Answer: 8:9
Step-by-step explanation: Two find this answer, you need to see what will be the greatest number they can divide by (greatest common divider), it needs to be the same number for both 18 and 16. What number can go into both numbers, and is the greatest number? The answer is two, now you divide 2 by 18 and 16, so you'll get 8:9.
Hope this helps have a BLESSED and wonderful day! :-)
-Cutiepatutie
Answer:
(a) The graphic representation is in the attached figure.
(b)
.
(c)
.
Step-by-step explanation:
(a) Given a complex number
we know, from Euler's formula that
. So, it is not difficult to notice that
![|e^{i\theta}|^2 = \cos^2(\theta)+\sin^2(\theta) =1](https://tex.z-dn.net/?f=%7Ce%5E%7Bi%5Ctheta%7D%7C%5E2%20%3D%20%5Ccos%5E2%28%5Ctheta%29%2B%5Csin%5E2%28%5Ctheta%29%20%3D1)
so it is on the unit circumference. Also, notice that the Cartesian representation of the complex number is
.
Now,
.
Notice that
has the same modulus that
, so it is on the unit circumference. Beside, its Cartesian representation is
.
So, the points
and
are symmetric with respect to the X-axis. All this can be checked in the attached figure.
(b) Notice that
![e^{i\theta} + e^{-i\theta} = \cos(\theta)+i\sin(\theta) + \cos(\theta)-i\sin(\theta) = 2\cos(\theta)](https://tex.z-dn.net/?f=e%5E%7Bi%5Ctheta%7D%20%2B%20e%5E%7B-i%5Ctheta%7D%20%3D%20%5Ccos%28%5Ctheta%29%2Bi%5Csin%28%5Ctheta%29%20%2B%20%5Ccos%28%5Ctheta%29-i%5Csin%28%5Ctheta%29%20%3D%202%5Ccos%28%5Ctheta%29)
Then,
.
(c) Notice that
![e^{i\theta} - e^{-i\theta} = \cos(\theta)+i\sin(\theta) - \cos(\theta)+i\sin(\theta) = 2i\sin(\theta)](https://tex.z-dn.net/?f=e%5E%7Bi%5Ctheta%7D%20-%20e%5E%7B-i%5Ctheta%7D%20%3D%20%5Ccos%28%5Ctheta%29%2Bi%5Csin%28%5Ctheta%29%20-%20%5Ccos%28%5Ctheta%29%2Bi%5Csin%28%5Ctheta%29%20%3D%202i%5Csin%28%5Ctheta%29)
Then,
.
Y = 2x + 3
y = -x + 6
2x + 3 = -x + 6
<u>+ x + x </u>
3x + 3 = 6
<u> - 3 - 3</u>
<u>3x</u> = <u>3</u>
3 3
x = 1
y = 2(1) + 3
y = 2 + 3
y = 5
(x, y) = (1, 5)
The third one. x is greater than it or equals to -7