Given:
The expression is:
![\dfrac{1}{2}(\cos (72)+i\sin (72))^5](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%28%5Ccos%20%2872%29%2Bi%5Csin%20%2872%29%29%5E5)
To find:
The
form for the given expression.
Solution:
According to De Moivre's theorem,
![(\cos \theta+i\sin \theta)^n=\cos (n\theta )+i\sin (n\theta )](https://tex.z-dn.net/?f=%28%5Ccos%20%5Ctheta%2Bi%5Csin%20%5Ctheta%29%5En%3D%5Ccos%20%28n%5Ctheta%20%29%2Bi%5Csin%20%28n%5Ctheta%20%29)
We have,
![\dfrac{1}{2}(\cos (72)+i\sin (72))^5](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%28%5Ccos%20%2872%29%2Bi%5Csin%20%2872%29%29%5E5)
Using De Moivre's theorem, we get
![=\dfrac{1}{2}(\cos (72\times 5)+i\sin (72\times 5))](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%28%5Ccos%20%2872%5Ctimes%205%29%2Bi%5Csin%20%2872%5Ctimes%205%29%29)
![=\dfrac{1}{2}(\cos (360)+i\sin (360))](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%28%5Ccos%20%28360%29%2Bi%5Csin%20%28360%29%29)
![=\dfrac{1}{2}(1+i(0))](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%281%2Bi%280%29%29)
![=\dfrac{1}{2}+0i](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%2B0i)
It is the
form of the given expression. Here,
.
Therefore, the required expression is
.
Answer:
4.4 inches
Step-by-step explanation:
Here, we are interested in calculating the value of x.
Mathematically, a line that comes from the center of the circle and extends to a chord, divides the chord into two equal parts.
This means what we have is a right angled triangle with the radius being the hypotenuse, the half of the length of the chord as the other side of the triangle.
3.7 is half the length of the chord i.e 7.4/2
Thus;
using Pythagoras’ theorem
x^2 = 2.4^2 + 3.7^2
Pythagoras’ posited that the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.
Thus;
x^2 =5.76 + 13.69
x^2 = 19.45
x = √(19.45)
x = 4.41 inches which is 4.4 inches to the nearest tenth
Collect and organize a set of data with between 20 and 30 values. Draw a dotplot<span> of the data; then determine the mode, the median, the mean and the </span>range<span> using the</span>dotplot<span>. Write an explanation of how you used the </span>dotplot<span> to determine each value. 2.</span>
hello again thanks for the points but why are you putting these questions because you passed the essay?
Area= 190
height= 2(width) - 1
area= length times width
190= (2(width) -1) x width
190 = 2w^2-w
w^2-w-190 = 0
use quadratic fomula, you'll get w= 10
so height will be 2(10)-1 = 19