help me please thanks

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Explanation:

We use De Moivre's Theorem. It says that if you started with

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

then raising both sides to the nth power leads to

[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

Learn more about the complex number here:

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Answer:

1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.

Step-by-step explanation:

2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.

To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.

8/20 + 15/20 = 23/20 or 1 3/20

Answer:

?????????

Step-by-step explanation:

What are u asking

Answer:

Step-by-step explanation:

what divided by 13 is 4​

4 * 13 = 52

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check

52 : 13 = 4

the answer is good

Answer:

52

Step-by-step explanation:

Answer:

355 ounces

Step-by-step explanation:

Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:

[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]

"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.

[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]

[tex]\frac{352oz}{1} + 3 = x[/tex]

[tex]352+3 = x[/tex]

[tex]x=355[/tex]

So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)

Answer:

180 667 777 98827

Step-by-step

the graaph has three differnt lines that connet

Answer:

Simplify the expression.

Exact Form:

28/15

Decimal Form:

1.8¯6

Mixed Number Form:

1 13/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Convert 2 1/3 to improper fraction

[tex]2\dfrac{1}{3}*\dfrac{4}{5}=\dfrac{7}{3}*\dfrac{4}{5}\\\\\\=\dfrac{7*4}{3*5}\\\\\\=\dfrac{28}{15}\\\\= 1\dfrac{13}{15}[/tex]

The solution is

The total amount for the lunch is given by the equation A = $ 45.648

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount for the lunch be represented as A

Now , the equation will be

The amount for the first lunch = $ 12.35

The amount for the second lunch = $ 14.22

The amount for the third lunch = $ 11.47

The percentage of tip = 20 %

So , the total amount for the lunch without tip = $ 12.35 + $ 11.47 + $ 11.47

On simplifying the equation , we get

The total amount for the lunch without tip = $ 38.04

The amount of tip = total amount for the lunch without tip x percentage of tip

Substituting the values in the equation , we get

The amount of tip = 38.04 x ( 20/100 )

The amount of tip = 38.04 x 0.20

The amount of tip = $ 7.608

So ,

The total amount for the lunch A = total amount for the lunch without tip +  amount of tip

Substituting the values in the equation , we get

The total amount for the lunch A = $ 38.04 + $ 7.608

The total amount for the lunch A = $ 45.648

Therefore , the value of A is $ 45.648

Hence , the total amount is $ 45.648

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Answer:  

Assuming the questions wants another form of 6x²+13x+5:

(2x+1)(3x+5) would work.

Step-by-step explanation:

Multiply (2x+1)(3x+5) and you'll get 6x^2+13x+5

Answer:

Observation

Step-by-step explanation:

He walked around seeing if every fifth person bought lunch

Survey - Requires asking questions

Simulation - Needs prior data to make an estimation

Experiment - Testing something

Observation - Just observing and watching

Study - Looking up data

The method he used to collect his data is observational method.

Observational study is usually chosen when the researches the system is likely to produce different result if interfered.

Sample survey is done if the population is too big to analyze or destructible as the analysis occurs.

Controlled experiment is done manually, specifically to deduce conclusions. Its steps are fixed.

Random experiment is done specifically to deduce conclusions, but it is done in a random manner.

We are given that;

He saw every fifth person in cafeteria

Now,

An observational study is a method of collecting data by observing and recording the behavior or characteristics of individuals or groups without interfering or manipulating any variables. Nico did not ask any questions or change any conditions, he just observed whether every fifth person in the cafeteria bought lunch or brought their own.

Therefore, by sampling the answer will be observational method.

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Step-by-step explanation:

Given length of diagonal of a cube = √12 cm Recall that length of diagonal of a cube = √3 × Length of edge of the cube ⇒ √12 = √3 × Length of edge of the cube ∴ Length of edge of the cube = √12 / √3 = 2√3 / √3 = 2 Thus the edge of the given cube is 2 cm

Answer:

26,530,000

Step-by-step explanation:

this is quite easy, first you can write this question differently

Just view this problem as 7 x 379 which is 2653, now count how many zeros 70,000 has, which is 4 and add it to the answer 2653, which will give you 26,530,000

The multiplication or products of 70,000 and 379 is 26,530,000

Given:

70,000 × 379

= 26,530,000

Where from the left,

In words, 26,530,000 is written as twenty six million, five hundred and thirty thousand.

Learn more about multiplication;

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Answer:

12 shirts

Step-by-step explanation:

I used the method keep, change, flip (KCF) to divide fractions and solve this problem.

This means Keep the first fraction, Change the division sign to a multiplication sign, and Flip the second fraction.

so keep 10 1/2, or 21/2, change sign, and flip the second fraction to 8/7.

that gives us the equation 21/2x8/7, and solving that gives us 168/14, or 168 divided by 14, so 12 shirts

Answer:

=34

Step-by-step explanation:

4x+12x-6=4(4x+7) ur question

using BODMAS

4x+12x-6=16x+28

16x-6=16x+28

16x-16x=28+6

0=34

but make sure your question is right, can you go through it again

Answer:

0.11<0.12<0.2<0.3

Step-by-step explanation:

Answer:

0.11, 0.12, 0.2, 0.3

Step-by-step explanation:

pls brainliesttt

143.25 °

is the correct answer.

please mark my answer as brainest and follow me to get the answer faster.

Answer:

16

Step-by-step explanation:

- 4 ( 5 - ( 36 ÷ 4 ) )

= - 4 ( 5 - 9 )

= - 4 ( - 4 )

= - 4 * - 4

= 16

Answer: cos(76°) ---> sin(14°)

9514 1404 393

Answer:

  (d)  The y-intercept of the graph of the relationship is ( 0, 1).

Step-by-step explanation:

The y-intercept of a proportional relation is always zero. If it is 1, the relationship must be non-proportional.

Answer:

-5 + -8 = -13

Step-by-step explanation:

-5 + -8 = -13

in total you owe $13 but seperat it’s $5 and $8.

also you show a debt with Integers by using negative numbers.

Answer:

Approximately [tex]12.9\; \rm km \cdot h^{-1}[/tex], assuming that this orbit is circular.

Step-by-step explanation:

The question is asking for a tangential velocity with the unit [tex]\rm km \cdot h^{-1}[/tex]. The unit of the given distance is already in [tex]\rm km[/tex] as required. Convert the unit of the orbital period to hours:

[tex]\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}[/tex].

Calculate the angular velocity [tex]\omega[/tex] of this planet from its orbital period:

[tex]\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}[/tex].

Given the radius [tex]r[/tex] of the orbit of this planet, the tangential velocity [tex]v_{\perp}[/tex] of this planet would be:

[tex]\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}[/tex].

If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: [tex]4.73\times 10^{3}\; \rm km \cdot h^{-1}[/tex].

Answer:

Step-by-step explanation:

Given polynomial function f(x) with:

With the least degree it is:

Answer:

-6

Step-by-step explanation:

Because 2×(-6) is - 12

Answer:

-24

Step-by-step explanation:

Answer:

Write an equation the represents the words.

6x - 7 = 4x + 9

To solve for x (the number), isolate it from the other variables.

Subtract 9 from both sides.

6x - 7 - 9 = 4x

Combine like terms.

6x - 16 = 4x

Subtract 6x from both sides.

-16 = 4x - 6x

Combine like terms.

-16 = -2x

Divide both sides by -2.

-16/-2 = x

x = 8

The number is 8.

Hope this helps! :)

Answer:

The number is 8.

Step-by-step explanation:

Hello there!

We're given an unknown number, let's call this number n

We know that 7 less than 6 times n is equal to 9 more than 4 times n

Let's break that statement down, starting with "7 less than 6 times n"

6 times n should be 6n, since 6 * n = 6n

"7 less" means subtraction.

So "7 less than 6n" should be 6n-7

Now with "9 more than 4 times n"

4 times n should be 4n, as 4 * n = 4n

"9 more" means addition

So "9 more than 4n" should be 4n+9

The statement says that 6n-7 is equal to 4n + 9, and so when we write it as an equation:

6n - 7 = 4n + 9

Now we can solve the equation

Subtract 4n from both sides

2n - 7 = 9

Add 7 to both sides

2n = 16

Divide both sides by n

n=8

The number is 8

PS. we can substitute 8 back into the equation as n to see if it works:

6(8)-7=4(8)+9

Multiply

48-7=32+9

41= 32 + 9

41=41

It works :))

Hope this helps!

Answer:

4x

Step-by-step explanation:

12x-9x

=4x

I hope my answer is correct

and if u like mark me as brainliest answer.

Answer:

12x - 9x

= 3x ( 4- 3)

= 3x ( 1)

= 3x

Answer:

Step-by-step explanation

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