Engineering Mathematics - Solved Assignments and Study Material

Engineering Mathematics
Student Name:
Instructor Name:
Course Number:
16th September 2019

Question #1:
a. Simplify the following expressions:
15 p4 q2 r
5 p q5 r =3 p3
q3 =3 p3 q−3
−16 N−2 ( N T 2 )
−2 N0 T−1 =8 N−2 ( N T2 ) T =8 N−1 T3
−35 x−1 y ( x2 y )
5 x y−1 =−7 x−2 y2 ( x2 y )=−7 y3
b. Change numbers in ordinary notation to scientific notation, or vice versa:
A certain computer has 60,000,000,000,000 bytes of memory =
6.0 ×1013 bytes of memory
Police radar has a frequency of 1.02 ×109 Hz = 1,020,000,000 Hz.
c. Solve for the indicated parameter:
V =π r2 L, for L
L= V
π r2
P= π2 EI
L2 , for E
E= P L2
π2 I
Z2
(1− λ
2a )=k , for λ
Z2
( 2 a−λ
2 a ) =k
2 a Z2−λ Z2
2 a =k
2 a Z2− λ Z2=2 ka
λ Z2=2 a Z2−2 ak
λ Z2=2 a ( Z2−k )
λ= 2a ( Z2−k )
Z2
λ=2 a ( 1− k
Z2 )
d. Fire forest
Let the distance be x mi
Time taken to travel from the fire to the pond is x mi/h
105 mi/h = x
105 h
Time taken to travel from the pond to the fire is x mi/h
70 mi/h = x
70 h

Total time taken: x
105 h+ x
70 h=0.5 h
x
105 + x
70 =0.5
2 x +3 x
210 =0.5
2 x+3 x=0.5∗210
5 x=105
x= 105
5 =21
Time taken to travel from the pond to the fire is
x mi
h
70 mi
h
= x
70 h
¿ 21
70 h= 3
10 h=0.3 h=18 minutes
Therefore it takes 18 minutes to travel from the pond to the fire.
Question #2:
a. Determine the indicated angles:
1. ¿ CGE=1800−1480=320
2. ¿ EGF=1800− ( 900+320 ) =1800 −1220=580
3. ¿ DGH=¿CGE=320
4. ¿ EGI=320 + 900=1220
b. Find the perimeter and area of the following shapes:
Triangle of sides 175 cm, 138 cm, 119 cm
P=175+ 138+ 119
¿ 432 cm
A= √ s ( s−a ) ( s−b ) ( s−c )
s= 175+138+119
2 = 432
2 =216
A= √216 (216−175 ) ( 216−138 ) (216−119 ) = √216 ( 41 ) (78 ) ( 97 )= √ 67,004,496
¿ 8185.63
Circle: d = 98.4 mm
P=πD =22
7 ∗98.4
¿ 309.2571
A=π r2