# Formulae

- Formula is an algebraic expression corresponding to a statement.
- The subject of a formula is a variable which is expressed in terms of the other variables involved in the formula. You also learnt how to change the subject of a formula.
- The method of finding the value of an algebraic expression by replacing all occurrences of variables with their particular values is called substitution.

## Exercise

- Write formulae for the following statements:

(i) The length of a rectangle is 10 units more than breadth and the perimeter is 7 times the breadth.

(ii) Anu is presently y years old. In 4 years time, she will be three times old as she was 2 years ago.

(iii) If you multiply a number by 2 and take away 12, you get 2 more the number.

(iv) A boy buys a number of pencils each costing Rs 2 and a number of erasers each costing Rs 3 and spends a total of Rs 26.

(v) The circumference of a circle is times its diameter.

(vi) A male daily wage labourer earns Rs 60 per day and a woman earns Rs 45 per day. Find the monthly earnings of x men and y women, assuming that there are 26 working days in a month. - Change the subject of each of the following formulae to the letter given against them

(i) 9C + 160 = 5F; C

(ii) 9C + 160 = 5F; F

(iii) v² = u² + 2as; s

(iv) v² = u² + 2as, u

(v) s = ut + (1/2)at²; a

(vi) m = n/(1 + n) ; n

(vii) l = a + (n - 1) d; n

(viii) (x + a)/(x + b) = c/d; x

(ix) S =(n/2)[2a + (n - 1)d]; d

(x) A = r²; r

(xi) V = r² h; r

(xii) V = r²h; h - When a = 2, b = 0 and c = - 3, find the value of

(a) a³ + b³ + c³

(b) (a + b + c)^{3}

(c) a² + b² + c² - 2ab - 2bc - 2ca

(d) (a - b - c)². - Find the value of the polynomial x
^{4}- x³ + 2x² - x + 5 when

(a) x = 3

(b) x = 0

(c) x = - 3 - When s = 3, t = 5, u = - 1, find the value of

(a) stu + 3

(b) s² + t² + u²

(c) (s + t + u) stu - The area A of a circle is given by A = r² where
= 22/7 and r is the radius.

(i) Find A when r = 14 cms

(ii) Find r when A = 99/14 cm². - If 9C + 160 = 5F, find

(i) C when F = 50

(ii) F when C = 50. - In the formula I = (P R T)/100, find R when I = 180, P = 2000, T = 9/2.

## Answers

**1.**(i)7x = 2 (x + x + 10) (ii) y + 4 = 3 (y - 2)

(iii) 2x - 12 = x + 2 (iv) 2x + 3y = 26

(v) C = D (vi) W = 26 (60x + 45y)

**2.**(i) C = (5/9)(F - 32) (ii) F =(9/5)C + 32 (iii) s =(v² + u²)/2a

(iv) u = ±(v² - 2as) (v) a = 2(s - u t)/t² (vi) n = m/(1 + m)

(vii) n =(l - a + b)/d (viii) x = (ad + bc)/(c - d) (ix) d = 2 (S - an)/[n (n - 1)]

(x) r = (xi) r =

(xii) h = V/ r²

**3.**(a) - 19 (b) - 1 (c) 29 (d) 25

**4.**(a) 74 (b) 5 (c) 134

**5.**(a) - 12 (b) 35 ( c) - 105

**6.**(i) 616 cm² (ii) 1.5 cm

**7.**(i) 10 (ii) 122

**8.**2