system written in polar coordinates is p' = r(r² – 1)? O' = -1.

Q: Evaluate e-y dy da by converting to polar coordinates.

A: Given: ∫-22∫04-x2e-x2-y2dydx We want to evaluate above integral by using polar coordinates

Q: Convert the equation rsin 0 = ln r + ln cos 0 from polar to cartesian.

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Q: Write the polar equation in rectangular form. r = 6 sin 0 Oy =-6x Oy =x- 3 O x² + (v – 3)² = 9 O (r…

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Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: dy at the point 1.- dx For the polar equation r=1–cos 0 , find the value of 2 O 1 O -1 O 2

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Q: Express y=x^2 in polar coordinates.

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Q: 4. Integrate L e-° dxdy by converting to polar coordinates, and ase that result to integrate J e dx.

A: This problem is convert to pollar form and then solve so,......

Q: Convert the Cartesian equation x² + y² + 3x = 0 to a polar equation. r² = = -3 cos 0 r= 3 cose r= -3…

A: Given x2+y2+3x=0To find polar equation:

Q: Write a polar equation for the conic with the given characteristics. e = 1.6; directrix: y = 4 6.4…

A: Given :  Eccentricity,   e=1.6       and  Directrix,         y=4

Q: Find a Cartesian equation for the curve represented by polar equation r= 14 cos - 6 sin e. OA. 2 (x…

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Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: Sketch the curve with polar equation r = 2 cos0

A: We first make a table of values θ 0 π/4 π/2 3π/4 π r 2 1.41 0 -1.41 -2

Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Find a Cartesian equation from the polar curve 4r sin 0 = 18(rcos 0) +14 1S is

A: Given polar equation is 4rsinθ=18rcosθ2+14  .....1

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: How do i write x^2 + y^2 = 2y in polar coordinates?

A: Given Data: Equation: x2+y2=2y ......1 The x coordinate relation with polar coordinate is, x=rcosθ…

Q: 1. Convert (V3,-3) from rectangular to polar coordinates with r>0 and 0<0< 2r. Give exact values for…

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Q: Find the exact length of the polar curve. r = 3 sin(0), 0≤0 ≤ π/4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the area inside the polar curve of r = 1+2 sine but outside the smaller loop.

A: Consider the graph: Consider the curve:

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: 13 Convert x 2 + y 2 - 2x = 0 to a polar equation. r = 2cosθ r² = 2cosθ r = 2sinθ

A: We have to find the polar equation

Q: he Cartesian equation (x – 10)2 + y² = 0 in polar form. %3D

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Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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Q: Find polar coordinates (r, 0) of the point (1, -V3), where r <0 and 0 s0 < 2m

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Q: Find e-a* -y" dx dy using polar coordinates.

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Q: Find two sets of polar coordinates for the point for 0 s0 < 2z. (r, 0) = (smaller r-value) (r, 0) =…

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Q: Find a Cartesian equation for the curve represented by polar equation r = 4cos 0-6 sin 0. OA. (x –…

A: Use the conversion from polar coordinate to Cartesian coordinate and simplify.

Q: Replace the Cartesian equation with an equivalent polar equation. x2-y2=4 O cos2e - sin20 = 4 O r…

A: 1. x2-y2=42. r2=26r cosθ-6r sinθ-9

Q: Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0≤ 0 < 2π r = √10 Enter exact value.…

A: Follow the procedure given below.

Q: 1. Convert from a rectangular equation to a polar equation. X-y= 10

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Q: Write the equations that are used to express a point withCartesian coordinates (x, y) in polar…

A: To convert Cartesian coordinates x,y in polar coordinates. In polar coordinates point is given r,θ.…

Q: Find the length of the curve over the given interval.                                     Polar…

A: Given: rθ=5cosθ; θ∈π2,π we know that arc lengthL for any given functionfx over interval a,b is given…

Q: The alternative polar coordinates that satisfies r 0 for

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Q: Q5) Evaluating in polar coordinates: *+ y*)dydx

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Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: Convert to Polar coordinates. (r 20 & 0 < 0 < 2n) (x, y) = ( -1, v3 )

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Q: Find the equation in xx and yy for the line tangent to the curve in polar coordinates…

A: Given that, the value of r=5+cos2θ and θ=π3. rθθ=π3=5+cos2π3=5+-12=92 Note that, the equation of the…

Q: 2. Convert Polar Equation to Rectangular Equation. 1 r = sin 0 – cos 0

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Q: Find polar coordinates to represent (-2, -2) with r >0 and 0 <0< 2T.

A: Cartesian to polar conversion (x,y)→(r,θ) where r=x2+y2 θ=tan-1yx

Q: 2. Evaluate Vr2 + y? dy dx by switching to polar coordinates.

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Q: b. Plot the polar curve r= 2(1- cos0) in interval t ,2n

A: Given equation is r=2(1-cosθ)  =2-2cosθ

Q: Evaluate /1-(y-1)² by first changing it to polar coordinates. 219 dx dy

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Q: Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with…

A: Solution:- At x = 2a, y = 2a  y1=k1x2  2a=k12a2 k1=12a At x = 0; y = a y2=c+k2x2 c = a…

Q: Find the area of the region. Interior of r = 4 + 3 sin 0 (below the polar axis)

A: Given that         r = 4 + 3 sin (theta) Here we have to find the area of the region below the polar…

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: 5 Convert the equation from polar to cartesian. r = sin 0 – 2 cos 0 -

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Q: Find the polar equation for the curve represented by the equation y = 1+ 3x. A 1 ,0) sin 0-3 cos 0 В…

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