Answer:
A
Step-by-step explanation:
By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)
Answer:
b=7
Step-by-step explanation:
Answer:
quick question for you to change in what way do you want to be a good day at work and I don't know how to share with you and I don't
Answer:
djdjdjeueueuududhfh ch by by CV
Part A
The given expression is:
![(-5(1+2i)+3i(3-4i)](https://tex.z-dn.net/?f=%28-5%281%2B2i%29%2B3i%283-4i%29)
We expand to get:
![-5-10i+9i-12i^2](https://tex.z-dn.net/?f=-5-10i%2B9i-12i%5E2)
Note that ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
![12-5-10i+9i](https://tex.z-dn.net/?f=12-5-10i%2B9i)
![-5-10i+9i+12](https://tex.z-dn.net/?f=-5-10i%2B9i%2B12)
![7-i](https://tex.z-dn.net/?f=7-i)
Part Bi)
The given expression is;
![\sqrt{-50}](https://tex.z-dn.net/?f=%5Csqrt%7B-50%7D)
We simplify to get:
![\sqrt{25\times 2\times -1}](https://tex.z-dn.net/?f=%5Csqrt%7B25%5Ctimes%202%5Ctimes%20-1%7D)
![\sqrt{25\times} \sqr{2}\times \sqrt{-1}](https://tex.z-dn.net/?f=%5Csqrt%7B25%5Ctimes%7D%20%5Csqr%7B2%7D%5Ctimes%20%5Csqrt%7B-1%7D)
Note that:
![\sqrt{-1}=i](https://tex.z-dn.net/?f=%5Csqrt%7B-1%7D%3Di)
![5\sqr{2}i](https://tex.z-dn.net/?f=5%5Csqr%7B2%7Di)
This is now of the form
, where
.
This explains why it is a complex number;
Part bii)
The given expression is :
![\frac{\sqrt{-50} }{\sqrt{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B-50%7D%20%7D%7B%5Csqrt%7B5%7D%7D)
We simplify to get
![\sqrt{\frac{-50 }{5}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B-50%20%7D%7B5%7D%7D)
![\sqrt{-25}](https://tex.z-dn.net/?f=%5Csqrt%7B-25%7D)
![\sqrt{-25}=\sqrt{25}\times \sqrt{-1}](https://tex.z-dn.net/?f=%5Csqrt%7B-25%7D%3D%5Csqrt%7B25%7D%5Ctimes%20%5Csqrt%7B-1%7D)
![\sqrt{-25}=5\times i](https://tex.z-dn.net/?f=%5Csqrt%7B-25%7D%3D5%5Ctimes%20i)
![\sqrt{-25}=5i](https://tex.z-dn.net/?f=%5Csqrt%7B-25%7D%3D5i)
Part C
We want to simplify:
![i^{22}](https://tex.z-dn.net/?f=i%5E%7B22%7D)
We rewrite in terms of ![i^2](https://tex.z-dn.net/?f=i%5E2)
![i^{22}=(i^2)^{11}](https://tex.z-dn.net/?f=i%5E%7B22%7D%3D%28i%5E2%29%5E%7B11%7D)
![i^{22}=(-1)^{11}](https://tex.z-dn.net/?f=i%5E%7B22%7D%3D%28-1%29%5E%7B11%7D)
![i^{22}=-11](https://tex.z-dn.net/?f=i%5E%7B22%7D%3D-11)