Last night. Harry hero saved the lives of 12 people. If Harry hero does that every night for a year 365 days how many people wil
1 answer:
You might be interested in
Answer:
38.46%
Step-by-step explanation:
There are no names or marking that can make the calculator look different, so the order is not important. Then we should use a combination to solve this problem.
There are 40 calculators in one shipment, 37 of them good items and 3 of them are defect items. We need to choose 19 good calculators and 1 defect calculator. The number of ways to do that will be:
*
= 37!
= 53017895700
The number of possible ways to choose 20 calculators out of 40 calculators will be:
=
=137846528820
The chance will be: 53017895700/ 137846528820 = 0.3846= 38.46%
By using <span>De Moivre's theorem:
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴![\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bz%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%5C%20%28cos%20%5C%20%20%5Cfrac%7B%5Ctheta%20%2B%20360K%7D%7Bn%7D%20%2B%20i%20%5C%20sin%20%5C%20%5Cfrac%7B%5Ctheta%20%2B360k%7D%7Bn%7D%20%29)
k= 0, 1 , 2, ..... , (n-1)
For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>
Part (A) <span>find the modulus for all of the fourth roots
</span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root =![\sqrt[4]{z} = \sqrt[4]{81} = 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7Bz%7D%20%3D%20%20%5Csqrt%5B4%5D%7B81%7D%20%3D%203)
Part (b) find the angle for each of the four roots
The angle of the given complex number =
There is four roots and the angle between each root =
The angle of the first root =
The angle of the second root =
The angle of the third root =
The angle of the fourth root =
Part (C): find all of the fourth roots of this
The first root =
The second root =
The third root =
The fourth root =
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴
k= 0, 1 , 2, ..... , (n-1)
For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>
Part (A) <span>find the modulus for all of the fourth roots
</span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root =
Part (b) find the angle for each of the four roots
The angle of the given complex number =
There is four roots and the angle between each root =
The angle of the first root =
The angle of the second root =
The angle of the third root =
The angle of the fourth root =
Part (C): find all of the fourth roots of this
The first root =
The second root =
The third root =
The fourth root =