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Lostsunrise [7]
2 years ago
12

Find the fourth roots of 256(cos 240° + i sin 240°).

Mathematics
1 answer:
Mashcka [7]2 years ago
8 0

Answer with Step-by-step explanation:

We are given that

We have to find the fourth roots of given complex number.

(256)^{\frac{1}{4}}=(4^4)^{\frac{1}{4}}=4^^{\frac{1}{4}\times 4}=4

By using the formula

(a^b)^x=a^{bx}

\theta=240^{\circ}

\theta=\frac{240}{4}=60^{\circ}

Angle of rotation=\frac{360}{4}=90^{\circ}

Therefore, the four roots of given complex number are

4(cos 60^{\circ}+i sin60^{\circ})

4(cos150^{\circ}+i sin150^{\circ})

4(cos240^{\circ}+isin 240^{\circ})

4(cos330^{\circ}+i sin330^{\circ})

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<em>5 or more round up, 4 or less round down
</em>As 1 is lower than 4, we round down.
36.11 therefore rounds down to 36.1
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3 years ago
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In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In th
KatRina [158]

This question is incomplete

Complete Question

In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?

a) 2x + 3x + 9

b) 2x + 3 + 9

c) 2x + 3x + 9x

d) 2 + 3x + 9

Answer:

a) 2x + 3x + 9

Step-by-step explanation:

Let the number of points shots a player scores = x

In a free throw, the player scored 9 points = 9

The player also scored a number of 2-point shots = 2x

In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half = 3x

The expression represents the total number of points the player scored in the game =

2x + 3x + 9

4 0
3 years ago
Liana can see that the measure of Angle L and Angle M form a straight line. Since Liana knows that a straight line has an angle
cricket20 [7]

Answer:

150 degrees

Step-by-step explanation:

Let's start off by looking at what we are working with in this specific problem:

We can see that we are looking at 2 angles, angle L and angle M, that add up to a total of 180 degrees (aka a straight line)

Now that we know that, we also have to keep is mind that angle L + angle M = 180 degrees.

Now that we've got all of that out of the way, let's set up a simple algebraic equation:

angle L + angle M = 180

We also know that angle L is 30 degrees so let's add it into the equation we have just created:

30 + angle M = 180

We now know that 30 plus angle M (whatever it might be) is equal to 180 so in order to solve this problem we have to do some simple subtraction.

180 - 30 = angle M

Now we are left with:

150 degrees = angle M

4 0
3 years ago
H is between points Q and R. QH=23 and HR=12. What is the length of QR
PSYCHO15rus [73]

Answer:

35

Step-by-step explanation:

Given:

GH = 23

HR = 12

Required:

Length big QR

SOLUTION:

Since H is a point in between points Q and R, points Q, H, R are collinear.

QH = 23

HR = 12

QH + HR = QR (segment addition postulate)

23 + 12 = QR (substitution)

35 = QR

Therefore, the length of QR is 35

3 0
3 years ago
Daisy is building a rectangular pen for her chickens along one wall in her back yard. She needs to build a fence
frosja888 [35]

Answer:

Daisy has one side of the rectangular pen along the wall, so she needs one width, w, and two lengths, 2ℓ. She has at most 125 feet of fencing materials to build the fence for her pen

1 second/24 frames

so if he started with 0 frames

time s = (1/24) (additional f)

but he already had at least 250 frames

so

time s = (1/24)( f-250) or maybe less time if he had more than 250

24 s </= f - 250

or

f >/= 24 s + 250

Step-by-step explanation:

7 0
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