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Access Mathematics. Transposition of Formulae . Learning objectives. After this session you should be able to: Recall simple formulae triangles to model simple engineering systems Transpose formulae in which the subject is contained in more than one term
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Access Mathematics Transposition of Formulae
Learning objectives • After this session you should be able to: • Recall simple formulae triangles to model simple engineering systems • Transpose formulae in which the subject is contained in more than one term • Transpose formulae which contain a root or a power
Equation: 3x+2 = 23 3x+2- 2= 23-2 3x = 23 - 2 x = (23-2)/3 x=7 Formula: gx + h = k gx + h- h= k- h gx = k- h x = (k - h)/g Recap: Make x the subject Last lecture we examined the differences between equations and formulae and their subsequent solution protocols:
Transposition Of Formulae • The rules are exactly the same as for algebra, except the final result is an algebraic expression instead of a numerical answer.
Simple Transposition • In the Science units you will come across very simple formulae for instance • Newton’s second law (mechanics) • Electrical charge • Ohms Law • Density
Recap: Simple Transposition • Here the same rules apply as the letters in the formulae are just numbers in disguise
Activity • In groups make the subject of the following formulae the variable in parenthesis for: • Density (m) • Electrical Charge (t) • Newton’s second law (a)
Mathematical Systematic Try this one yourselves: Transposition of Elementary formulae
Mathematical v=u+at;t v-u=u+at-u v-u=at (v-u)/a=at/a t=(v-u)/a Systematic v=u+at;t v-u=at (v-u)/a=t Extra terms Try this yourself but this time transpose for a instead
Transposition & substitution • Use any either of the methods to transpose find the the value of R given that: • H=126, t=7 & I=3. Consider: What if m=2, v=5 and T=10
Example: • The pressure p in a fluid of density at a depth h is given by: Where pais the atmos pressure and g is gravitational acceleration. • Make h the subject
Work in groups Discuss the solution for one the following problems Select a group member to share your solution with the class Group Activities
(a,b) Class Discussion/Exercise
In these cases we proceed as before isolating the power or the root first Thereafter we simply us the inverse operation in order isolate the required variable i.e. take the root or raise to the power respectively e.g. Try Subjects with Roots or Powers
The same procedure is employed where roots are involved. However to negate the root we raise to the appropriate power: E.g. or Try: Transposition inc. Roots/Powers
Summary • Have you met the learning objectives • Specifically are youable to: • Recall simple formulae triangles to model simple engineering systems • Transpose formulae in which the subject is contained in more than one term • Transpose formulae which contain a root or a power