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Gemiola [76]
1 year ago
15

Consider the line 3x - 4 y = 7.

Mathematics
1 answer:
Trava [24]1 year ago
3 0

Answer:

The slope of a line perpendicular to this line is -1/3. The slope of a line parallel to this line would be 3.

Step-by-step explanation:

Perpendicular lines have opposite(sign) and reciprocal slopes.

Parallel lines have the same slope.

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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
[Related Rates]
Orlov [11]
Below is the solution: 

A(final)=16cm^2 ds/dT=6 da/dT=? 

<span>A=(s)^2 A=16cm^2 , s=sqrt(A) , s=sqrt(16) , s=4cm </span>

<span>da/dT=2(s)(6cm/sec) , da/dT=12cm/sec(s) , da/dT=12cm/sec (4cm) 
</span>
<span>Answer should be da/dT=48cm^2/sec
</span>
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

6 0
3 years ago
Describe the steps you used to solve the equation and find the amount of Carrie’s allowance. Linear equation:  1/4 a + 1/3 a + 8
zzz [600]

Answer:24

Step-by-step explanation:

Subtract 8 from 22 = 1/4a+1/3a=14

Add the fractions together =7/12a=14

Divide 14 by 7/12 and a=24

4 0
3 years ago
Read 2 more answers
On Thursday a local shop sold a combination of 417 hamburgers and cheese burgers. The number of cheeseburgers sold was two times
seropon [69]

Answer:

The number of hamburgers sold was 139 and the number of cheeseburgers  sold was 278.

Step-by-step explanation:

Let

x -----> the numbers of hamburgers sold on Thursday

y -----> the numbers of cheeseburgers sold on Thursday

we know that

x+y=417 ----> equation A

y=2x ----> equation B

Substitute the equation B in equation A and solve for x

x+2x=417

3x=417

x=139

Find the value of y

y=2(139)=278

therefore        

The number of hamburgers sold was 139 and the number of cheeseburgers  sold was 278.

8 0
3 years ago
a decorative pillow is in the shape of a parallelogram. it's base is 28 centimeters, and it's height is 24.5 centimeters. what i
erica [24]
24.5•28=686 centimeters
7 0
3 years ago
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