1answer.
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
oksian1 [2.3K]
3 years ago
9

Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b

y first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."

Mathematics
1 answer:
trapecia [35]3 years ago
7 0

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) \cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}

( 2 ) \sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}

These two identities makes sin(π / 10) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and cos(π / 10) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}.

Therefore cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, and sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}. Substitute,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right]

And now simplify this expression to receive our answer,

6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right] ÷ 2\sqrt{2}\left[0-i\right] = -\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i,

-\frac{3\sqrt{5+\sqrt{5}}}{4} = -2.01749\dots and \:\frac{3\sqrt{3-\sqrt{5}}}{4} = 0.65552\dots

= -2.01749+0.65552i

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}, sin(2π / 5) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}, cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}

We know that 6\sqrt{5+\sqrt{5}} = 16.13996\dots and -\:6\sqrt{3-\sqrt{5}} = -5.24419\dots . Therefore,

Solution : 16.13996 - 5.24419i

Which rounds to about option b.

You might be interested in
Given g(x) = 3x + 14 , find x if g(x) = 20
Helga [31]

Answer: x = 2

Step-by-step explanation: If g(x) = 3x + 14, and g(x) = 20 also, you first can set 3x+14 = 20. To find the value of x, you want to isolate the variable. You can subtract 14 from both sides to get 3x = 6. Finally, to find out the value of x, divide 3 from both sides. This leaves you with x = 2. You can check this by plugging two back into the original equation 3 times 2 = 6, and 6 plus 14 equals 20.

4 0
3 years ago
The measures of the angles of a triangle are shown in the figure below. solve for x.
Lina20 [59]

Answer:

33

Step-by-step explanation:

7 0
2 years ago
A house with a rectangle base is built on a plot of land. The southwest corner of the plot is designated with coordinates (0,0).
serious [3.7K]

Answer:

The width of the base of the house is 25 feet

The length of the base of the house is 35 feet

Step-by-step explanation:

Displayed in the attachment is the plot of land drawn out in WXYZ(not to scale)

With the southwest corner coordinate (0,0) as the reference point

Plotted out is the base of the house built on it with coordinates (20,20),(5,40),(33,61),(48,41)

With A and B labelled width and length respectively

Length between coordinates is given as

Length=√(〖(x2-x1)〗^2+(〖y2-y1)〗^2 )

To find the width A,the points with coordinates (20,20) and (5,40) are used or (33,61) and (48,41)

Using point with coordinates (20,20) and (5,40)

Width, A=√(〖(5-20)〗^2+(〖40-20)〗^2 )=35

with x1=20, y1=20, x2=5, y2=40

Also try using points with coordinates (33,61) and (48,41).You will get same answer(opposite sides of a rectangle are equal)

To find the length B,the points with coordinates (48,41) and (20,20) are used or (5,40) and (33,61)

Using point with coordinates (48,41) and (20,20)

Length,B=√(〖(48-20)〗^2+(〖41-20)〗^2 )=25

with x1=20, y1=20, x2=48, y2=41

Also try using points with coordinates (5,40) and (33,61).You will get same answer(opposite sides of a rectangle are equal)

3 0
3 years ago
there are 60 teams attend a chess tournament. every team will play with every other team exactly once. Supposed each team has a
Karolina [17]

The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³

The reason for arriving at the above probability is as follows:

The given parameters are;

The number of teams in the tournament, n = 60

The chance of a team winning a game = 50% = 0.5

The number of ties = No ties

The required parameter:

The probability that no two teams win the same number of games

Method:

Calculate the number of ways no two teams win the same number of games, and divide the result by the total number of possible outcomes

Solution:

The number of matches played, n = \dbinom {60} {2} = 1,770

The possible outcomes = 2; Winning or losing

The total number of possible outcomes, n_p = 2¹⁷⁷⁰

The number of games won by each team is between 0 and 59

The ways in which no two teams won the same number of games is given by the games won by the teams to be 0, 1, 2,..., 57, 58, 59

Therefore, the number of ways no two teams won the same number of games, the required outcomes, n_k = 59!

Probability = \dfrac{Number \ of \ possible \ outcomes}{Number \ of \ required\ outcomes}

The probability that no two teams win the same number of games is given as follows;

\mathbf{P(No \ two \ teams \ won \ the \ same \ number \ of \ games)} = \dfrac{n_k}{n_p}

Therefore;

P(No \ two \ teams \ won \ the \ same \ number \ of \ games) = \dfrac{59!}{2^{1,770}} \approx \mathbf{2.084 \times 10^{-453}}

The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³

Learn more about probability theory here:

brainly.com/question/1539712

3 0
2 years ago
What is the midpoint of the line segment with endpoints (–1, 7) and (3, –3)?
Kipish [7]
The coordinates consist of x coordinate and y coordinate
(x₁,y₁) = (-1,7)
(x₂,y₂) = (3,-3)

To find the midpoint of x coordinate, use this following formula
x midpoint = (x₁ + x₂)/2
x midpoint = (-1 + 3) / 2
x midpoint = 2/2
x midpoint = 1

To find the midpoint of y coordinate, use this following formula
y midpoint = (y₁ + y₂)/2
y midpoint = (7 + (-3))/2
y midpoint = (7 - 3)/2
y midpoint = 4/2
y midpoint = 2

ANSWER
The midpoint is (1,2)
6 0
3 years ago
Other questions:
  • Use a calculator to find the standard deviation of this data set:
    8·1 answer
  • Please help me<br><br> f(x) =3x^2 + 2x - 1 <br> what is f(5)
    13·2 answers
  • Combining like terms 6w+9w-4
    13·2 answers
  • Which of the following equations produces a linear function?
    6·1 answer
  • A cookie recipe calls for 6 cups of flour
    6·2 answers
  • Derek works at a lab with a huge circular particle accelerator. It has a diameter of 6 kilometers. What is the accelerator's rad
    13·1 answer
  • Tuition for one year at the University of Houston is about $12,300. Azul plans to attend this university and will save money eac
    15·1 answer
  • In his last football game, Sean rushed for 89 yards. If his season total is now 871 yards, how many total yards did he have to p
    5·2 answers
  • Which is the graph of y = x + 1 - 2?
    11·1 answer
  • A function is shown in the table.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!