Topic Content:
- Formulae & Substitution
One of the major uses of AlgebraAlgebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. More is to express mathematical relationships in form of formulae.
A formulae is an equation that describes the relationship between two or more quantities.
Letters are used to represent unknown values in a formulae.
For example the frequency f in cycles per unit time i.e.
F = \(\frac {\omega}{2\pi} \)
This formulae shows the relationship between frequency (f) and circular velocity (\( \scriptsize \omega \))
F is called the subject of the formulae or equation.
Worked Example 8.1.1:
i. If, F = ma, find F when m = 10 and a = 6
ii. If y = mx + c, find y when m = 5, x = -2, c = -3.
iii. If, V = mgh find v when m = 10, g = 9.8 and h = 5
iv. If y = 16x2 – 9z2, find y when x = 7, and z = 5
v. The sum of terms in a geometric progression is given as:
s = \( \frac{a( 1 \; – \; r^n)}{1 \; – \; r} \)
Calculate s when n = 4, a = 3 and r = 3
vi. Here’s a formulae for finding the area of a triangle;
A = \( \scriptsize \sqrt{s(s \; – \; a)(s \; – \; b)(s \; – \; c)} \)
Where s = \( \frac{a + b + c}{2} \) and a, b and c are the three sides.
Find the area of a triangle when a = 5 cm, b = 8 cm, c = 11 cm.
i. If, F = ma, find F when m = 10 and a = 6
Solution
F = ma
F = 10 × 6
F = 60N
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