58
Basic Engineering Mathematics
b =a 1+b
Rearranging gives: Multiplying both sides by (1 + b) gives:
b = a(1 + b)
Removing the bracket gives:
b = a + ab
Rearranging to obtain terms in b on the LHS gives: b − ab = a
Dividing both sides by ( p − y − t) gives: q2 =
Taking the square root of both sides gives: r( y + t) q= p−y−t
b(1 − a) = a
Factorizing the LHS gives:
a b= 1−a
Dividing both sides by (1 − a) gives:
Problem 20. Transpose the formula V = the subject.
Er to make r R+r
D = Problem 22. Given that d terms of D, d and f .
f +p , express p in f −p
D f +p = f −p d f +p D2 = 2 f −p d
Rearranging gives:
Squaring both sides gives: Er =V R+r
Rearranging gives:
r( y + t) ( p − y − t)
Cross-multiplying, i.e. multiplying each term by d 2 ( f − p),
Multiplying both sides by (R + r) gives:
Er = V (R + r)
gives:
d 2 ( f + p) = D2 ( f − p)
Removing the bracket gives:
Er = VR + Vr
Removing brackets gives:
d 2 f + d 2 p = D2 f − D2 p
Rearranging to obtain terms in r on the LHS gives:
Rearranging, to obtain terms in p on the LHS gives:
Er − Vr = VR r(E − V ) = VR
Factorizing gives: Dividing both sides by (E − V ) gives:
r=
Problem 21. Transpose the formula y = to make q the subject
Rearranging gives: and
VR E−V
pq2 −t r + q2
Factorizing gives:
pq2 −t = y r + q2 pq2 = y+t r + q2
pq2 = ry + rt + q2 y + q2 t
Factorizing gives:
q2 ( p − y − t) = r( y + t)
p=
f (D2 − d 2 ) (d 2 − D2 )
Now try the following exercise Further problems on transposition of formulae (Answers on page 274)
Make the symbol indicated the subject of each of the formulae shown in Problems 1 to 7, and express each in its simplest form. 1. y =
a2 m − a2 n x
2. M = π (R4 − r 4 )
(a) (R)
r 3+r
(r)
4. m =
µL L + rCR
(L)
5. a2 =
b2 − c 2 b2
(b)
3. x + y =
Rearranging to obtain terms in q on the LHS gives: pq2 − q2 y − q2 t = ry + rt
p(d 2 + D2 ) = f (D2 − d 2 )
Dividing both sides by (d 2 + D2 ) gives:
Exercise 32
Multiplying both sides by (r + q2 ) gives: pq2 = (r + q2 )( y + t) Removing brackets gives:
d 2 p + D2 p = D2 f − d 2 f