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
olga2289 [7]
2 years ago
14

Find the fifth roots of 32(cos 280° + i sin 280°).

Mathematics
1 answer:
ikadub [295]2 years ago
3 0
<span>Use the formula: r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ] where k = 0,1,2,3,4

</span><span>First 5th root: k = 0
r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ]
  (32)^(1/5)*[ cos( (280+360*k)/5 ) + i*sin( (280+360*k)/5 ) ]
  (32)^(1/5)*[ cos( (280+360*0)/5 ) + i*sin( (280+360*0)/5 ) ]
   2*[ cos( (280+360*0)/5 ) + i*sin( (280+360*0)/5 ) ]
  2*[ cos( (280+0)/5 ) + i*sin( (280+0)/5 ) ]
  2*[ cos( 280/5 ) + i*sin( 280/5 ) ]
  2*[ cos( 56 ) + i*sin( 56 ) ]
   -------------------------------------------------------------------
 Second 5th root: k = 1
  r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ]
  (32)^(1/5)*[ cos( (280+360*k)/5 ) + i*sin( (280+360*k)/5 ) ]
  (32)^(1/5)*[ cos( (280+360*1)/5 ) + i*sin( (280+360*1)/5 ) ]
  2*[ cos( (280+360*1)/5 ) + i*sin( (280+360*1)/5 ) ]
  2*[ cos( (280+360)/5 ) + i*sin( (280+360)/5 ) ]
  2*[ cos( 640/5 ) + i*sin( 640/5 ) ]
  2*[ cos( 128 ) + i*sin( 128 ) ]
 -------------------------------------------------------------------
 Third 5th root: k = 2
  r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ]
  (32)^(1/5)*[ cos( (280+360*k)/5 ) + i*sin( (280+360*k)/5 ) ]
  (32)^(1/5)*[ cos( (280+360*2)/5 ) + i*sin( (280+360*2)/5 ) ]
  2*[ cos( (280+360*2)/5 ) + i*sin( (280+360*2)/5 ) ]
   2*[ cos( (280+720)/5 ) + i*sin( (280+720)/5 ) ]
  2*[ cos( 1000/5 ) + i*sin( 1000/5 ) ]
  2*[ cos( 200 ) + i*sin( 200 ) ]
  -------------------------------------------------------------------
 Fourth 5th root: k = 3
  r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ]
  (32)^(1/5)*[ cos( (280+360*k)/5 ) + i*sin( (280+360*k)/5 ) ]
  (32)^(1/5)*[ cos( (280+360*3)/5 ) + i*sin( (280+360*3)/5 ) ]
  2*[ cos( (280+360*3)/5 ) + i*sin( (280+360*3)/5 ) ]
  2*[ cos( (280+1080)/5 ) + i*sin( (280+1080)/5 ) ]
  2*[ cos( 1360/5 ) + i*sin( 1360/5 ) ]
  2*[ cos( 272 ) + i*sin( 272 ) ]
   -------------------------------------------------------------------
 Fifth 5th root: k = 4
  r^(1/n)*[ cos( (theta+360*k)/n ) + i*sin( (theta+360*k)/n ) ]
  (32)^(1/5)*[ cos( (280+360*k)/5 ) + i*sin( (280+360*k)/5 ) ]
  (32)^(1/5)*[ cos( (280+360*4)/5 ) + i*sin( (280+360*4)/5 ) ]
  2*[ cos( (280+360*4)/5 ) + i*sin( (280+360*4)/5 ) ]
  2*[ cos( (280+1440)/5 ) + i*sin( (280+1440)/5 ) ]
  2*[ cos( 1720/5 ) + i*sin( 1720/5 ) ]
  2*[ cos( 344 ) + i*sin( 344 ) ]</span>
You might be interested in
Which of the following accurately lists all of the discontinuities for the graph below?
Murljashka [212]

Answer:

jump discontinuity at x = 0; point discontinuities at x = –2 and x = 8

Step-by-step explanation:

From the graph we can see that there is a whole in the graph at x=-2.

This is referred to as a point discontinuity.

Similarly, there is point discontinuity at x=8.

We can see that both one sided limits at these points are equal but the function is not defined at these points.

At x=0, there is a jump discontinuity. Both one-sided limits exist but are not equal.

3 0
2 years ago
Read 2 more answers
On Friday, there were x students at the baseball game. On Monday, there were half as many students at the game as there were on
Brut [27]

Number of tickets sold on
Friday = x tickets
Monday = (1/2) x
Wednesday = x - 32

8 0
2 years ago
Read 2 more answers
The table shows the number of hours of sleep all members of a theater group got the night before their musical.
Neko [114]

The Sample Mean of hours slept of the ten men asked is 8.4 hours.

The population Mean of hours slept of all the members of the theater group is 8.3 hours.

8 0
2 years ago
Read 2 more answers
Which statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied?
Sunny_sXe [5.5K]
I dont see any statements. When you multiply the two you get: 30x^2 - 26x -12.
8 0
2 years ago
The function f is continuous son the interval [2, 10] with some of its values given in the table below. Use a right Riemann Sum
Marta_Voda [28]

The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].

Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.

Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.

Then the integral is approximately

\displaystyle\int_2^{10}f(x)\,\mathrm dx\approx3\cdot2+8\cdot3+15\cdot2+18\cdot1=78

so 78.0 is the correct answer.

8 0
2 years ago
Read 2 more answers
Other questions:
  • Using a sheet of graph paper, solve the following system of equations graphically. Be sure to show any work, use a straight edge
    14·2 answers
  • Andy,Taylor and Ben share their team payment in a ratio of 1:3:4. What % dies Andy receive
    12·2 answers
  • Adante begins to evaluate the expression 3 and one-third times 5 and one-fourth using the steps below. 3 and one-third times 5 a
    7·2 answers
  • Kate had 70 brooms; Alisa had 20 more brooms than Kate. What was the ratio of Kate’s brooms to Alisa’s brooms?
    9·1 answer
  • A business school professor uses multiple choice tests. Each question on his exams has five possible answers which are assumed t
    13·1 answer
  • PLEASE HELP ASAP!!!! WILL MARK BRANLIEST!!!!!!!! Six friends, four boys, and two girls went to a movie theater. They wanted to s
    15·2 answers
  • An art teacher needs to buy at least 60 brushes for her class. The brushes are sold in packs of 8.
    10·1 answer
  • The result of which expression will best estimate the actual product of (Negative four-fifths) (three-fifths) (Negative StartFra
    6·1 answer
  • At a desert resort, the temperature at 7 a.m. was 3°C. The temperature increased by an average of 3.4°C each hour until it reach
    15·1 answer
  • A hair stylist knows that 87% of her customers get a haircut and 40% get their hair colored on a regular basis. Of the customers
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!