De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
The correct question is
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8-x^-1 intersect are the solutions of the equation 4−x = 8-x^-1<span>.
Part B: Make tables to find the solution to 4−x = </span>8-x^-1<span>. Take the integer values of x between −3 and 3.
Part C: How can you solve the equation 4−x = </span>8-x^-1 graphically?
Part A. We have two equations: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two graphs will cross and that is the common point that satisfies both equations.
Part B
see the attached table
the table shows that one of the solutions is in the interval [-1,1]
Part C To solve graphically the equation 4-x = 8-x^-1
We would graph both equations: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
using a graph tool
see the attached figure N 2
the solutions are the points
(-4.24,8.24)
(0.24,3.76)
Answer:
categorical variable
Step-by-step explanation:
Solution:-
- This questions pertains to the type of data obtained after receiving responses from a questionnaire/survey.
- The options on the questionnaire/survey have been categorized according to key words, "Are you happy, indifferent, or unhappy with the performance per dollar spent on the Blu-ray. Giving us responses classified into 3 types of categories for how "satisfied" are you with the performance per dollar spent on Blu-ray.
- Category 1: Are you happy
Category 2: Are you indifferent,
Category 3: Are you unhappy
- Such type of data is quantized as "categorical variable".
Answer:
16.8 
Step-by-step explanation:
Find your answer by using the formula of a cone (v=
π
h)
r= 2 (half of your diameter, which is 4)
h= 4
By inserting your radius and height, you get v=
π(
)4.
Put that into a calculator and you get 16.75516, which rounds to 16.8.
Answer:
v
Step-by-step explanation: