(b) Amira takes 9 hours 25 minutes to complete a long walk. (i) Show that the time of 9 hours 25 minutes can be written as 113 1
2 answers:
You might be interested in
The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
The denominator is
Therefore
The real part of 1/ = 1/ (constant).
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
The denominator is
Therefore
The real part of 1/ = 1/ (constant).
Answer:
A dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
Step-by-step explanation:
To graph the solution set of the inequality 2x - 3y < 12, first plot the dashed line 2x - 3y = 12 (dashed because the inequality has sign < without notion "or equal to"). This line passes through the points (0,-4) and (3,-2) (their coordinates satisfy the equation of the line). this line has positive slope because
and the slope of the line is 2/3.
Now, identify where the origin is (in the region or outside the region). Substitute (0,0) into the inequality:
This means coordinates of the origin satisfy the inequality, so origin belongs to the shaded region. Thus, shade that part which contains origin.
