84 Basic Engineering Mathematics
Rearranging gives
2gh = v
2
Dividing both sides by 2g gives
2gh
2g
=
v 2
2g
Cancelling gives
h =
v
2
2g
Problem 5. If I =
V
R
, rearrange to make V the
subject
I =
V
R
is Ohm’s law, where I is the current, V is the
voltage and R is the resistance.
Rearranging gives
V
R
= I
Multiplying both sides by R gives R
V
R
= R(I )
Cancelling gives
V = IR
Problem 6. Transpose a =
F
m
for m
a =
F
m
relates acceleration a, force F and mass m.
Rearranging gives
F
m
= a
Multiplying both sides by m gives m
F
m
= m(a)
Cancelling gives
F = ma
Rearranging gives
ma = F
Dividing both sides by a gives
ma
a
=
F
a
i.e.
m =
F
a
Problem 7. Rearrange the formula R =
ρ L
A
to
make (a) A the subject and (b) L the subject
R =
ρ L
A
relates resistance R of a conductor, resistivity ρ, conductor length L and conductor cross-sectional
area A.
(a) Rearranging gives
ρ L
A
= R
Multiplying both sides by A gives
A
ρ L
A
= A(R)
Cancelling gives
ρ L = AR
Rearranging gives
AR = ρl
Dividing both sides by R gives
AR
R
=
ρ L
R
Cancelling gives
A =
ρL
R
(b) Multiplying both sides of
ρ L
A
= R by A gives
ρ L = AR
Dividing both sides by ρ gives
ρ L
ρ
=
AR
ρ
Cancelling gives
L =
AR
ρ
Problem 8. Transpose y = mx + c to make m the
subject
y = mx + c is the equation of a straight line graph,
where y is the vertical axis variable, x is the horizontal
axis variable, m is the gradient of the graph and c is the
y-axis intercept.
Subtracting c from both sides gives
y − c = mx
or
mx = y − c
Dividing both sides by x gives
m =
y − c
x
Now try the following Practice Exercise
Practice Exercise 46 Transposing formulae
(answers on page 344)
Make the symbol indicated the subject of each of
the formulae shown and express each in its simplest
form.
1. a + b = c − d − e
(d)
2. y = 7x
(x)
3. pv = c
(v)
4. v = u + at
(a)
5. V = IR
(R)
6. x + 3y = t
(y)
7. c = 2πr
(r)
8. y = mx + c
(x)