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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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
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6 / 12 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
Transcribed Image Text:6 / 12 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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