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
brilliants [131]
3 years ago
8

Express the equation in rectangular form a) r = 2sin(2Θ) b) r = 4cos(3Θ)

Mathematics
1 answer:
Dafna11 [192]3 years ago
5 0

Answer:

a.  sqrt(x^2+y^2) * (x^2+y^2) = 4xy

b.  (x^2+y^2)^2 = 4x{ (x^2 - 3 y^2}

Step-by-step explanation:

a) r = 2sin(2Θ)

r* = 2 sin 2 theta

We know  sin 2theta = 2 sin theta cos theta

r = 2 * 2 sin theta cos theta

sin theta = y/r  and cos theta = x/r

r = 4 y/r * x/r

r = 4xy / r^2

Multiply each side by r^2

r^3 = 4xy

r * r^2 = 4xy

We know r = sqrt(x^2+y^2)  and r^2 = (x^2+y^2)

sqrt(x^2+y^2) * (x^2+y^2) = 4xy

b) r = 4cos(3Θ)

we know that cos 3 theta = cos^3(theta) - 3 sin^2(theta) cos(theta)

r = 4 *cos^3(theta) - 3 sin^2(theta) cos(theta)

Factor out a cos theta

r = 4 *cos(theta){ cos^2 (theta) - 3 sin^2(theta) }

We know that  sin theta = y/r  and cos theta = x/r

r = 4 (x/r) { (x/r)^2 - 3 (y/r)^2}

r = 4 *(x/r) { (x^2/r^2 - 3 y^2/r^2}

Multiply by r

r^2 = 4x { (x^2/r^2 - 3 y^2/r^2}

Multiply by r^2

r^2 *r^2 = 4x { (x^2 - 3 y^2}

r^4 = 4x{ (x^2 - 3 y^2}

We know  r^2 = (x^2+y^2)

(x^2+y^2)^2 = 4x{ (x^2 - 3 y^2}

You might be interested in
Part A Mr. Bade spends an average of $42.50 during a five-day workweek on lunch.if he eats every day during his 5-day workweek,
trasher [3.6K]

Answer:

Part A: He spends an average of $8.50 per day

Part B:  He would save $17 per week

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
At what interest rate must you invest $4500 to have $7,000 after 6 years, if the interest is compounded quarterly?
labwork [276]

Answer:

The amount is $8358.7 and the interest is $3858.7.

Step-by-step explanation:

Explanation

STEP 1: To find amount we use formula:

A=P(1+rn)n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

P=$4500 , r=7% , n=2 and t=9 years

After plugging the given information we have

AAAA=4500(1+0.072)2⋅9=4500⋅1.03518=4500⋅1.857489=8358.7

STEP 2: To find interest we use formula A=P+I, since A=8358.7 and P = 4500 we have:

A8358.7II=P+I=4500+I=8358.7−4500=3858.7

4 0
3 years ago
A string is tied to the top of a plant to keep it stabilized. The plant is 5 feet tall and the string is connected to the ground
Rasek [7]
R<span> = √(2² + 5²) = √29 = 5 and change. Simple Pythagorean calc. Draw a picture and you will see it.</span>
4 0
2 years ago
Read 2 more answers
Using a metric line as taught in your lesson, convert the following metric measurement. (Remember to use the same number of sign
weqwewe [10]

Answer:

Option B.

Step-by-step explanation:

We need to express 505 kL in L.

Here, kL means kiloliter and L means liter.

We know that

1 kL = 1000 L

Using this conversion we can easily convert 505 kL in L.

Multiply both sides by 505.

505 × 1 kL = 505 × 1000 L

505 kL = 505,000 L

The value of 505 kL can be expressed as 505,000 L.

Therefore, the correct option is B.

4 0
2 years ago
Read 2 more answers
HELPPPPPPPPPPPPPPPPPP
snow_tiger [21]

Answer:

The answer to this d=0.6t because evry minute it is .6

5 0
3 years ago
Other questions:
  • Is the relation a function? Why or why not?
    14·2 answers
  • (y+3) (y^2-3y+9) What is the product? y3 + 27 y3 – 27 y3 – 6y2 + 27 y3 + 6y2 + 27
    10·2 answers
  • If AC= 40 find the length of jk​
    7·1 answer
  • there are 84 students in the 8th grade. if they are split evenly into 6 groups how many students will be in each group
    13·2 answers
  • What does 6x − 9 = 45 equal?
    11·2 answers
  • Write each of the following in completely factored form. These will involve slightly more difficult final trinomial expressions
    5·2 answers
  • If you help me and explain how you got your answer you will get brainlisyt
    5·1 answer
  • What is the meaning of the point with an x coordinate of 2 ​
    7·1 answer
  • Does anyone know this ? i'm stuck.. i'll give you brainliest and 15 points !! pls show work.
    11·1 answer
  • 5.3 Q4
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!