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Alika [10]
3 years ago
5

Describe the set of all complex numbers that are at a distance of 2 units from the origin.

Mathematics
1 answer:
Andreyy893 years ago
8 0

Answer:

The description of the set is A = \{s\in \mathbb{C}|\|s\| = 2\}.

Step-by-step explanation:

From Complex Analysis, we remember that complex numbers are numbers whose form is:

s = a+i\, b, a,b \in \mathbb{R} (1)

Where i = \sqrt{-1}.

In addition, the distance from the origin is defined by the following Pythagorean identity:

\|s\| = \sqrt{a^{2}+b^{2}} (2)

The following condition must be satisfied:

\|s\| = 2

Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:

A = \{s\in \mathbb{C}|\|s\| = 2\} (3)

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The area of a triangle is 150 cm^2. If the area of a triangle is given by the formula A=0/5b*h, write an equation which relates
taurus [48]

Answer:

Step-by-step explanation:

If the area of a triangle is 150cm^2, the formula would look like:

150=0.5b*h

So, if we were to solve for the base in terms of h, we'd simply divide both sides by 0.5b getting:

(150)/(0.5b)=h

which simplifies to

h=300b

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A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by
TiliK225 [7]
A=πr²

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first option is answer
6 0
3 years ago
(15 points!!) please help!! If you can answer the other questions on my page I will Venmo u!
Anon25 [30]

Answer:

y = (x - 3)² - 4      Vertex form

(3, -4)    Vertex

Step-by-step explanation:

f(x) = x² - 6x + 5

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y = (x - 3)² + 5 - 9

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7 0
3 years ago
Rewrite the Cartesian equation y=-3 as a polar equation.
andreev551 [17]

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

4 0
3 years ago
If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Se
viktelen [127]

Answer:

The sum of all exterior angles of BEGC is equal to 360° ⇒ answer F only

Step-by-step explanation:

* Lets revise some facts about the quadrilateral

- Quadrilateral is a polygon of 4 sides

- The sum of measures of the interior angles of any quadrilateral is 360°

- The sum of measures of the exterior angles of any quadrilateral is 360°

* Lets solve the problem

- DEGC is a quadrilateral

∵ m∠BEG = (19x + 3)°

∵ m∠EGC = (m∠GCB + 4x)°

∵ The sum of the measures of its interior angles is 360°

∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360

∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ add the like terms

∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ -3 from both sides

∴ 23x + 2m∠GCB + m∠CBE = 375

∵ The sum of measures of the exterior angles of any quadrilateral is 360°

∴ The statement in answer F is only true

3 0
3 years ago
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