Basic Engineering Mathematics, Fifth Edition

Answerstopracticeexercises 345

9.T=

I

PR

10. L=

XL

2 πf

11. R=

E

I

12. x=a(y− 3 )


13. C=

5

9

(F− 32 ) 14. f=

1

2 πCXC

Exercise 47 (page 87)

1.r=

S−a

S

or 1−

a

S

2.x=

d

λ

(y+λ)ord+

yd

λ

3. f=

3 F−AL

3

orf=F−

AL

3

4. D=

AB^2

5 Ey

5.t=

R−R 0

R 0 α

6. R 2 =

RR 1

R 1 −R

7. R=

E−e−Ir

I

orR=

E−e

I

−r

8.b=

√(

y

4 ac^2

)

9. x=

ay

√

(y^2 −b^2 )

10. L=

t^2 g

4 π^2

11. u=

√

v^2 − 2 as

12. R=

√(

360 A

πθ

)

13. a=N^2 y−x


14. L=

√

Z^2 −R^2

2 πf

, 0. 080

Exercise 48 (page 89)

1.a=

√(

xy

m−n

)

2. R=^4

√(

M

π

+r^4

)

3.r=

3 (x+y)

( 1 −x−y)

4. L=

mrCR

μ−m

5.b=

c

√

1 −a^2

6.r=

√(

x−y

x+y

)

7.b=

a(p^2 −q^2 )

2 (p^2 +q^2 )

8.v=

uf

u−f

, 30

9.t 2 =t 1 +

Q

mc

, 55 10.v=

√(

2 dgh

0. 03 L

)

, 0. 965

11. L=
    8 S^2
    3 d

+d, 2. 725

12. C=

1

ω

{

ωL−

√

Z^2 −R^2

}, 63. 1 × 10 −^6

13. 64mm 14. λ=^5

√(

aμ

ρCZ^4 n

) 2

Chapter 13

Exercise 49 (page 92)

1. x= 4 ,y= 2 2. x= 3 ,y= 4


2. x= 2 ,y= 1. 5 4. x=4,y= 1


3. p= 2 ,q=− 1 6. x= 1 ,y= 2


4. x= 3 ,y= 2 8. a= 2 ,b= 3


5. a= 5 ,b= 2 10. x= 1 ,y= 1


6. s= 2 ,t= 3 12. x= 3 ,y=− 2


7. m= 2. 5 ,n= 0. 5 14. a= 6 ,b=− 1


8. x= 2 ,y= 5 16. c= 2 ,d=− 3

Exercise 50 (page 94)

1. p=− 1 ,q=− 2 2.x= 4 ,y= 6


2. a= 2 ,b= 3 4.s= 4 ,t=− 1


3. x= 3 ,y= 4 6.u= 12 ,v= 2


4. x= 10 ,y= 15 8.a= 0. 30 ,b= 0. 40

Exercise 51 (page 96)

1. x=

1

2

,y=

1

4

2.a=

1

3

,b=−

1

2

3. p=

1

4

,q=

1

5

4. x= 10 ,y= 5


5. c= 3 ,d= 4 6.r= 3 ,s=

1

2

7. x= 5 ,y= 1

3

4

8. 1

Exercise 52 (page 99)

1.a= 0. 2 ,b= 4 2.I 1 = 6. 47 ,I 2 = 4. 62

3.u= 12 ,a= 4 ,v= 26 4.£15500,£12800

5.m=− 0. 5 ,c= 3

6.α= 0. 00426 ,R 0 = 22. 56 7.a= 12 ,b= 0. 40

8.a= 4 ,b= 10 9.F 1 = 1. 5 ,F 2 =− 4. 5

Exercise 53 (page 100)

1. x= 2 ,y= 1 ,z= 3 2. x= 2 ,y=− 2 ,z= 2


2. x= 5 ,y=− 1 ,z=− 2 4. x= 4 ,y= 0 ,z= 3