Which of the following polar equations shows a limacon with a dent? A) r = 6 + 4 sin 0 B) r = 4 – 6 cos 0 C) r = 6 – 8 sin 0 D) r = 2 +2 cos 0 A

Q: Find the area of the intersection of the two polar circles, r = 2 * cos(Θ) r = 1

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Q: Find the area of the region. Interior of r = 10 + 7 sin 0 (below the polar axis)

A: Explained below

Q: a) Reproduce the algebra required to convert this Cartesian equation to the polar form r = sin(20).…

A: Given the algebraic equation, (x2+y2)3=4x2y2 ⋯⋯(1) (a) Take x2+y2=r2, x=rcosθ, and y=rsinθ Then…

Q: 24. Which of the following polar curves is a cardioid? A. r= cos () B. r= 2+3sin® C. r = 3– 20ose…

A: 24)      A. r=cos2θ2                                                         B)r=2+3sinθ…

Q: Consider the following polar curve: = sin(20) (a) Sketch the graph of the curve (a rose with four…

A: Follow the steps below to get the answer, don't shade the region I have done that for your…

Q: Please Write down the solution clearly.

A: The complex form is , z=2cos2π4+isin2π4. To convert into polar form,  z=reiθ. In the given complex…

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 9 + 7i r = • 0…

A: The given complex number is: z=9+7i

Q: (a) Name the polar curve r=4-4 sin O and perform all three symmetry tests for 1 ie curve.

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Q: Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(θ…

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Q: Which one of the following polar equations is equivalent to y=x-4. 4 r = cos 0 + sin 0 cos 0 – sin 0…

A: By using some important replacements we can easily change cartesian equation into polar equation…

Q: Find the area of the region in the polar coordinate plane . Inside the “figure eight” r = 1 + cos 2u…

A: r = 1 + cos 2u and outside the circle r = 1

Q: 1 By first changing to polar coordinates, evaluate 1+ x + y dA, where R is the quarter-disk region…

A: Given integral is ∫1+x2+y2dA over the region R where R is quarter disk region shaded above. Use the…

Q: Consider the polar equations r= 3+2 cos(0) and r = 3+2 sin(0), whose graphs are shown below. 2- 1…

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Q: In polar coordinates, r is the ________ ________ on the terminal side of an angle uwhose vertex is…

A: The given statements is "In polar coordinates, r is the ________ ________ on the terminal side of an…

Q: Given: polar curves C₁ : r = √2- cos 0 and C₂ : r = √2+ sin intersecting at A(³√2, 37) and B(2,7) 2…

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Q: The polar form of the Cartesian equation x = 4 is Select one: a. r sin 0 = 4 b. r= 4 cosec 0 c. r= 4…

A: We have to find the polar form of the Cartesian equation  x = 4

Q: Find zw and z/w, Leave your answers in polar form.

A: Given the complex numbers  z=2(cos5π3+isin5π3)w=3(cosπ3+isinπ3)

Q: The polar form of the Cartesian equation x = 4 is ... ...... Select one: a. r sin 0 = 4 %3D b. r=4…

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Q: Find the area of the inner loop of the limacon with polar equation r = 9 cos e – 4 01 = cos- ()…

A: The area of the inner loop of the limacon is given by: A=12∫-θ1θ1r2dθ We are given that…

Q: The polar form of the Cartesian equation x = 4 is Select one: a. r sin 0 = 4 b. r=4 cosec 0 c. r=4…

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Q: Write in Polar form: *(cos e + z sin 8). i sin 0). (0 < 0 < 2n and round to 3 decimal places) - 17 +…

A: We have to find value of r and θ Consider ,z=-17+12iHere x=-17 and y=12 Here we will use the…

Q: . Convert the following conics to rectangular form. 1 2 10 (a) r (b) r = (c) r = 5 – 5 sin 0 1+2 cos…

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Q: Find the area of the inner loop of the limacon with polar equation r = 5 cos 0 – 2 -1 = COS (금)

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Q: Find the areas of the regions in the polar coordinate plane described Enclosed by the limaçon r = 2…

A: The limacon is symmetric around the x-axis thus doubling the area of the part over the x axis gives…

Q: If z = r cos 0 + ir sin 0 then 1 / z has absolute value __ and angle __ . Its polar form is __ .…

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Q: Show that the polar equation r = asin(θ)+ bcos(θ), where ab≠0, represents a circle, and find its…

A: We have to proof

Q: Find the Cartesian coordinates of the following points (given in polar coc 7n a. V2,4 b. (4,0) с. 0,…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Find the areas of the regions in the polar coordinate plane described Enclosed by one leaf of the…

A: Area of the region bounded by r=fθ between the radial line α to β is A=12∫αβr2dθ

Q: Prove that the distance, d, between two points with polar coordinates (r, 01) and (r2, 02) is d =…

A: Distance (d) between two points x1, y1 and x2, y2 is  d=x1-x22+y1-y22   ....1

Q: 7. The equivalent Cartesian equation of the polar equation r=cot ese e is a) y=x c) y=x b) xy 1 d)…

A: Using Cartesian coordinate.

Q: Use De Moivre's Theorem to solve for z and leave your answer in polar form with the angle in radians…

A: If z=rcosθ+isinθ then the nth root is zn=rncosθ+2πkn+isinθ+2πkn and if z=a+ib then r=a2+b2 and…

Q: Convert the following polar curves into Cartesian r=2/(4-cos theta)

A: We know that--&gt; r2 = x2 + y2  x = rcosθ y = rsinθ

Q: Which one of the following polar equations is equivalent to y =x- 4. 4 r = sin 0 – cos 0 cos 0 – sin…

A: We have to find

Q: Find the area enclosed by r= 5 + 4sinθ in the Polar coordinate system, but only the part that is in…

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Q: Consider the rose curve with polar equation r = cos(20), whose graph is shown below. 0.5 -0.8-0.4서…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: 1. How many petals does the polar curve r=5cos(6theta)?  2. At what points the curves…

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Q: Which of the following polar equations describes a circle centered at (G, 5) with radius 2 O r =…

A: Given, center=(12,12) radius=12

Q: 2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant…

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Q: Which of the following is one of the points of intersection of the polar curves r = 3 cos @ and r =…

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Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) - 4 – 16i r = ,0…

A: The given number -4-16i

Q: Find zw and W Leave your answers in polar form. - TC TO Z= 6 cos + i sin 11 11 TO W = 6| cos COS + i…

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Q: What is the polar form of the equation? (x + 2)² + y² = 4 O r(r+4sin 0) = 0 O p2 = 4r cos O O r(r+4…

A: We transform the equation by putting the formula.

Q: Find the the area of the region enclosed by the polar equation 3 sin(20), 0<0 < T/2.

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Q: Find the area inside the polar curve r = 2+2 cos 0.

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Q: If z = 3 (cos 15° + j sin 15°), find z* in polar form. (Express the argument in de- grees.)

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Q: Show that the polar equation r = a sin θ + b cos θ where ab ≠ 0 represents a circle, and find its…

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Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 19 – 4i r = .0 =

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Q: 8. Determine the area in one loop of following polar equations. Sketch after. (a) r = 8 sin(40) (b)…

A: The area with the polar coordinates can be calculated using the integration. The formula for the…