Answer:
After solving the power:

Rectangular form:

Step-by-step explanation:
Given the complex number:

To find:
The indicated power by using De Moivre's theorem.
The complex number in rectangular form.
Rectangular form of a complex number is given as
where a and b are real numbers.
Solution:
First of all, let us have a look at the De Moivre's theorem:

First of all, let us solve:
Let us apply the De Moivre's Theorem:
Here, n = 3
Now, the given complex number becomes:

Let us put the values of
and 

So, the rectangular form of the given complex number is:

Answer: Circumcenter
This is the center of the circle that goes through the three vertices of the triangle. This circle is known as the circumcircle. It is the smallest circle possible in which the circle encompasses the triangle and none of the triangle spills outside the circle.
Answer:
Stephen's claim is correct.
Step-by-step explanation:
The given function is

Put x=0 to find the y-intercepts.

The y-intercept of the function is at (0,15). It means jeremiah's statement is incorrect.
Put f(x)=0, to find the x-intercept.



The x-intercepts are at (-3,0) and (-5,0). It means Lindsay's statement is incorrect.




.... (1)
The vertex form of a parabola is
.... (2)
Where, (h,k) is vertex.
From (1) and (2) it is clear that the vertex of the parabola is (-4,-1), Stephen's claim is correct.
The midpoint between the x-intercepts is

The midpoint between the x-intercepts is at (-4, 0). It means Alexis's statement is incorrect.
Answer:
180.6 cubic inches. (Nearest tenth is the same as 1 decimal place)
Step-by-step explanation:
The volume of a cylinder formula is:
V
=
π
r
2
h
The diameter is
10
inches, well half of the diameter is
5
inches which is the radius. Radius is half of the diameter.
If you want the diameter back, just double it.
5
+
5
=
10
.
So we can now plug the numbers into the formula.
V
=
π
(
5
2
)
(
2.3
)
V
=
π
(
25
)
(
2.3
)
(5 Squared =25)
V
=
57.5
π
But if you didn't want it in terms of
π
, so you multiply:
57.5
×
3.14
=180.55
but rounding that to the nearest tenth is the same as rounding to
1 decimal place so you get
180.6 cubic inches.