answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lubov Fominskaja [6]
2 years ago
13

Find the fifth roots of 243(cos 300° + i sin 300°).

Mathematics
1 answer:
Stels [109]2 years ago
7 0
In looking for the fifth roots, we will use De Moivre's theorem.
The formula for this problem is z^5 = 243 (cos 300 degress + i sin 300 degrees)

Where you'll also need the following data:
300/5 = 60
360/5 = 72
- you'll input these two after the cos and i sin (60+k*72) where k = 0,1,2,3,4

solution:

z^5 = 243 (cos 300 degrees + i sin 300 degrees)
z= 243^1/5 (cos 300 degrees + i sin 300 degrees)
z= 3 (cos (60 + k*72) degrees) + (i sin (60 + k*72) degrees)

so the following are the roots:

3 (cos 60 degrees + i sin 60 degrees)
3 (cos 132 degrees + i sin 132 degrees)
3 (cos 204 degrees + i sin 204 degrees)
3 (cos 276 degrees + i sin 276 degrees)
3 (cos 348 degrees + i sin 348 degrees)
You might be interested in
1.An object falls from rest on a high tower and takes 5.0 s to hit the ground. Calculate the object’s position from the top of t
Arte-miy333 [17]
We will be using this equation for this problem
d = ut + ½.at²
<span>Given:</span>
<span>initial velocity, u = 0 (falling from rest) </span>
<span>acceleration, a = +9.80 m/s²(taking down as the convenient positive direction) </span>
<span>Time = 1.0s, 2.0s, 3.0s, 4.0s, 5.0s </span>

<span>Using .. d = ½.at² each time (each calculation is the distance from the top) </span>
<span>For 1.0s .. d = ½ x 9.80 x (1²) = 4.90 m </span>
<span>For 2.0s .. d = ½ x 9.80 x (2²) = 19.60 m </span>
<span>3.0s .. d = 44.10m (you show the working for the rest) </span>
<span>4.0s .. d = 78.40 m </span>
<span>5.0s .. d = 122.50m </span>

<span>Plot distance (displacement from the top) on the y-axis against time on the x-axis (label axes and give units for each).The line of best fit will be a smoothly upward curving line getting progressively steeper. Do not join graph points with straight lines.</span>
8 0
2 years ago
Read 2 more answers
Do the numbers show a pattern 11.23,10.75,10.3,9.82,9.37,8.89
sattari [20]

Answer:

is this a yes or no question

7 0
2 years ago
Beth wrote a system of equations to determine when a referee will earn the same salary working the East Conference and West Conf
notka56 [123]

Answer:

She is incorrect

Step-by-step explanation:

Step 1: substitute

135 into x in both equations

Step 2: Solve the equations. Once you do this you will get y = 5375 for the first one and y = 4720 for the second one, therefore she is incorrect

6 0
2 years ago
7+6x14-9=37 insert parentheses
d1i1m1o1n [39]

Answer:

7+6\times(14-9)=37

Step-by-step explanation:

The given expression is

7+6\times14-9

If we evaluate the expression as it is  we will get;

7+84-9=82

But we want to insert parenthesis so that we will use PEDMAS to obtain 37 as the result.

The only way this can be achieved is when we insert the parenthesis as shown below;

7+6\times(14-9)=7+6(5)=7+30=37

4 0
2 years ago
A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the
stiv31 [10]
Speed of current ------ y km/h 

<span>distance with the current = 4(x+y) </span>
<span>distance against the current = 5(x-y) </span>

<span>we know that 3.5(x+y) = 70 </span>
<span>x+y = 20 </span>

<span>but 4(x+y) = 4(20) = 80 </span>
<span>then 5(x-y) = 80 </span>
<span>x-y = 16 </span>

<span>x+y=20 </span>
<span>x-y=16 </span>
<span>add them </span>
<span>2x = 36 </span>
<span>x = 18 , then y = 2 </span>
5 0
2 years ago
Other questions:
  • sam lives in Massachusetts and wants to buy a television that costs $2000. the sales tax in Maine is only 5% which is less than
    10·1 answer
  • The point (-3/5,y)in the third quadrant corresponds to angle θ on the unit circle.
    9·2 answers
  • Paul wants to add new mulch to the top of all five garden beds. the new mulch will be 10 centimetres (cm) deep. about how much n
    6·2 answers
  • What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?
    10·2 answers
  • From $2003$ onward, the number of daily visitors to a website increased by $200\%$ every two years. So, for example, the number
    6·1 answer
  • Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyron
    15·2 answers
  • In Amy's garden the ratio of herbs to plants is 5:2. If there are 40 herb plants, how many vegetable plants are in her garden?
    12·1 answer
  • Mia has 1/2 of a pizza. She divides it equally among 4 people. Which model shows the fraction of a whole pizza each person gets
    14·1 answer
  • The graph shows a distribution of data.
    5·2 answers
  • We are told that the two players, taken together, scored a total of 49 points. What is the probability that player A scored firs
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!