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3 years ago

Can someone help and tell me how you got the answer

Mathematics

1 answer:

neonofarm [45]3 years ago

8 0

Answer:

x = 15

Step-by-step explanation:

x/3 + 10 =15

Subtract 10 from each side

x/3+10-10 =15-10

x/3 = 5

Multiply each side by 3

x/3*3 = 5*3

x=15

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Express the complex number in trigonometric form -6 + 6sqrt3i

marusya05 [52]

$\large\begin{array}{l}\\\\ \textsf{This is a complex number in }\mathsf{a+bi}\textsf{ form:}\\\\ \mathsf{z=-6+6\sqrt{3}\,i}\\\\ \textsf{where }\mathsf{a=-6~~and~~b=6\sqrt{3}.} \end{array}$

$\large\begin{array}{l}\\\\ \bullet~~\textsf{1}\mathsf{^{st}}\textsf{ step: Find the absolute value of z (complex modulus of z):}\\\\ \mathsf{|z|=\sqrt{a^2+b^2}}\\\\ \mathsf{|z|=\sqrt{(-6)^2+(6\sqrt{3})^2}}\\\\ \mathsf{|z|=\sqrt{36+36\cdot 3}}\\\\ \mathsf{|z|=\sqrt{36\cdot 108}}\\\\ \mathsf{|z|=\sqrt{144}}\\\\ \mathsf{|z|=12} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{2}\mathsf{^{nd}}\textsf{ step: Find the argument }\mathsf{\theta}\textsf{ of z:}\\\\ \mathsf{arg(z)=\theta}\\\\ \textsf{is an angle that satisfies the following conditions:}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{a}{|z|}=\dfrac{a}{\sqrt{a^2+b^2}}}\\\\ \mathsf{sin\,\theta=\dfrac{b}{|z|}=\dfrac{b}{\sqrt{a^2+b^2}}} \end{cases}\qquad\quad-\pi$

$\large\begin{array}{l}\textsf{For }\mathsf{z=-6+6\sqrt{3}\,i,}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{-6}{12}=-\,\dfrac{1}{2}}\\\\ \mathsf{sin\,\theta=\dfrac{6\sqrt{3}}{12}=\dfrac{\sqrt{3}}{2}} \end{cases}\\\\\\ \textsf{Since}\\\\ \mathsf{cos\,\theta0,}\\\\ \theta\textsf{ lies in the 2}\mathsf{^{nd}}\textsf{ quadrant.}\\\\\\\textsf{Therefore,}\\\\ \mathsf{\theta=\dfrac{2\pi}{3}~rad~~(120^\circ)} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{3}\mathsf{^{rd}}\textsf{ step: Express z in the trigonometric form:}\\\\ \begin{array}{rcl} \mathsf{z}&\!\!=\!\!&\mathsf{|z|\cdot (cos\,\theta+i\,sin\,\theta)}\\\\ \mathsf{-6+6\sqrt{3}\,i}&\!\!=\!\!&\mathsf{12\cdot \left(cos\, \dfrac{2\pi}{3}+i\,sin\,\dfrac{2\pi}{3}\right)\qquad\quad\checkmark} \end{array} \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154167

$\large\textsf{I hope it helps.}$

Tags: <em>complex number trigonometric form trig absolute value modulus argument angle</em>

4 0

3 years ago

At 7:17AM this morning, it was 83˚F outside. What is 83˚F in Celsius? What is 83˚F in Kelvin?

Temka [501]

Answer: 28.33 Celsius and 301.483 Kelvin

83°F − 32) × 5/9 = 28.333°C

(83°F − 32) × 5/9 + 273.15 = 301.483K

4 0

3 years ago

The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold f

OleMash [197]

Answer:

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

Step-by-step explanation:

Cost of tickets

Adults = $6

Teachers = $4

Students = $2

Total tickets sold = 280

Total revenue = $1010

Let

x = number of adults tickets

y = number of teachers tickets

z = number of students tickets

x + y + z = 280

6x + 4y + 2z = 1010

If the number of adult tickets sold was twice the number of teacher tickets

x = 2y

Substitute x=2y into the equations

x + y + z = 280

6x + 4y + 2z = 1010

2y + y + z = 280

6(2y) + 4y + 2z = 1010

3y + z = 280

12y + 4y + 2z = 1010

3y + z = 280 (1)

16y + 2z = 1010 (2)

Multiply (1) by 2

6y + 2z = 560 (3)

16y + 2z = 1010

Subtract (3) from (2)

16y - 6y = 1010 - 560

10y = 450

Divide both sides by 10

y = 450/10

= 45

y = 45

Substitute y=45 into (1)

3y + z = 280

3(45) + z = 280

135 + z = 280

z = 280 - 135

= 145

z = 145

Substitute the values of y and z into

x + y + z = 280

x + 45 + 145 = 280

x + 190 = 280

x = 280 - 190

= 90

x = 90

Therefore,

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

5 0

3 years ago

Please help!!!!!!!!!!!!!!!!!!!!!!

DENIUS [597]

Answer:

Try 30

Step-by-step explanation:

I really hope this helps have a great afternoon:)

3 0

2 years ago

At a grocery store, blue berries come packaged in 8-ounce containers for $2.80. At a farmers market, blueberries cost $4.20 for

Sever21 [200]

Answer: Grocery store

Step-by-step explanation:

I dont really get the question but i will do my best

If you buy two packs of blue berry at the store it would be $5.60 and it would be 16 pounds. the farm would be $8.40 for 28 ounces or 1 pound and 12 ounces

(are you trying to get 16 ounces?)

6 0

3 years ago