Algebraic Methods for Analytical Methods for Engineers

MODULE TITLE: ANALYTICAL METHODS FOR ENGINEERS
TOPIC TITLE: ALGEBRAIC METHODS
TUTOR MARKED ASSIGNMENT 1 (v2.1)

1. Formula manipulations and calculations
a) Making v the subject of the formula:
f = uv
u+v multply by ( u+ v ) both sides fu+ fv=uv rewritefu=v ( u−f ) divide by ( u−f ) both sides
v= fu
u−f
b) Finding the value of x in:
3.42 x+3=8.5ln ( 3.42 x+3 ) =ln ( 8.5 )( 2 x+3 ) ln (3.4 )=ln ( 8.5 )2 x+3= ln ( 8.5 )
ln ( 3.4 ) x=
ln ( 8.5 )
ln ( 3.4 ) −3
2
¿−0.6256295444
c) Finding the value of t, when θ= 58, V= 255, R= 0.1 and L= 0.5 in;
θ=V e
−Rt
L Maket the subject of the formula e
− Rt
L = θ
V
−R
L t=ln ( θ
V )t=
ln ( θ
V )
−R
I
=
ln ( 58
255 )
−0.1
0.5
∴ t=7.404102673
d) Finding L, if ω= –2.6, L0= 16 and h= 1.5, in:
ω= 1
h ln ( L
L0
−1 ) make Lthe subject of the formulaln ( L
L0
−1 )=ωh L
L0
−1=eωh
L=L0 ( eωh+ 1 )
∴ L=16 ( e−2.6 × 1.5+ 1 )=16.32387058
2. Division of a polynomial.
a) Determining the quotient using long division
3 x3−5 x2 +10 x+ 4
3 x+1 ∴ 3 x3−5 x2+10 x +4
3 x +1 =x2−2 x+ 4
b) Proofing