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
MissTica
3 years ago
10

Transform the following polar equation into an equation in rectangular coordinates: r=2 cos theta A. x + y = 2 B. y = 2x C. x =

2 D. (x-1)^2+y^2=1
Mathematics
2 answers:
Mila [183]3 years ago
8 0
r=2\cos\theta
r^2=2r\cos\theta
\implies x^2+y^2=2x
x^2-2x+y^2=0
x^2-2x+1+y^2=1
(x-1)^2+y^2=1
yuradex [85]3 years ago
8 0

Answer:

The correct option is D. (x - 1)² + y² = 1

Step-by-step explanation:

Given the equation in polar coordinates : r = 2 cosθ

To change the given equation in rectangular coordinates, we use the relation : x = r cosθ and y = r sinθ

⇒ x² + y² = r²

Now, r = 2 cosθ

Multiplying by r on both the sides

⇒ r² = 2r cosθ

⇒ x² + y² = 2x

⇒ x² - 2x + y² = 0

Making the variable x, the complete square by adding 1 on both the sides

⇒ x² - 2x + 1 + y² = 0 + 1

⇒ (x - 1)² + y² = 1

Hence, This is our required rectangular coordinate form of the given equation.

Therefore, The correct option is D. (x - 1)² + y² = 1

You might be interested in
Differentiate the equation to find the functions for <br> Velocity v= ds/dt
horrorfan [7]

Differentiation from First Principles is a formal method for determining a tangent's gradient.

<h3>What is meant by differentiation?</h3>

Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.

According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.

Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.

s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c

substituting the values t = 3, we get

s(-3) = (-cos(-3π))/π + c = 0

simplifying the above equation, we get

(-cos(3π))/π + c = 0

1/π + c = c

c = -1/π

Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.

The complete question is:

Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0

To learn more about Differentiation refer to:

brainly.com/question/954654

#SPJ13

7 0
1 year ago
4(h+11)-15<br> The solution
skad [1K]

Answer:

=4h+29

Step-by-step explanation:

I hope this helps you

7 0
3 years ago
Darren has a wooden board that is Three-fifths of a meter long. He cuts the board into 3 equal parts. How long is each section o
Alik [6]

Answer:

Each section of the board is 1/3 or 0.334(0.333333333333) of a meter

Step-by-step explanation:

3/5 divided by 3 is the equation we have to do.

3/5 divided by 3 is also equal to 3/5 times the reciprocal of 3 or 1/3

3/5 * 1/3

3*1 = 3

5*3 = 15

3/15 which can simplify to 1/3. (divide numerator and denominator by 3.)

Each section of the board is 1/3 or 0.334(0.333333333333) of a meter

8 0
2 years ago
a computer store bought a program at a cost of ​$10 and sold it at a selling price of ​$14. Find the percent markup.
GREYUIT [131]
The percent markup would be 40%. 10+40%=14

Hope this helps!
Can u plz mark me as brainliest? I really need it!
4 0
3 years ago
Read 2 more answers
hi friends..please help me..it's very urgent... please give the solutions of the given bits... please....​
Komok [63]
Hey I don’t know much of this but I really recommend you to re ask this question but choose the other option to talk to an expert :)
3 0
2 years ago
Other questions:
  • Question 9 i mark as brainliest ​
    10·2 answers
  • Is two ratios are formed at random from the four numbers 1,2,4, and 8 what is the probability that the rations are equal? Show w
    14·2 answers
  • A theater has 50 seats in the front row.There are 4 additional seats in each row following row. Write a rule to represent the nu
    13·1 answer
  • Solve the system. x – 4y – z = 21 6x – 3y – z = –4 –x +2y –5z = 19 Answer: x =      , y =      , z =      
    15·1 answer
  • Find the center and radius of the circle whose equation is x2 + y2 - 6x-2y+4= 0
    14·1 answer
  • 12) A family stayed at a hotel for n nights. The cost was $80 per night plus a one-time fee of $20. Write an expression that rep
    11·1 answer
  • 65 ppl are at a movie and if 40% of them purchase sodas, how many ppl is this that have a soda?
    13·2 answers
  • What is the graph of the step function f(x)=3⌊x⌋-4
    6·1 answer
  • Help me I don't understand
    9·1 answer
  • 1. Abbie is going out for pizza with her friends. For $60 total, they can buy p pizzas. Each
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!