A9chsasaubj
3
C. Leech, Coventry University, June 2000. MATHEMATICS SUPPORT CENTRE Title: Changing the subject 2. Target: On completion of this worksheet you should be able to change the subject of formulae where the desired subject occurs more than once in the formulae. Sometimes when we are changing the subject of a formula the variable that we want to make the subject occurs more than once. In this case it is necessary to transform the formula so that the variable is only written once. We can do t his by • Getting all the terms with the variable on one side of the formula. • Taking the variable out as a common factor. Example. Make x the subject of t he formula a) cx + dx = m and b) xy = x – bx + c [ ] . ) ( ) ( ) d c m x d c m d c x a + = ⇒ + ÷ = + [ ] [ ] [ ] . 1 ) 1 ( ) 1 ( ) − + = ⇒ − + ÷ = − + ⇒ = − + ⇒ − + = + ⇒ + + − = b y c x b y c b y x c x bx xy x c x bx xy bx c bx x xy b Exercise. Make the letter in brackets the subject. 1. h ey by = + ( y) 2. ms t st ct = − + 3 (t ) 3. p x mx mnx 4 2 3 = − + ( x) 4. gs ft ys rt − = + (t ) 5. 5 4 3 + − = − sq tq p pq (q) (Answers: , 2 3 4 , 3 , − + = − + = + = m mn p x s c ms t e b h y .) 3 4 5 , s t p p q f r ys gs t + − + = − − − = It often simplifies a pro blem involving fractions if we first tr ansform the formula to one without fractions by multiplying the entire for mula by the denominator of the fraction. Example. Make x the subject of the formula . r x yx I + = [ ] [ ] [ ] . ) ( ) ( ) ( ) ( x I y Ir I y I y x Ir Ix yx Ir Ix yx Ir Ix yx r x I r x r x yx I = − ⇒ − ÷ − = ⇒ − = ⇒ − = + ⇒ = + ⇒ + × + =
Transcript of A9chsasaubj
7242019 A9chsasaubj
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7242019 A9chsasaubj
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983209C Leech Coventry University June 2000
Exercise
Make the letter in brackets the subject
1 d
sd g
+= (d )
2 p f
p f
d
D
minus+
= ( p)
3 2
222
y
r y x
minus= ( y)
4 g m M
l m M T
)2(3
)3(4
++
= π (m)
(Answers
(
1
22
)22
2 Dd
d D f p
g
sd
+minus
=minus
=
1
2 xr yminus
= ))8(6
)163(22
22
gT l l gT M m
minusminus=
π
π
Exercise
Make the letter in brackets the subject
1 plxmx += ( x)
2rcR L
uLm
+= ( L)
3S
neme P
22 minus= (e)
4 y
y xa+
=+2
( y)
5 K c
b K
x 53
241
+minus
= ( K )
(Answers mu
mrcR L
l m
p x
minus=
minus=
1
)(2
xa
xa y
nm
Pse
minusminus+
=minus
= )54
23
minus+
= x
bxc K
When powers and roots are involved we should
deal with them as late as possibleExample
Make p the subject of the formula
4
u gp
q pt g
minus+
=
[ ]
[ ]
[ ]
[ ]
4
44
4
4
44
4)(
)(4
4
4
2
2
222
22
222
22
2
2
2
minus
+=
minus
divide
+=
minus
+=minus
+=
minusminus
minus+=
minus
+=
minus
minustimesminus+
=
bullminus+
=
divideminus+
=
t
g g
t
g uq
p
t
g g
t
g uq
t
g g p
t
g uq p p
t
g g
t
g uq
t
g u p p
t
g g
pq p
t
g u p
t
g g
q pt
g u gp
u gpu gp
q p
t
g
u gp
q p
t
g
t u gp
q pt g
7242019 A9chsasaubj
httpslidepdfcomreaderfulla9chsasaubj 22
983209C Leech Coventry University June 2000
Exercise
Make the letter in brackets the subject
1 d
sd g
+= (d )
2 p f
p f
d
D
minus+
= ( p)
3 2
222
y
r y x
minus= ( y)
4 g m M
l m M T
)2(3
)3(4
++
= π (m)
(Answers
(
1
22
)22
2 Dd
d D f p
g
sd
+minus
=minus
=
1
2 xr yminus
= ))8(6
)163(22
22
gT l l gT M m
minusminus=
π
π
Exercise
Make the letter in brackets the subject
1 plxmx += ( x)
2rcR L
uLm
+= ( L)
3S
neme P
22 minus= (e)
4 y
y xa+
=+2
( y)
5 K c
b K
x 53
241
+minus
= ( K )
(Answers mu
mrcR L
l m
p x
minus=
minus=
1
)(2
xa
xa y
nm
Pse
minusminus+
=minus
= )54
23
minus+
= x
bxc K
When powers and roots are involved we should
deal with them as late as possibleExample
Make p the subject of the formula
4
u gp
q pt g
minus+
=
[ ]
[ ]
[ ]
[ ]
4
44
4
4
44
4)(
)(4
4
4
2
2
222
22
222
22
2
2
2
minus
+=
minus
divide
+=
minus
+=minus
+=
minusminus
minus+=
minus
+=
minus
minustimesminus+
=
bullminus+
=
divideminus+
=
t
g g
t
g uq
p
t
g g
t
g uq
t
g g p
t
g uq p p
t
g g
t
g uq
t
g u p p
t
g g
pq p
t
g u p
t
g g
q pt
g u gp
u gpu gp
q p
t
g
u gp
q p
t
g
t u gp
q pt g
