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

Q: r = 2 cos 0,

A: To find the exact length of the polar curve.

Q: The transform curve of polar equation r 4 cos@+4 sin e to rectangular coordinates (x-2)° – y² = 8…

A: Given that: r=4cosθ+4sinθ

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

A:

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: 43/2-x f(x,y,z) dzdydx is rewritten in spherical coordinates as g(p.p,0) dpdwde, then…

A: By integral, x2+y2⩽z⩽43-x2-y2----1 0⩽y⩽43/2-x2------2 0⩽x⩽43/2----------3

Q: 24. A particle moves round the polar curve r = a(1+ cos e) with constant angular velocíty w. The…

A: We have constant angular velocity = w  r = a(1+ cosθ)

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Consider the following equation: r=21-sinθ Relation between Polar and Cartesian coordinates:…

Q: V18-x2-y Convert (x² + y + z?)dzdxdy into spherical coordinates. 2n/3 3V2 4 p* cos pdpdpdO /2 -n/2

A:

Q: Find the length of the polar curve: r = cos 0, where 0 < 0 < 2n.

A: We need to find the length of the polar curve

Q: Q3//A:- Verify that dV = p² sin p dp d0 do when using spherical coordinates.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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

A:

Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

Q: 3 4. Sketch the region described in polar coordinates by r < Cos e

A: We need to sketch the region.

Q: Which of the following polar curves is a cardioid? * r = cos? r = 2 + 3 sin 0 O Option 1 Option 2…

A:

Q: 2. By changing to cylindrical coordinates, evaluate 2 2π Stt. [²* * cos p² sin³ o dp do dô 0

A: To Evaluate: The integral ∫02π∫0π/4∫02/cosϕρ4sin3ϕ dρdϕdθ by converting it to cylindrical…

Q: Converted into polar coordinates, the integral r1/2 1-y L" Pydzdy becomes Select one: r3 cos? 0 sin…

A: We will first identify the region of the integration then we will obtain the limits in polar…

Q: Assume 0 <0< T. The number of points where the two polar curves r = cos (0) and r = sin(0) intersect…

A:

Q: 3. Consider the curves given by the polar equations r = 2 and r = 4 cos 0.

A: r = 2 r = 4 cosϴ

Q: 8. Find the area of the surface of revolution r = 2 cos 0 revolved about the π polar axis 0 < 0 <

A:

Q: Given the curve in polar equation r = 8 cos 0, 0<0 Use integration to find the area of surface…

A: Given the curve in polar equationr=8 cos θ, 0≤θ≤π2.By using the integration to find the area of…

Q: The equation of the polar curve above is E. r = 3 + 2 sin 0 F. r = 3 - 2 sin 0 G. r = 3+ 2 cos 0 H.…

A: From the direction of the cardioid, extending horizontally, that you…

Q: For spherical polar coordinate system 1 Z -Zr Zr 3/2 4/2 a exp(-()sin OCoso 2a px a V WmdV = 8 = ?…

A:

Q: 1. Describe the graphs of the equation (a) r = cos 20 in cylindrical coordinates. (b) p= sec otan 0…

A: First change cylindrical and spherical coordinates system to Cartesian coordinates system

Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

Q: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

A:

Q: If D is the region in the third quadrant between x +y? = 1 and x2 + y? = 4, then using the polar…

A: We have to convert given double integration into polar coordinates integration.

Q: . A particle is moving round the polar curve r = 1+ sin0 with constant angular velocity w. The…

A:

Q: p = 4 cos 0 sin

A: Given: ρ=4cosθsinϕ To Find: Give the corresponding equation in Cartesian coordiantes considering…

Q: Consider the following parametric equation. - 5(cos 0 + 0 sin 0) %3D y = 5(sin 0 – 0 cos 0)

A: Given,         The parametric equations are x=5cosθ+θsinθ and y=5sinθ-θcosθ

Q: Transform C = cos p a, - sin p a, + cos p sin p az into spherical coordinates and then at P (2, T/4,…

A:

Q: 2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

A:

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

A:

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: (e) Graph the surface in R' whose spherical equation is p = cos 20.

A:

Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

A:

Q: 4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations…

A:

Q: Q.No 05: Find the expressions for the spherical harmonics Y30 (0, 9) and Y3,+1(0, 9). Y30 (0, 9) =…

A: Given  Y3,0θ,φ=716π5cos3θ-3cosθY3,±1θ,φ=2164πsinθ5cos2θ-1e±iφ

Q: 1 If the parametric equatioms are: x= sin-t and y= cos,t, 1 %3D - nstSn 2 then the Cartesian…

A: Given x=sint2, y=cost2, -π⩽t⩽π

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: Q3/|A:- Verify that dV = p² sin o dp do dp when using spherical coordinates. %3D

A:

Q: 1-For spherical polar coordinate system Zr Zr (2² exp(- 2a 1 Z. -) sin OCosø 42 `a а Jy„V„dV = 8_ =?…

A: For spherical polar co-ordinate system ψpx=142Za32exp-Zr2aZrasinθcosϕTo find:∫ψpxψpxdV=δxx

Q: Find the length of the polar curve r = 5°; 0 <e< 2n

A: Given ,r=5θdifferentiate w.r.t.θdrdθ=5θ.ln(5)Weknow that length of the curve…

Q: Use polar coordinates to evaluate sin (2² + y²)³ dA, where R is the region enclosed by the curves…

A: Given : R is the region enclosed by the curves with polar equations       θ=0, r=π3, and r=θ To…