Basic Engineering Mathematics, Fifth Edition

Revision Test 5 : Transposition and simultaneous equations

This assignment covers the material contained in Chapters 12 and 13.The marks available are shown in brackets at
the end of each question.

1. Transposep−q+r=a−bforb.(2)


2. Makeπthe subject of the formular=

c

2 π

(2)

3. TransposeV=

1

3

πr^2 hforh.(2)

4. TransposeI=

E−e

R+r

forE.(2)

5. Transposek=

b

ad− 1

ford.(4)

6. Makegthe subject of the formulat= 2 π

√

L

g

(3)

7. TransposeA=

πR^2 θ

360

forR.(2)

8. Make r the subject of the formula
   x+y=

r

3 +r

(5)

9. Make L the subject of the formula
   m=

μL

L+rCR

(5)

10. The surface area A of a rectangular prism is
    given by the formulaA= 2 (bh+hl+lb).Eval-
    uateb when A=11750mm^2 ,h=25mm and
    l=75mm. (4)


11. The velocityvof water in a pipe appears in

the formula h=

0. 03 Lv^2

2 dg

.Evaluatev when

h= 0. 384 ,d= 0. 20 ,L=80 andg=10. (3)

12. A formula for the focal length f of a convex
    lens is

1

f

=

1

u

+

1

v

.Evaluatevwhenf=4and

u=20. (4)

In problems 13 and 14, solve the simultaneous equa-

tions.

13. (a) 2x+y=6(b)4x−^3 y=^11
    5 x−y= 22 3 x+ 5 y= 30 (9)


14. (a) 3a− 8 +

b

8

= 0

b+

a

2

=

21

4

(b)

2 p+ 1

5

−

1 − 4 q

2

=

5

2

1 − 3 p

7

+

2 q− 3

5

+

32

35

= 0 (18)

15. In an engineering process two variablesxandy
    are related by the equationy=ax+

b

x

,wherea

andbare constants. Evaluateaandbify= 15

whenx=1andy=13 whenx=3. (5)

16. Kirchhoff’s laws are used to determine the current
    equations in an electrical network and result in the
    following:

i 1 + 8 i 2 + 3 i 3 =− 31

3 i 1 − 2 i 2 +i 3 =− 5

2 i 1 − 3 i 2 + 2 i 3 = 6

Determine the values ofi 1 ,i 2 andi 3 (10)