Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
![*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)](https://tex.z-dn.net/?f=%2Az%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D%5B2%5E%7B5%7D%5D%5E%7B%5Cfrac%7B1%7D%7B5%7D%20%7D%20%28cos%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29%2Bisin%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29)
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
1.Sometimes
2.Sometimes
3.Always
Answer:
the perimeter is 152, the area is 910
Step-by-step explanation:
perimeter = 20+50+20+10+6+15+6+25
=152
area = (20×50)-(6×15)
= 1000-90
= 910
hope that helped!
<span> The place value
relationship of 0.5 and 0.05 in the given number
=> 0.5 and 0.05 are decimal numbers because they are place next to the
decimal points.
=> 0.5 placed next to decimal point is tenths and 0.05 is in hundredths.
Now, what’s the relation of both numbers?
=> 0.5 is 10 times greater than 0.05
=> How? Let’s try solving it
= 0.5 = 5/10
=> 0.05 = 5/100
=> 0.05 x 10 = 0.5
=> 0.5 + 0.05 = 0.55
</span>
The answer is y=(1/3)x+7, use y=mx+b and solve for b where m is slope
