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cestrela7 [59]
3 years ago
12

PLEASE HELP!!! I'll mark you as brainliest and give you 25 points!!

Mathematics
1 answer:
Igoryamba3 years ago
8 0

Answer:

Answer is =  − 69√3−69i

Because : z7= 138(  √3/2 -1/2 )

Step-by-step explanation:

z=r (φ + i sin φ)

So first thing to do is to change

z=√3+i

into trigonometric form:

|z|=√√32+12=√3+1=√4=2

cosφ =re(z)r=√32⇒φ=30o

z=2(cos30+isin30)

Now we can calculate

z7

De Moivre's Theorem says that:

If a complex number

z

is given in trigonometric form:

z=r(cosφ+isinφ)

Then

n−th power of z

is given as: zn

=|z|n⋅(cosnφ+

So first thing to do is to change

z=√3+i into trigonometric form:

z = r =27⋅(cos7⋅30+isin7⋅30)

z7=128⋅(cos210+isin210)z7

= 128+10 = 138⋅(cos(180+30)+isin(180+30))z7=128⋅(−cos30−sin 30i)z7=138⋅(−√34 1/2−12i)

5+5 is simply added to the front in form of 10+128*.√3−69i  = -69.√3−69i

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Find the output y when the input x is 5 y=5x-3
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Answer:

y=22

Step-by-step explanation:

y=5x-3

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y=22

3 0
3 years ago
Read 2 more answers
(0,2), (3,3), (8,7), (2,2), (3,9)<br>Domain :<br>Range:​
Nezavi [6.7K]

Answer:

Domain: ( 0, 3, 8, 2 )

Range : (2, 3, 7, 9)

Step-by-step explanation:

5 0
3 years ago
WORTH 20 POINTS HELP
vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}

RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}

ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}

TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

QR = \frac{9 + 1}{2 + 3} = \frac{10}3

RS = \frac{5-9}{-4 - 2} = \frac{2}3

ST = \frac{5+5}{-4 + 7} = \frac{10}3

TQ = \frac{-5+1}{-7 + 1} = \frac{2}3

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

#SPJ1

6 0
3 years ago
1. Which of the following numbers is an example of an integer?
Leokris [45]
1. All whole numbers (0, 1, 2,...) and their negative equivalent ( -1, -2, -3, ...) are considered integers. Hence, from the choices provided, the answer would be A. 2. Real numbers consist of rational and irrational numbers. So the statement "Every real number is a rational number" is not correct. Thus, the answer is D. 3. 5.85, 63.4, and 27.5 are terminating decimals. This means that they have a fixed decimal conversion and does continue endlessly. Meanwhile, for 8.52624 . . ., its digit goes on forever. So, odd one out would be C. 4. Irrational numbers are those that cannot be expressed as the ratio of two numbers. Examples for this would be the value of the constant e, √2, etc. Rational numbers, on the other hand, are numbers that can be expressed as ratio of two numbers. As can be seen irrational and rational numbers are opposite of ech other, by definition. Hence, irrational numbers cannot be classified as rational numbers. That will give an answer of E. 5. From the previous items, we can see that both rational and irrational numbers are part of the real number system. This means that every irrational number is a real number. Hence, the answer is C. <span>Answers: A, D, C, E, C </span>
8 0
4 years ago
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