Cambridge International Mathematics

Formulae and simultaneous equations (Chapter 7) 157

EXERCISE 7D

1 Makexthe subject of:

a 3 x+a=bx+c b ax=c¡bx c mx+a=nx¡ 2

d 8 x+a=¡bx e a¡x=b¡cx f rx+d=e¡sx

2 Make:

a rthe subject of A=¼r^2 , r> 0 b x the subject of N=

x^5

a

c rthe subject of V=^43 ¼r^3 d x the subject of D=

n

x^3

e xthe subject of y=4x^2 ¡ 7 f Q the subject of P^2 =Q^2 +R^2

3 Make:

a athe subject of d=

p

a

n

b l the subject of T=^15

p

l

c athe subject of c=

p

a^2 ¡b^2 d dthe subject of

k

a

=

5

p

d

e l the subject of T=2¼

r

l

g

f b the subject of A=4

q

a

b

4 Make:

a athe subject of P=2(a+b) b hthe subject of A=¼r^2 +2¼rh

c rthe subject of I=

E

R+r

d q the subject of A=

B

p¡q

e xthe subject of A=

3

2 x+y

f ythe subject of M=

4

x^2 +y^2

, y> 0

5 Makexthe subject of:

a y=

x

x+1

b y=

x¡ 3

x+2

c y=

3 x¡ 1

x+3

d y=

5 x¡ 2

x¡ 1

e y=

4 x¡ 1

2 ¡x

f y=

3 x+7

3 ¡ 2 x

g y=1+

2

x¡ 3

h y=¡2+

5

x+4

i y=¡ 3 ¡

6

x¡ 2

6 The formula for determining the volumeV of a sphere of radiusris V=^43 ¼r^3 :

a Makerthe subject of the formula.

b Find the radius of a sphere which has volume:

i 40 cm^3 ii 1 000 000cm^3.

7 The force of attraction between two bodies with massesm 1 kg andm 2 kg which aredmetres apart, is

given by F=G

m 1 m 2

d^2

Newtons, whereG=6: 7 £ 10 ¡^11 is the gravitational force constant.

a Makedthe subject of this formula, assuming d> 0.

b Find the distance between two bodies of mass 4 : 2 £ 1018 kg if the force of attraction between

them is:

i 2 : 4 £ 1010 Newtons ii 1 : 3 £ 106 Newtons.

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