Evaluate ²y dA where D is the top half of the disk, centered at the origin with radius 2.

Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

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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: Find the length of the polar spiral r = 0² from 0 < 0 < V5.

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

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Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Use the parametric equations of an ellipse, x = 5 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2π, to find the area…

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Q: Consider the plot of the solid r = 1 + Sin[a*phi]*Sin[b*theta]] in a spherical coordinate system.…

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Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. Sx(t) Lyct) =…

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Q: 8-a2-y By converting to spherical coordinates, evaluate 2² dz dx dy

A: Let us consider the rectangular coordinates (x,y,z) then the relation between spherical coordinate…

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 the area of the shaded region given the polar equations: r = sinx and r = cosx

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Q: How to get the center of r = 6sinθ in polar coordinates. Need detailed explanation.

A: We have to find the centre of r= 6sinθ.

Q: Convert the rectangular equation (z+3)´ + (y + 13)*= 178 into a polar equation. No spaces. Use @for…

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Q: Cannot solve

A: To convert rectangular equation into polar equation put x = r cosθ and y = r sinθ then rearrange the…

Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o

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Q: The region shown at the right is bounded by portions of the y-axis, the line x = y, and the circles…

A: Given line is y=x  Inner circle radius=2 Outer radius=4

Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: Give two polar representations for the point (x, y) = (0, 1), one with negative r and one with…

A: Check the polar representation.

Q: Sketch the polar curve r = sin? 0.

A: We have given a curve; We have to plot the polar curve on;

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

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Q: ) Identify the conic section given by the polar equation r =

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Q: Identify the surface whose equation in spherical coordinates is given by p= 8 cos o

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Q: duct z,z2 and the quotients 1 and (Express your answers in polar form.) Z2

A: We will solve the problem on complex numbers.

Q: find the area of the polar curve.   r=3-sin@

A: To calculate the area of the given polar curve , using integration

Q: Plot the point given in polar coordinates. (3/2, 4.71)

A: The given point is x,y=32,4.71.

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given:r=eaθ,0≤θ≤π2,about θ=π2

Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: Use the parametric equations of an ellipse, D=5 cos(@), y - 4 sin(6), 0 O 27, to find the area that…

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Q: а. Use technology to graph these two polar functions, and then sketch the region R below. b. Find…

A: The area bounded by two polar curves 0≤r1θ≤r2θ , α≤θ≤β is given by 12∫αβr12-r22dθwe have given the…

Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), o sos 2r, to find the area…

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Q: 4. y = sin2r, 0 sa Find the area of the surface of rotation obtained by rotating the curved segment…

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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: Which of the following is the spherical coordinates of the point (0, v3, 1) which is given by…

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Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

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Q: Express the polar equation r=2 sin 0 in cartesian coordirates.

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Q: WrWiterirte=(x + y)2 = xy + 6 as an equation in polar coordinates. 2 cos θcos θ − sin θas an…

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Q: DESCRIPTIONS C. Cardioid, F. Rose with four petals, I. Inwardly spiraling spiral, L. Lemacon, M.…

A: To match each polar equation to the best description.

Q: Use the parametric equations of an ellipse, x = 2 cos(8), y = 3 sin(8), 0 < 0 < 27, to find the area…

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Q: Identify the surface whose equation in spherical coordinates is given by p = 8 cos %3D

A: The given equation in the spherical polar co-ordinates is ρ=8cosϕ. In spherical polar co-ordinates,…

Q: Paove that the distane, b, points with between two polar coordinates (s, Bq) aud (s2,E2) is…

A: TO PROVE : THE DISTANCE BETWEEN TWO POINTS WITH POLAR COORDINATES s1 , θ1 AND s2 , θ2  IS…

Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: Convert the rectangular equation to polar form. (x² + y2j2 = 6(x² – y²) 6 cos 0

A: In the question we have to convert given function into polar form.

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

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Q: 11.) Find a rectangular equation for the Surface whose Spherical equation is a sin ($) Sin (e)

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Q: Qz: sketeh in polar %3D

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Q: Identify the surface whose equation in spherical coordinates is given by p= 6 cos

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Circle:  x = h +…

A: x=h+r cosθ , y=k + sinθ

Q: Use the parametric equations of an ellipse, x a cos(0), y = b sin(0), 0 seS 2n, to find the area…

A: Given that the parametric equation of an ellipse is  x= a cos(θ) , y=b sin(θ) , 0≤ θ ≤ 2π . Here we…