15:7.5:30
This is because 15 is the smallest, which is half of 4(30). And right between 15 and 30 is 7.5.
Hope this helps
Answer:
hi.
Step-by-step explanation:
download photo math
The parametric equations seem to describe a circle of radius 3. Its area will be
A = πr² = π·3²
The appropriate choice seems to be
D. 9π
Answer:
44.3 is the one
Step-by-step explanation:
mark me and give my 5 start and heart
Answer:
See explanation
Step-by-step explanation:
The given complex number are:
![z_1=-3\sqrt{3}+3i](https://tex.z-dn.net/?f=z_1%3D-3%5Csqrt%7B3%7D%2B3i)
and
![z_2=6\cos 150\degree+6i\sin 150\degree](https://tex.z-dn.net/?f=z_2%3D6%5Ccos%20150%5Cdegree%2B6i%5Csin%20150%5Cdegree)
When we rewrite
in complex form, we obtain;
![z_1=r(\cos \theta+i\sin \theta)](https://tex.z-dn.net/?f=z_1%3Dr%28%5Ccos%20%5Ctheta%2Bi%5Csin%20%5Ctheta%29)
where
![r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28-3%5Csqrt%7B3%7D%29%5E2%2B3%5E2%20%7D%3D%5Csqrt%7B36%7D%3D6)
and
![\theta=tan^{-1}(\frac{y}{x})](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%28%5Cfrac%7By%7D%7Bx%7D%29)
![\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctheta%3Dtan%5E%7B-1%7D%28%5Cfrac%7B-3%5Csqrt%7B3%7D%7D%7B3%7D%29%3D150%5Cdegree)
Hence,
![z_1=6(\cos 150\degree+i\sin 150\degree)](https://tex.z-dn.net/?f=z_1%3D6%28%5Ccos%20150%5Cdegree%2Bi%5Csin%20150%5Cdegree%29)
![z_1=6\cos 150\degree+6i\sin 150\degree](https://tex.z-dn.net/?f=z_1%3D6%5Ccos%20150%5Cdegree%2B6i%5Csin%20150%5Cdegree)
Hence
![z_1=z_2](https://tex.z-dn.net/?f=z_1%3Dz_2)