1. Option 4
2. Option 2
3. Option 2
4. Option 4 (not completely sure)
5. Option 2
6. Option 1 (not completely sure)
7. Option 4
8. <span>Isotopes are caused by different numbers of neutrons in the electron cloud
9. Not sure of the question
10. Positive charge
11. nucleus
</span>
It sounds like it’s true i don’t know tho i’m so sorry if it’s wrong
Answer:
∠ YZX ≈ 19.7°
Step-by-step explanation:
using the sine ratio in the right triangle.
sin YZX =
=
=
, then
∠ YZX =
(
) ≈ 19.7° ( to 3 significant figures )
Answer:
y=4
Step-by-step explanation:
From the graph we can see that-
when, x=-3 , y=4
That is , the graph passes through (-3 , 4)
So,
for x=-3 ,
we get y=4
So, the answer is y=4
Answer:
1+i
Step-by-step explanation:
To find the 8th roots of unity, you have to find the trigonometric form of unity.
1. Since
then

and

This gives you 
Thus,

2. The 8th roots can be calculated using following formula:
![\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bz%7D%3D%5C%7B%5Csqrt%5B8%5D%7B%7Cz%7C%7D%20%28%5Ccos%5Cdfrac%7B%5Cvarphi%2B2%5Cpi%20k%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B%5Cvarphi%2B2%5Cpi%20k%7D%7B8%7D%29%2C%20k%3D0%2C%5C%201%2C%5Cdots%2C7%5C%7D.)
Now
at k=0, ![z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;](https://tex.z-dn.net/?f=z_0%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%200%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%200%7D%7B8%7D%29%3D1%5Ccdot%20%281%2B0%5Ccdot%20i%29%3D1%3B)
at k=1, ![z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%201%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%201%7D%7B8%7D%29%3D1%5Ccdot%20%28%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3B)
at k=2, ![z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;](https://tex.z-dn.net/?f=z_2%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%202%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%202%7D%7B8%7D%29%3D1%5Ccdot%20%280%2B1%5Ccdot%20i%29%3Di%3B)
at k=3, ![z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};](https://tex.z-dn.net/?f=z_3%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%203%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%203%7D%7B8%7D%29%3D1%5Ccdot%20%28-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3B)
at k=4, ![z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;](https://tex.z-dn.net/?f=z_4%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%204%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%204%7D%7B8%7D%29%3D1%5Ccdot%20%28-1%2B0%5Ccdot%20i%29%3D-1%3B)
at k=5, ![z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};](https://tex.z-dn.net/?f=z_5%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%205%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%205%7D%7B8%7D%29%3D1%5Ccdot%20%28-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D-i%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D-i%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3B)
at k=6, ![z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;](https://tex.z-dn.net/?f=z_6%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%206%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%206%7D%7B8%7D%29%3D1%5Ccdot%20%280-1%5Ccdot%20i%29%3D-i%3B)
at k=7, ![z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};](https://tex.z-dn.net/?f=z_7%3D%5Csqrt%5B8%5D%7B1%7D%20%28%5Ccos%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%207%7D%7B8%7D%2Bi%5Csin%20%5Cdfrac%7B0%2B2%5Cpi%20%5Ccdot%207%7D%7B8%7D%29%3D1%5Ccdot%20%28%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D-i%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D-i%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3B)
The 8th roots are

Option C is icncorrect.