a) Given are the following three numbers in their respective bases: b = 4738, c = 9DA16 a = 1100111012, evaluate in the octal system. i) the sum a+b+c ii) the product ac iii) Convert each number into its decimal, along with the answer, to verify your result. b) A motor boat is set to head south-west from the mainland to the near island, lying approximately 30 km away. The journey should take 50 minutes. If a tide of 4 km/h flows from south-east direction and the wind blows from the north-north-east at 30 km/h, determine, using complex numbers, the maximum speed and the direction the boat should
a) Given are the following three numbers in their respective bases: b = 4738, c = 9DA16 a = 1100111012, evaluate in the octal system. i) the sum a+b+c ii) the product ac iii) Convert each number into its decimal, along with the answer, to verify your result. b) A motor boat is set to head south-west from the mainland to the near island, lying approximately 30 km away. The journey should take 50 minutes. If a tide of 4 km/h flows from south-east direction and the wind blows from the north-north-east at 30 km/h, determine, using complex numbers, the maximum speed and the direction the boat should
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Task 1
a) Given are the following three numbers in their respective bases:
a=
1100111012, b = 473g,
10
evaluate in the octal system.
i) the sum a+b+c
ii) the product ac
iii) Convert each number into its decimal, along wi the answer, to verify your result.
c) If Z₁ = −4+j8, Z₂ = −8 − j9, Z3 = 6x - 60° and Z4
i) Convert each number into its polar form
ii) Evaluate
b) A motor boat is set to head south-west from the mainland to the near island, lying approximately
30 km away. The journey should take 50 minutes.
If a tide of 4 km/h flows from south-east direction and the wind blows from the north-north-east at
30 km/h, determine, using complex numbers, the maximum speed and the direction the boat should
be headed.
e) By equating the real parts of
show that
75%
Z =
Also express
Y
iii) Evaluate ln(Z₁)
d) Determine the three cubmroots of the complex number (-10 + j6)5 in both polar and Cartesian
forms and show the roots on an Argand diagram.
Z₁ Z₂ Z3 Z4
Z1 Z2 Z3 Z4
cos 50
sin 50 as powers of sin 8.
= 16cos50
c = 9DA16
=
= 5x1.2
cos 50+ jsin 50 (cos+j sin 0)5
20cos³0+5 cos 0.
DELL
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