ANSWER
a = 1.554
b = 1.258
![Z_1\text{ = }1.554\text{ + 1.258 i}](https://tex.z-dn.net/?f=Z_1%5Ctext%7B%20%3D%20%7D1.554%5Ctext%7B%20%2B%201.258%20i%7D)
EXPLANATION
Step 1: Given that:
![\text{ The absolute value or the modulus (r) = }|z_1|\text{ = 2}](https://tex.z-dn.net/?f=%5Ctext%7B%20The%20absolute%20value%20or%20the%20modulus%20%28r%29%20%3D%20%7D%7Cz_1%7C%5Ctext%7B%20%3D%202%7D)
![\text{The argument of the complex number (}\theta)=39^0](https://tex.z-dn.net/?f=%5Ctext%7BThe%20argument%20of%20the%20complex%20number%20%28%7D%5Ctheta%29%3D39%5E0)
Step 2: The rectangular form of a complex number is given by:
![Z_1\text{ = a + bi}](https://tex.z-dn.net/?f=Z_1%5Ctext%7B%20%3D%20a%20%2B%20bi%7D)
Step 3: Using basic trigonometric ratios to determine a and b
![\begin{gathered} \sin \text{ 39 = }\frac{b}{2} \\ b\text{ = 2 sin 39 = 1.258} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csin%20%5Ctext%7B%2039%20%3D%20%7D%5Cfrac%7Bb%7D%7B2%7D%20%5C%5C%20b%5Ctext%7B%20%3D%202%20sin%2039%20%3D%201.258%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \cos \text{ 39 = }\frac{a}{2} \\ a\text{ = 2 cos 39 = 1.554} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%20%5Ctext%7B%2039%20%3D%20%7D%5Cfrac%7Ba%7D%7B2%7D%20%5C%5C%20a%5Ctext%7B%20%3D%202%20cos%2039%20%3D%201.554%7D%20%5Cend%7Bgathered%7D)
Hence, the rectangular form of the complex number is:
![Z_1\text{ = }1.554\text{ + 1.258i}](https://tex.z-dn.net/?f=Z_1%5Ctext%7B%20%3D%20%7D1.554%5Ctext%7B%20%2B%201.258i%7D)
There’s no picture u should repost
Answer: The answer is 16√2 cm.
Step-by-step explanation: Given that there is a rectangle with length 3 times than its width. We are to find the perimeter of the rectangle.
Let 'w' represents the width of the rectangle.
Then, its length will be 3w.
Also, area of the rectangle = 24 square inches.
Therefore,
![3w\times w=24\\\\\Rightarrow 3w^2=24\\\\\Rightarrow w^2=8\\\\\Rightarrow w=2\sqrt 2.](https://tex.z-dn.net/?f=3w%5Ctimes%20w%3D24%5C%5C%5C%5C%5CRightarrow%203w%5E2%3D24%5C%5C%5C%5C%5CRightarrow%20w%5E2%3D8%5C%5C%5C%5C%5CRightarrow%20w%3D2%5Csqrt%202.)
So, width = 2√2 inches and length = 6√2 inches.
Thus, perimeter of the rectangle = 4√2 + 12√2 = 16√2 cm.
For this case we have a function of the form:
y = A (b) ^ x
Where,
A: initial amount
b: growth rate
x: time (in months)
We have the following equation:
f (x) = 15 (3) ^ x
We observed that:
b = 3
Therefore, the number of bees triples each month.
Answer:
b = 3
the number of bees triples each month.
The third one.
Simply divide one by 40, and add a negative sign.