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dimulka [17.4K]
3 years ago
11

Find an equation in rectangular coordinates for the cylindrical equation r = 2sintheta

Mathematics
1 answer:
frutty [35]3 years ago
3 0

Answer:

x^2+(y-1)^2=1

Step-by-step explanation:

The given cylindrical equation is

r=2\sin \theta

Multiply both sides by r.

r^2=2r\sin \theta           .... (1)

The required formulas are

x=r\cos \theta,y=r\sin \theta,r^2=x^2+y^2

Substitute r\sin \theta =y,r^2=x^2+y^2 in equation (1).

x^2+y^2=2y

x^2+y^2-2y=0

Add 1 on both sides.

x^2+(y^2-2y+1)=1

(x-0)^2+(y-1)^2=1^2                    [\because (a-b)^2=a^2-2ab+b^2]

It is the equation of a circle centered at (0,1) with radius 1.

Therefore, the equation in rectangular coordinates is x^2+(y-1)^2=1.

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3 years ago
‼️‼️10 points‼️‼️
My name is Ann [436]

Answer:

The correct answer is B.

Step-by-step explanation:

There is no clear rule regarding the relationship with these numbers. So it is not linear.

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7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
bagirrra123 [75]

The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

<h3>How to find the equation of a line?</h3>

The equation of a line can be represented as follows:

y = mx + b

where

  • m = slope
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Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

5x - 4 = 3y

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m₁ = 5 / 3

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m₂ = - 3 / 5

Hence,

using (-4, 5)

5 = - 3 / 5 (-4) + b

5 = 12 / 5 + b

b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5

Therefore,

y = -3 / 5 x + 13 / 5

learn more on equation of a line here: brainly.com/question/10727767

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Step-by-step explanation:

4 0
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X = 7 + 3y
pogonyaev
<h3>Given Equation:</h3>

x = 7 + 3y

or, x - 3y - 7 = 0 ........ (i)

5x + 6y = 14

or, 5x + 6y - 14 = 0 .........(ii)

<h3>To Find:</h3>

The value of x and y.

<h3>Solution:</h3>

By dividing eq. ii by 2, we get

5/2x + 3y - 7 = 0 ........ (iii)

By adding eq. i and eq. iii, we get

15/2x = 0

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