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

Q: /25– x² 1. Evaluate (x2 + y? )3 dy dx by converting to polar coordinates.

A: Evaluate the double integral by using the charge of polar coordinates

Q: Use polar coordinates to evaluate (x² + y° )% dy dr.

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Q: Find the distance between the points with polar coordinates (4, T/3) and (6, 21/3).

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Q: 4y-y² y(x² + y²)² -dxdy o Jy *use polar coordinates

A: The given integral is: I=∫02∫y4y-y2 yx2+y22x5 dx dy

Q: A particle a of mass m moves inside a bowl. If the surface of the bowl is given by the equation Z m…

A: As per the question we are given the 3d equation of a surface in cartesian coordinates as :  z =…

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos 0 = 0 and 2-cos-r=0

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Q: Find a polar equation for x? + y² = 2

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Q: Convert the given Cartesian equation into a polar equation. x² + y? = 2x + 3y Select the correct…

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Q: find a polar equation for the curve represented by the given cartesian equation 5x^2 +y^2 = 8x (r is…

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Q: 3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

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Q: Convert to polar coordinates in the xz-plane, similar to Example 3 in the book. r2 63 – 2x? – 2z? –…

A: The limits lead to interpretation that,   From (2), Comparing the above result with  r=3

Q: find the exact length of the polar curve r = θ2,    0 ≤ θ ≤ 2π

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Q: Q2: Use polar coordinate system to sketch and find the common area r = 2 + 2cose and x? + y2 = 1

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Q: Find the exact length of the polar curve. r = = 02, 0 < 0 < 3t/4

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Q: Find the slope of the polar curve r= e® at 0 = n/3.

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Q: Find the exact length of the polar curve. = 02, 0<0 s T/2

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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: For spherical polar coordinate system (3² exp(x)sin Cosø 4/2 `a 1 -Zr,„Zr. 2a a |W„Y„dV = 8¸ = ? px…

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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: 11n Plot the points with polar coordinates 3, TT and using the pencil. 4 5n TE 6. 2 4 11n 6 6 5n 4.…

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Q: Find polar coordinates (r, 0) of the point, where r> 0 and 0 s0

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Q: 5n using the pencil. Plot the points with polar coordinates (-6, -a) and 4, 2n 3n SR 2. Jix Sn 4 Sx…

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

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Q: Q.3) Use the polar coordinates to evaluate A) L (r+ 2y) dydz

A: In this question we have to evaluate the Double Integration in polar form.

Q: 25-r2 Evaluate (x2 + y?)3 dy dx by converting to polar coordinates.

A: we have to evaluate the following

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

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Q: Q 4/ Use polar coordinate to evaluate 1v1- x2 + y? dydx

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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 the points of horizontal tangency to the polar curve r = 2 csc    + 3 .

A: Consider the given curve , r=2cscθ+3 Find the points of horizontal tangency . The relations between…

Q: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: Find the exact length of the polar curve. r=0², 0≤0 ≤ 6π

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Q: 3) (a) Find the intersection points of the polar curves r = 3 + 2sin0 and r = 2

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Q: 7) Evaluate IT !! (x + y)dxdy y by switching to polar coordinates.

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Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

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Q: 7T What are the rectangular coordinates of the point with polar coordinates (r, 0) = [2, ? 4 (х, у)…

A: Given: r,θ=2,7π4

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

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Q: 2T and 3 5n using the pencil. -5, -- Plot the points with polar coordinates 3, 2n 2. 12 4. 11m w/

A: To plot the points on polar coordinates

Q: 5. Evaluate ffi dA, where R= {(r, y)|1<r² + y² < 9, z20, y 2 0} %3D (Hint: Use polar coordinates.)

A: Given that, The double integration is, ∬xx2+y2dA Where,  1≤x2 + y2 ≤9,     x≥0,    y≥0 We have to…

Q: Determine the length of the polar curve r = 2°, 0<0<.

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Q: V8-x2 Use polar coordinates to evaluate 6 I dy dx. x2+y2+5

A: To evaluate the given integral by using polar coordinates

Q: Find the exact length of the polar curve. r = 0², 0≤ 0 ≤ 4π X

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Q: Converting 4-y2 4-y2 2² +y? f(x, Y, z)dV into polar coordinates gives

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Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos 0-r=0

A: The value of the cosine function  cos0=1cosπ6=32cosπ4=12cosπ3=12cosπ2=0cosπ=-1cos3π=-1cos2π=1

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

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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: The Cartesian equation of the polar curve r = 6 sin 0 is (x – 6)² + y? = 36 - (x – 3)² + y² = 9 O a?…

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Q: Q2:- find the polar coordinates for the fol 1:-(-2,2) 2:- (-1, /3) 3:- (2/3,2)

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Q: 3 V9-y2 / / (x² + y²) dx dy

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Q: Find the slope of the polar curve at the indicated point. A) V3 r = 1- sin(0), 03= 3 C) 2

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