SIMPLE EQUATIONS AND VARIATIONS
CONTENT
- Formulae, substitution and change of subject of formulae.
- simple binary operations.
- Variations (i) Direct and inverse, (ii) joint and partial.
- Application of variation.
SUBJECT OF A FORMULA
The subject of a formula is the variable that is expressed in terms of the other variables. In the relation \(y = x + 4\), y is called the subject of the formula. To make x the subject means rewriting this relation in an equivalent form, where x will be alone on one side of the equality sign. The relation is normally written with the subject on the left-hand side of the formula. For example, \(y = 2 × -3 \), the x can be made subject of formula as follows, \(x = \frac{y + 3}{2}\)
SUBSTITUTION
A formula is an equation in which letters represent quantities. The value of one variable in a formula or algebraic equation may be found by substituting (i.e replacing) known values in the same formula
Examples 1: The sum of the squares of the first n integers is given by
\(s_n = \frac{n(n + 1)(2n + 1)}{6}\)
Calculate (a) s20 (b) the sum of the squares from 21 to 40 inclusive.
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