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3 years ago

Solve for x -6x+14< -28 or 9x+15≤−12

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

8 0

$- 3 \geqslant x > 6$

Step-by-step explanation:

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Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

3 years ago

The probability that Shelly will go to a movie (event A) on Friday is 0.78, and the probability that Danielle will go to a movie

seropon [69]

The right answer for the question that is being asked and shown above is that: "c. Events A and B are dependent because P(A|B) = P(A) x P(B)."The probability that Shelly will go to a movie, given that Danielle goes to a movie, is 0.87.

5 0

4 years ago

Chad has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 4 minutes, what is the pr

scoray [572]

Answer:

first you add all the candies together to get 20 in the bag

2+11+7=20

jelly treat:

now we divide 11 by 20 to get a decimal

11/20= .55

multiply .55 by 100 to change it to a percentage

.55*100=55

first part of answer: He has a 55% chance of getting a jelly treat

mint stick:

divide 2 by 20 to get a decimal

2/20=.1

change .1 to a percent by multiplying by 100

.1*100=10

second part of answer: he has a 10% chance of getting a mint stick

Step-by-step explanation:

7 0

3 years ago

Simplify the expression - 3/6 - 5/7 can you show me how?

mote1985 [20]

-3/6 -5/7

-21/42 - 30/42

-51/42

- 51/42 = - 1 9/42

hope this help

3 0

3 years ago

Which expression can be used to convert 22 Australian dollars to US dollars?

STatiana [176]

Answer:

22 AUD × (1 USD)/(1.2 AUD)

Step-by-step explanation:

1.2 AUD = 1 USD

Divide both sides by 1.2 AUD.

(1.2 AUD)/(1.2 AUD) = (1 USD)/(1.2 AUD)

(1 USD)/(1.2 AUD) = 1

The conversion factor from AUD to USD is (1 USD)/(1.2 AUD)

Answer: 22 AUD × (1 USD)/(1.2 AUD)

4 0

3 years ago