1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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
You might be interested in
How does the Counting Principle help when determining the sample space for a probability distribution?
andreyandreev [35.5K]

Answer:

This is also known as the Counting rule.

The Fundamental Counting Principle is used in determining all the possible outcomes and the total possible ways different events can be combined with each other. It is usually done by multiplying all the events together to get the total possible outcome. Doing this also helps in determining the sample space of a probability.

For example there are events a, b and c. The total sample space or possible outcome will be a*b*c.

7 0
3 years ago
Find the area of a circle with a diameter of six. Either enter an exact answer in terms of pie or use 3.14 for pie and enter you
miss Akunina [59]

Answer:

The area of the circle is 28.26

The area of the circle in terms of pi is 9π

Step-by-step explanation:

radius = half of diameter

d = 6

r = 6/2 = 3

To solve this problem we need to use the area formula of a circle:

a = area

r = radius = 3

π = pi

a = π * r²

we replace with the known values

a = π * (3)²

a = π * 9

a = 9π

The area of the circle in terms of pi is 9π

9 * 3.14 = 28.26

The area of the circle is 28.26

4 0
3 years ago
A line passes through the point (-3,-3) and has a slope of 1/2 what is the equation of the line ?
Bezzdna [24]

Answer:

y = 1/2x -1.5

Step-by-step explanation:

The equation of a line is typically written as y = mx + b.

m is the slope of the line, while b is the y-intercept. y is the y-coordinate and x is the x-coordinate.

Since it indicated that the line has a slope of 1/2, we can substitute the m in the equation with 1/2.

y = 1/2x + b

In order to find the intercept of the line, we use the equation of a line to substitute the y-coordinate and x-coordinate of (-3,-3) to discover the y-intercept of b.

-3 = 1/2(-3) + b

One half of -3 is -1.5.

-3 = -1.5 + b

Add -1.5 to both sides of the equation.

-3 = -1.5 + b

+1.5  +1.5

-1.5 = b

Since we found the y-intercept, we can now place it into our equation.

y = 1/2x -1.5 and that's the answer!

7 0
3 years ago
What is the formula for area of a quarter circle
GuDViN [60]

Answer:

πr²/4

Step-by-step explanation:

Area of a circle if πr²

so Area of a quarter of a circle (or 1/4 of a circle) = πr²÷4

3 0
3 years ago
1. Calculate the slope of a line going trough A (-4,3) and B (0,6)
lesya [120]
1. 1/2 2. 3 3. x=-1.5x+7.5
8 0
2 years ago
Other questions:
  • Give an example of a pair of independent event.
    15·1 answer
  • The graph of g(x) is the graph of f(x)=x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up.
    15·1 answer
  • Write as a fraction greater than 1 example 2 1/4
    9·1 answer
  • can someone simplify these like terms do not solv just simplify if you do not no how to do this do not try because i need this d
    10·2 answers
  • Linear or nonlinear <br><br><br> Will mark brainliest hurry
    14·2 answers
  • 25 points!! please answer
    13·2 answers
  • On a coordinate plane, an absolute value graph has a vertex at (negative 1, negative 3).
    11·2 answers
  • The question is in the picture (explain if u can pls)
    9·2 answers
  • Help :( explain the meaning of -500 in context to the problem,
    15·2 answers
  • Hannah sells computers. The amount of her monthly sales for the first half of the year are listed below:
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!