Basic Engineering Mathematics, Fifth Edition

84 Basic Engineering Mathematics

Rearranging gives^2 gh=v^2

Dividing both sides by 2ggives

2 gh

2 g

=

v^2

2 g

Cancelling gives h=

v^2

2 g

Problem 5. IfI=

V

R

, rearrange to makeVthe

subject

I=

V

R

is Ohm’s law, whereIis the current,Vis the

voltage andRis the resistance.

Rearranging gives V

R

=I

Multiplying both sides byRgives R

(

V

R

)

=R(I)

Cancelling gives V=IR

Problem 6. Transposea=

F

m

form

a=

F

m

relates accelerationa,forceFand massm.

Rearranging gives F

m

=a

Multiplying both sides bymgivesm

(

F

m

)

=m(a)

Cancelling gives F=ma

Rearranging gives ma=F

Dividing both sides byagives

ma

a

=

F

a

i.e. m=F

a

Problem 7. Rearrange the formulaR=

ρL

A

to

make (a)Athe subject and (b)Lthe subject

R=

ρL

A

relates resistanceRof a conductor, resistiv-

ityρ, conductor lengthLand conductor cross-sectional

areaA.

(a) Rearranging gives

ρL

A

=R

Multiplying both sides byAgives

A

(

ρL

A

)

=A(R)

Cancelling gives ρL=AR

Rearranging gives AR=ρl

Dividing both sides byRgives

AR

R

=

ρL

R

Cancelling gives A=

ρL

R

(b) Multiplying both sides of

ρL

A

=RbyAgives

ρL=AR

Dividing both sides byρgives

ρL

ρ

=

AR

ρ

Cancelling gives L=

AR

ρ

Problem 8. Transposey=mx+cto makemthe

subject

y=mx+cis the equation of a straight line graph,

whereyis the vertical axis variable,xis the horizontal

axis variable,mis the gradient of the graph andcis the

y-axis intercept.

Subtractingcfrom both sides gives y−c=mx

or mx=y−c

Dividing both sides byxgives m=

y−c

x

Now try the following Practice Exercise

PracticeExercise 46 Transposing formulae

(answers on page 344)

Make the symbol indicated the subject of each of

theformulaeshown and express each in its simplest

form.

1. a+b=c−d−e (d)


2. y= 7 x (x)


3. pv=c (v)


4. v=u+at (a)


5. V=IR (R)


6. x+ 3 y=t (y)


7. c= 2 πr (r)


8. y=mx+c (x)