Let z = 2 - 2√3 i. In polar form, we have
[tex]z = |z| e^{i\arg(z)}[/tex]
where
[tex]|z| = |2-2\sqrt3| = \sqrt{2^2 + (-2\sqrt3)^2} = 4[/tex]
[tex]\arg(z) = \tan^{-1}\left(-\dfrac{2\sqrt3}2\right) = -\tan^{-1}(\sqrt3) = -\dfrac\pi3[/tex]
Equivalently,
[tex]z = 4\left(\cos\left(-\dfrac\pi3\right) + i\sin\left(-\dfrac\pi3\right)\right)[/tex]
Let w be a complex number such that w ² = z. By DeMoivre's theorem,
[tex]z = 4\left(\cos\left(-\dfrac\pi3\right) + i\sin\left(-\dfrac\pi3\right)\right) \\\\ \implies z^{1/2} = 4^{1/2} \left(\cos\left(\dfrac{-\frac\pi3+2k\pi}{2}\right) + i \sin\left(\dfrac{-\frac\pi3+2k\pi}{2}\right)\right)[/tex]
where k ∈ {0, 1}. So the two square roots of z are
[tex]z^{1/2} = \begin{cases}2\left(\cos\left(-\dfrac\pi6\right) + i\sin\left(-\dfrac\pi6\right)\right) & \text{for }k=0 \\\\ 2\left(\cos\left(\dfrac{5\pi}6\right) + i\sin\left(\dfrac{5\pi}6\right)\right) & \text{for }k=1\end{cases}[/tex]
[tex]z^{1/2} = \begin{cases}2\left(\dfrac{\sqrt3}2 - \dfrac12 i\right) & \text{for }k=0 \\\\ 2\left(-\dfrac{\sqrt3}2 + \dfrac12 i\right) & \text{for }k=1\end{cases}[/tex]
[tex]\boxed{z^{1/2} = \begin{cases}\sqrt3 - i & \text{for }k=0 \\ -\sqrt3 + i & \text{for }k=1\end{cases}}[/tex]
If RS = x + 2 and ST = 2x, what is ST?
Answer:
ST = 2x
Step-by-step explanation:
if not please elaborate on the question.
Enter the missing values in the area model to find 6(8p-7)
Step-by-step explanation:
→ 6(8p - 7)
→ 48p - 42 ← ans.
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how is five hundred two thousand,seven and four hundredths written in expanded nataion?
Answer:
502,007.004
Step-by-step explanation:
because I smart middle schooler
Answer:
502,007.004
Step-by-step explanation:
because I smart middle schooler
What is the solution of |2x+5|<19?
Answer:
[tex]2x + 5 < 19 \\ 2x < 19 - 5 \\ 2x < 14 \\ x < 7[/tex]
Answer:
The result can be shown in multiple forms.
Inequality Form:
−12< x < 7
Interval Notation:
(−12,7)
Step-by-step explanation:
first write |2x+5|<19 as a piece wise
2x+5≥0
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
[tex]\frac{2x}{2}[/tex] ≥[tex]\frac{5}{2}[/tex] divide
x ≥−[tex]\frac{5}{2}[/tex] cancel common factor of 2
x ≥ −5/2.
To find the interval for the second piece, find where the inside of the absolute value is negative.
2x+5 < 0
substract by 5
2x < −5
divide by 2x
2x/2< −5/2
simplify to left side
x < −5 / 2
Simplify the right side.
x < −5/2
In the piece where 2x+5 is negative, remove the absolute value and multiply by −1
− (2x+5) < 19
Write as a piecewise.
{2x+5 <19 x ≥ − 5/2
− (2x+5) < 19 x <− 5/2
Simplify −(2x+5)<19.
{2x+5<19 x≥−5/2
−2x−5<19 x<−5/2
Solve 2x+5 < 19 when x ≥ −5/2.
2x+5<19 for x.
Move all terms not containing x to the right side of the inequality.
2x < 14
divide by 2
x < 7
Find the intersection of x < 7 and x ≥−5/2.
−5/2 ≤x <7
Solve −2x−5 <19 when x <−5/2.
Move all terms not containing x to the right side of the inequality.
−2x<24
divide by -2
x>−12
Find the intersection of x > −12 and x <−5/2.
Find the union of the solutions.
−12 < x < 7
find csc θ and sec θ if cot θ= 3/2 and cos θ>0
Since both cot(θ) and cos(θ) are positive, it follows that sin(θ) is also positive:
cot(θ) = cos(θ)/sin(θ) > 0 ===> sin(θ) > 0
Recall the Pythagorean identity:
sin²(θ) + cos²(θ) = 1
Multiplying both sides by 1/sin²(θ) yields another form of the identity,
sin²(θ)/sin²(θ) + cos²(θ)/sin²(θ) = 1/sin²(θ)
1 + cot²(θ) = csc²(θ)
so that
csc(θ) = + √(1 + cot²(θ))
csc(θ) = √(1 + (3/2)²)
csc(θ) = √13/2
By definition of cosecant, we have
csc(θ) = 1/sin(θ)
so that
sin(θ) = 2/√13
Then using the Pythagorean identity once more, we have
cos(θ) = + √(1 - sin²(θ))
cos(θ) = √(1 - (2/√13)²)
cos(θ) = 3/√13
so that, by definition of secant,
sec(θ) = 1/cos(θ)
sec(θ) = √13/3
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will give branliest to right answer
Answer:
i think it is b
Step-by-step explanation:
(w2x−3)÷10⋅z when w=−9, x = 2.7, and z=−2/5
[tex]\\ \sf\longmapsto \dfrac{w^2x-3}{10z}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(-9)^2(2.7)-3}{10(-2/5)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{81(2.7)-3}{-2(2)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{218.7-3}{-4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{215.7}{-4}[/tex]
Rounding up numerator[tex]\\ \sf\longmapsto \dfrac{216}{-4}[/tex]
[tex]\\ \sf\longmapsto -44[/tex]
Step-by-step explanation:
(-9)^2(2.7)-3/10(-2/5
= 81(2.7)-3/-2(2)
= 218.7-3/-4
= 215.7/-4
= -44
What is the sum of the first 50 terms in the sequence 4,-4,4,-4,4...?
Answer:
0
Step-by-step explanation:
If there is an even number of 4 and -4s. They should all cancel each other out and equal 0.
When reading a data set in ascending order (from smallest value to largest value), which of the following is the correct order of values that you would observe:
20th percentile, 1st quartile, 4th decile, median
30th percentile, median, third quartile, 6th decile
2nd decile, median, 1st quartile, 70th percentile
10th percentile, third quartile, median, 8th decile
Answer:
el equivalente a 23.79 no daré explicación
Select all the equations that are true.
83=43= 210
0 112 = 83= 135
25= 34 = 3.5
0123 = 62 = 27
111=1
=
Find the area and perimeter.
5.6 cm
Answer:
A= 5.6 x 5.6 = 31.36
P= 5.6 × 4 = 22.4
Step-by-step explanation:
to find the area of a square, just take the length of 1 side and square it (A= length^ 2)
to find the perimeter of a square multiply length by 4 sides.
*these formulas only hold true for squares bc the length of each side is the same.
17 percent of what is 40
45 of 155 is what
What percent of 153 is 137
Answer:
Number 1 :If you are using a calculator, simply enter 40×100÷17, which will give you the answer.
Number 2: 45 percent of 155 is 69.75.
Number 3: 137 is what percent of 153? = 89.54
What is an equation of the line that passes through the points (-2, 1)(−2,1) and (-6, -5)(−6,−5)?
Answer:
ind the slope of the original line and use the point-slope formula y − y 1 = m ( x − x 1 )
to find the line parallel to x + 4y = 28 .
Step-by-step explanation:
Check all solutions to the equation. If there are no solutions, check "None."
x1 = 2
Someone please help ASAP!
Answer:
C -2
Step-by-step explanation:
it's -2 since lxl = -2 or 2
Last quarter Rachel earned a grade of 92. This quarter she earned an 88. What is the percent decrease in her grade?
Answer:
[tex]$4.\overline{54}[/tex]
Step-by-step explanation:
The percent decrease is [tex]$92/88-1=23/22-1=1/22=4.5454545...$[/tex].
So, the answer is [tex]$\boxed{4.\overline{54}}$[/tex] percent decrease.
help please this is kinda difficult .
im pretty sure that the slope for both lines would be 2
Wich of the following powers is the same as 2^5
None. There is no solution. None of them are equal. 2 to the fifth power is 32.
Most of them equal to something above 80 or are between 50 and 200.
Following the October 15, 2019, fourth Democratic debate, Drudge Report ran an online poll on its website and asked readers who won the debate. A total of 208,001 votes were cast, with Gabbard receiving 79,881 votes (38%), Yang receiving 37,944 votes (18%), Buttigieg receiving 25,337 votes (12%), Warren receiving 14,405 votes (7%), Kloubachar receiving 13,142 votes (6%), Biden receiving 11,246 votes (5%), Steyers receiving 7,791 votes (4%), Sanders receiving 7,672 votes (4%), and the remaining candidates each receiving 1% or fewer votes. The sample size for this poll is much larger than is typical for polls such as the Gallup Poll. Explain why the poll may give unreliable information about the voting population, even with such a large sample size.
Although the sample size for the poll is much larger than is typical for polls such as the Gallup Poll, the poll may give unreliable information about the voting population, even with such a large sample size, due to the following reasons:
First, it is an online survey, where the interviewer does not decide who to interview and, therefore, the sample from which the result is obtained has not passed through the necessary heterogeneity filters. Second, because even in the case of a large number of people, since these voters are voluntary, there is no certainty that their responses are objective or neutral, which affects the final result.
Learn more in https://brainly.com/question/1590463
It is claimed that 79% of all Americans live in cities with population greater than 100,000 people.
Based on this, if 41 Americans are randomly selected, find the probability that
a. Exactly 30 of them live in cities with population greater than 100,000 people.
b. At most 33 of them live in cities with population greater than 100,000 people.
c. At least 34 of them live in cities with population greater than 100,000 people.
d. Between 28 and 33 (including 28 and 33) of them live in cities with population greater than
100,000 people.
Find the value of x.........
Answer:
Would x not be 70 degrees as it corresponds to the 70 on the bottom line?
Step-by-step explanation:
Solve 2^2 + x - 4 = 0.
Answer:
x=0
Step-by-step explanation:
2^2 + x - 4 = 0
2^2 = 4
4+x-4 = 0
Combine like terms
x=0
Pa help pleas ineed po
Answer:
As shown in the attachment,
Step-by-step explanation:
refer to the attachment
A farmer is enclosing a square area for his pigs as shown below. Use the formula A = s to the second power to find the area of the pig pen.
The area of the given figure that is mentioned is 64.
A square has congruent angles on each side. The square's area is thus equal to its square divided by its side length.
Let a represent the square's side length. The area of the square will be calculated as:
Area of the square = a² square units
The side provided is 8 ft
The area will be
= a²
= 8²
=64
More about the area of the square here,
https://brainly.com/question/1658516
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Explain how you can take an imaginary number and multiply it by another imaginary
number and get a real number.
Answer:
When you multiply two imaginary numbers, you are essentially multiplying them by itself or squaring them. If we recall, an imaginary number is the square root of -1. By squaring this number, you're eliminating the square root, ending up with -1 (aka a real number).
Graph system of inequalities
Y>|2/3x-3
Y>|-4/3x+3
The Graphs are in attachment !
1st graph is for equation :
[tex]y > \dfrac{2}{ 3}x - 3[/tex]2nd graph is for equation :
[tex]y > - \dfrac{4}{3} x + 3[/tex]Given system of inequalities:-
[tex]y = \frac{2}{3}x - 3[/tex]
and
[tex]y = \frac{ - 4}{3}x + 3[/tex]
So, the graph for the given system of inequalities is attached along with this answer.
Please refer the attachment for the graph.
✍️ By Benjemin ☺️
Pls i need this as soon as possible
8) Cashews cost $8.90 per pound. If Austin buys 2.45 pounds of cashews, what is the total cost?
Round to the nearest.cent.
$
Answer:
9.00 and 2.00
Step-by-step explanation:
8.90 rounds to 9.00 because 8.90 is more than more then 0.50 so it makes the cents round to the nearest cent. 2.45 round to 2.00 because 2.45 is less than 0.50
I recently had work done on my car. The estimate was $234.78 but the actual was $365.99.
What is the relative error in the estimate?
Round to 2 decimal places.
Answer:
35.85%
Step-by-step explanation:
first, find the difference between the real value and the estimated value:
365.99 - 234.78 = 131.21
now divide the difference by the real value:
131.21 / 365.99 = 0.358507
now multiply 0.358507 by 100 to get a percentage, then round to 2 decimals:
35.85%
71 degrees Determine the value of x.
A) 109 degrees
B) 71 degrees
C) 142 degrees
D) 35.5 degrees
Answer:
A) 109 degrees
The answer is 109 degrees because each opposite angle added equals 180°. 180-71= 109
Good luck on your assignment ⊂(◉‿◉)つ