The greatest counting number that divides 17, 25 and 41 and leaves the same remainder in each case is 8
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).
Answer: She should have asked more people.
Step-by-step explanation:
Given: Matilda asked 20 random people in the street if they would like to discuss what they want to do during the summer break.
Here sample size=20
We can see the sample is biased because the sample size is too small.
Through them we cannot decide the answer of the population.
She should have asked more people in the street if they would like to discuss what they want to do during the summer break. Then she need to make a list of their answers in approach to the answer.
We know that
Applying the law of cosines:
<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a,b and c are sides of the triangle and C is the angle opposite side c </span>
<span>that is </span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>
<span>solve for C </span>
<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500-57,600-40,000 = -96,000cos(C)
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)--------> C=38.53°°
<span>hence, </span>
<span>he should turn in the direction of island b by
180 - 38.53 </span><span>= 141.47 degrees</span>
Answer:
0 points
Step-by-step explanation:
So first we see that she gets 2 questions correct,
2 * 5 = 10
Then we see that she gets 5 questions wrong,
5 * -2 = -10
Then we see that she doesn't attempt three questions,
3 * 0 = 0;
Now we add up the points,
10 - 10 + 0 = 0 points