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2 years ago

I’m in need of serious help I don’t know how to do this

Mathematics

2 answers:

Vinil7 [7]2 years ago

8 0

Line A horizontal slope, line B negative slope, line c vertical slope, line D undefined slope

Illusion [34]2 years ago

3 0

Answer:

Line A, (horizontal slope), Line B, (Negative slope) Line C, (Vertical slope) Line D, (Undefined slope)

Step-by-step explanation:

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Which expression is a fourth root of -1+isqrt3?

aleksklad [387]

Answer:

Step-by-step explanation:

$\sf n^{th}$ roots of a complex number is given by DeMoivre's formula.

$\sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}$

Here, k lies between 0 and (n -1) ; n is the exponent.

$\sf -1 + i\sqrt{3}$

a = -1 and b = √3

$\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}$

$\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}$

$\sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})$

$\sf = \dfrac{-\pi }{3}$

n = 4

For k = 0,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi }{12}+iSin \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]$

For k =1,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]$

For k =2,

$z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]$

For k = 3,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]$

For k = 4,

$\sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]$

4 0

1 year ago

Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of converge

tresset_1 [31]

Answer:

Radius of the convergence is R = $\frac{1}{21}$

and,

The Interval of convergence is $-\frac{1}{21}$

Step-by-step explanation:

Given function : Σ(21x)^k

Now,

Using the ratio test, we have

R = $\lim_{n \to \infty} |\frac{21x^{k+1}}{21x^{k}}|$

R = $\lim_{n \to \infty} |\frac{21x^{k}\times21x^{1}}{21x^{k}}|$

R = $\lim_{n \to \infty} |21x^{1}|$

now,

for convergence R|x| < 1

Therefore,

$\lim_{n \to \infty} |21x^{1}|$ < 1

$-\frac{1}{21}$

and,

Radius of the convergence is R = $\frac{1}{21}$

and,

The Interval of convergence is $-\frac{1}{21}$

8 0

2 years ago

Is this a reflection

myrzilka [38]

Answer:

yes

Step-by-step explanation:

it is reflected across the y axis

4 0

2 years ago

Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean

vovikov84 [41]

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so, when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e. $\sum(x - \bar x) = 0$

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

3 0

2 years ago

Need help asap!

Alik [6]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers