Use polar coordinates to evaluate sin (2² + y²)³ dA, where R is the region enclosed by the curves with polar equations 0 = 0, r = ñ, and r = 0, as shown below. 24 2

Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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

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Q: Find the slope of the polar curve r = 2( 1 – cosx ) when x = pi/4 . a. 1.707 b. 2.414 c. 1.866 d.…

A: Given equation of curve : r=21-cosx   ,  x=π4. drdx=2sinx The slope of polar curve   r=21-cosx  at…

Q: Convert the polar equation r 2 cos 0 to rectangular form. O g2 + y? 2 x2 + y ? = 2x x² + y? = 2x

A: solution:-r=2cosθconversion equationspolar to rectangularx=r cosθx=r sinθr=x2+y2

Q: Convert the rectangular coordinates to polar coordinates with r>0 and 0s 0 < 27T. (-võ-v2) (r, O) =…

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Q: Convert to polar coordinates with r > 0 and 0 < 0 < 2T. (- 1, 1/3)

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Q: Sketch the curve given in polar coordinates. r = 2 + 4sine , 0 < 0 < 2n

A: Consider the polar curve  r=2+4sinθ                             0≤θ≤2π

Q: For the polar equations r1=1-cosx and r2=1, (1)sketch the graphs of r1 and r2 in the same coordinate…

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

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Q: Calculate the slope of the polar curve  r=4cos3θ  at the point where θ=5π/6

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Q: Q2 Find the points of intersection of the polar curves r=1+cos and r= -cos

A: Given polar curves are  r=1+cos θ r=-cos θ Find the points of intersection. At first, the value of θ…

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: .Find the rectangular equation of the polar curve defined by r = sin 20. A. x+y-2xy= 0 B. (x² + y² }…

A: The polar coordinate system is a coordinate system  in which each coordinate point will be of the…

Q: Consider the polar curves Cı : r = 1+ cos 0 and C2 : r = 2 cos 0, and let R be the shaded region as…

A: Integral