNIT {5 we learn how to rearrange formulae- . 1 Exermses 1. If V L —3— m-Zs and. r = s. h = 14. find the value of v. 22 [Take the constant it to he —-—.] .? 2. lfv:u+atandur5.a=32,t=1U,finclv. 3. If v2 = [12 + Zoo and ti = 15, a : 32, s =1Crfl.fincl v. 9 4- IfF=S=C+323ndC21QflndE RT . . 5. IfA=P l+fi andP=EGD,R:r1,'I':1U,fmdA. Solutions 1. v = 528 2. v = 325 3. v = 31.4 4. 13:50.5. A'— FUU ...
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