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andreev551 [17]
2 years ago
7

Find a cartesian equation for the curve. r = 9 sin(θ)

Mathematics
1 answer:
Paul [167]2 years ago
6 0
For this case we have the following equation:
 r = 9 sin (θ)
 In addition, we have the following change of variables:
 y = r * sine (θ)
 Rewriting the equation we have:
 r = 9 sin (θ)
 r = 9 (y / r)
 r ^ 2 = 9y
 On the other hand:
 r ^ 2 = x ^ 2 + y ^ 2
 Substituting values:
 x ^ 2 + y ^ 2 = 9y
 Rewriting:
 x ^ 2 + y ^ 2 - 9y = 0
 Completing squares:
 x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
 Rewriting:
 x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
 4x ^ 2 + (2y-9) ^ 2 = 81
 Answer:
 
The Cartesian equation is:
 
4x ^ 2 + (2y-9) ^ 2 = 81
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18) What value of x makes R(x) = 10
Illusion [34]
<h3>Two Answers:  <u>x = 2 and x = 10</u></h3>

========================================================

Explanation:

Draw a horizontal line through 10 on the y axis. This is because R(x) = 10 is the same as y = 10. The output of the function is the y value.

See the diagram below.

The horizontal line crosses the parabola at two locations. From those points, draw a vertical line straight down to the x axis. Note how we land at x = 2 and x = 10. This means that R(2) = 10 and R(10) = 10.

8 0
3 years ago
What is the length of x?
Marat540 [252]

Answer:

The length of 'x' is 4

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

The pythagorean theorem is:

a ^{2}  + b^{2}  =  {c}^{2}

a ^{2}  + b^{2} =  c^{2}  \\  {3}^{2}  +  {b}^{2}  = 5^{2}  \\ 9 +   {b}^{2}  = 25 \\  \frac{ - 9 \:  \:  \:  \:  \:  \:  \:  \:  =  - 9}{b ^{2}  =  \sqrt{16} }  \\ b = 4

Therefore x = 4

8 0
2 years ago
If c= the number of cars in a parking lot, which algebraic expression
DIA [1.3K]

Answer:

Option C) c+9 is correct

The sum of the number of cars and 9=c+9 is correct algebraic expression representation for given phrase

Step-by-step explanation:

Given that c=the number of cars in a parking lot.

The phrase given is "the sum of the number of cars and 9"

To find the algebraic expression which represents the given phrase :

The algebraic expression to the given phrase is c+9

That is option C) c+9 is correct

The sum of the number of cars and 9=c+9 is correct algebraic expression representation for given phrase

5 0
3 years ago
Please Complete the question.
Norma-Jean [14]

Answer:

0.0174 is the answer you are looking for

5 0
3 years ago
1. A fish is 12 meters below the surface of the ocean. What is its elevation? meters 2. A sea bird is 28 meters above the surfac
Vlad1618 [11]

Answer:

- 12 meters

28 meters

40 meters

Step-by-step explanation:

Given that:

A fish is 12 meters below the surface of the ocean. What is its elevation?

Position of fish = 12 meters below the surface = - 12 ;

Sea level = 0

Elevation = sea level + position

Elevation = 0 + (- 12)

= - 12 meters

2. A sea bird is 28 meters above the surface of the ocean. What is its elevation?

Position of bird = 28 meters below the surface = (28) ;

Sea level = 0

Elevation = sea level + position

Elevation = 0 + 28

= 28 meters

3. If the bird is directly above the fish, how far apart are they?

If bird is directly above the fish;

Distance between bird and fish :

Elevation of bird - elevation of fish

28 - (-12)

28 + 12

= 40 Meters

3 0
3 years ago
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