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3 years ago

6y - 6 = 9x - 36 PLESSSSSS HELPPPPPPP

Mathematics

2 answers:

Bas_tet [7]3 years ago

4 0

Answer:

3x-2y=10

Step-by-step explanation:

Zepler [3.9K]3 years ago

3 0

Answer:

y= 3 /2 x−5

Step-by-step explanation: Brainlist:)

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Find all the complex roots. Write the answer in exponential form.

dezoksy [38]

We have to calculate the fourth roots of this complex number:

$z=9+9\sqrt[]{3}i$

We start by writing this number in exponential form:

$\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}$ $\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}$

Then, the exponential form is:

$z=18e^{\frac{\pi}{3}i}$

The formula for the roots of a complex number can be written (in polar form) as:

$z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1$

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

$r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}$

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

$\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})$

We can now calculate for each value of k:

$\begin{gathered} k=0\colon \\ z_0=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{0}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{0}{2}))) \\ z_0=\sqrt[4]{18}\cdot(\cos (\frac{\pi}{8})+i\cdot\sin (\frac{\pi}{8}) \\ z_0=\sqrt[4]{18}\cdot e^{i\frac{\pi}{8}} \end{gathered}$ $\begin{gathered} k=1\colon \\ z_1=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{1}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{1}{2}))) \\ z_1=\sqrt[4]{18}\cdot(\cos (\frac{5\pi}{8})+i\cdot\sin (\frac{5\pi}{8})) \\ z_1=\sqrt[4]{18}e^{i\frac{5\pi}{8}} \end{gathered}$ $\begin{gathered} k=2\colon \\ z_2=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{2}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{2}{2}))) \\ z_2=\sqrt[4]{18}\cdot(\cos (\frac{9\pi}{8})+i\cdot\sin (\frac{9\pi}{8})) \\ z_2=\sqrt[4]{18}e^{i\frac{9\pi}{8}} \end{gathered}$ $\begin{gathered} k=3\colon \\ z_3=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{3}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{3}{2}))) \\ z_3=\sqrt[4]{18}\cdot(\cos (\frac{13\pi}{8})+i\cdot\sin (\frac{13\pi}{8})) \\ z_3=\sqrt[4]{18}e^{i\frac{13\pi}{8}} \end{gathered}$

Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

5 0

1 year ago

At 6:00 A.M. the temperature was 33°F. By noon the temperature had increased by 10°F and by 3:00 P.M. it had increased another 1

chubhunter [2.5K]

So let's see here...

6:00 A.M. temperature is 33°F.

12:00 P.M temperature increased by 10°F making it 43°F.

3:00 P.M. temperature increased by another 12°F making it 55°F.

At 10:00 P.M it would decrease by 15°F making it 40°F.

The temperature would need to fall (or decrease) by 7°F to reach the original temperature of 33°F

Hope this helped!

3 0

3 years ago

Match each table with the equation that represents the same proportional relationship. Match each table with the equation that r

Alisiya [41]

29 tables of relationships is the answer to your equation above … THANK ME LATER

7 0

3 years ago

A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. how far will it travel in 21 minutes? in 1 hour?

GaryK [48]

Answer:

Step-by-step explanation:

1¾ miles/(2⅓ minutes) = (7/4 miles)/(7/3 minutes) = ¾ mile/minute

21 minutes × ¾ mile/minute = 15.75 miles

60 minutes × ¾ mile/minute = 45 miles

8 0

3 years ago

Betty can travel 61 centimeters in 5 minutes. Please calculate Betty's rate of speed. (round to 2 decimal places)

iren [92.7K]

Answer:

61/5= 12.2 centimeters per minute

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers