1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2. Changes from cartesian equation to equivalent in polar coordinate: sece T-4 cote

Q: Find the polar coordinates of the point with r> 0 and o ses 2n. (r, 8) = 2 0.5 1.5 2,5 3,5

A: Consider

Q: Explain why in spherical coordinates the graph of = c is a half-plane and not an entire plane.

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Q: Match the surface to its corresponding equation in spherical coordinates. 37 4 -3 -2 -1 0 1 2 3 3…

A: To solve this we have to find the relation of equation

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A: Polar coordinate system

Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Verify the re- lation |V? = u; + zuổ Hint:…

A: Let u = u(x, y) and let (r, θ) be polar coordinates.

Q: Describe the given region in polar coordinates. Ay 6- 3- -6 -3 -3- R:

A: The graph in polar coordinate is given by

Q: Which of the following is equivalent to S SY Jya dy da in polar Vz²+y? coordinates? O 2 dr de O 4 i…

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Q: express in polar coords with: Cりり me point whose Ty-Coords are a.r>o and OsoL2

A: Introduction: The polar coordinates r,θ of rectangular coordinates (x,y) in two-dimensional…

Q: Convert the point (x, y) from Rectangular to polar coordinates (r, 0). 3. (–1, v3)

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Q: osen y

A: Is it sen y =x

Q: Sketch the following polar rectangle. 2x = {(r,0): 4sr5,

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Q: 1/A) Replace the polar equation by equivalent Cartesian equation r2cose + 2sino

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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: Find the areas of the regions in the polar coordinate plane described in Exercises 47-50. 47.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Draw the polar region {(r, θ): 1 ≤ r ≤ 2, 0 ≤ θ ≤ π/2}. Why is it called a polar rectangle?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Plot the points with polar coordinates 4, and 3, using the pencil. 4 2n 3 4 0. 4. 9. 11n 9. 5T 4 4…

A: Topic:- Geometry

Q: Consider the area inside the circle T= 6 cos 0 but outside the cardioid r = 2(1 + cos 0) a. draw the…

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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: If a point is represented as (x,y) in the Cartesian plane and (r,0) in the polar plane, then 0 = tan…

A: A point in cartesian plane is (x,y) and (r,θ) in the polar coordinate, then θ=tan-1yx.

Q: The location of the polar coordinates (2, -TT/3) is in the second quarter of the x-y axis. O True O…

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Q: Describe the projections of the circle r(t) =〈sin t, 0, 4 + cost〉onto the coordinate planes.

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Q: Find the areas of the regions in the polar coordinate plane described Enclosed by the limaçon r = 2…

A: The limacon is symmetric around the x-axis thus doubling the area of the part over the x axis gives…

Q: Convert thepoint (x,Y) from rectangular to polar Coordinates Cr,e). 4)(2,-2)

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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: 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: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse

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Q: Derive the formula for the distance between points P1(p1,q1,z1) and P2(p2,q2,z2) given in spherical…

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

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Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

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Q: Find the number of points of intersection of the polar curves r=2cos0 and r=1+2sin0. O 1 3 O 2

A: Number of point of intersection of polar curves r=2cosx and r=1+2sinx

Q: The Cartesian equation of the polar curver= 2sin0 + 2cos0 is Select one: O r + y? = 2 O x+y=2 O y? –…

A: Note that : 1) x^2+y^2=r^2 2) x=r(cos(theta)) 3)y=r(sin(theta))

Q: Find polar coordinates with positive r and 0s 0 < 2n for each of the four points. (x, V) = (,8 (a)…

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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: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

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Q: A radar, using the polar coordinate system, detects that two airplanes are currently located at…

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Q: b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the…

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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: Find the polar coordinates, -π ≤ θ &lt; π and r≤ 0, of thefollowing points given in Cartesian…

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Q: Let D be the region between the circles of radius 6 and radius 8 centered at the origin that lies in…

A: Here, the region D is between the circles with radius r=6 and r=8 centered at the origin. i.e. 6≤r≤8…

Q: 2. Use polar coordinates to evaluate 2 1. √4+7++5² dy dz. Jo

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Q: SSVitzý +Z% dA and then converting to polar. This The surface atea of a sphere ot radius I is As=4r.…

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Q: Convert the rectangular equation to polar form and sketch its graph. y = 6 a/2 7/2 12 15 10 8F 10 4…

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Q: What are the polar coordinates (r, 0) of the point with Cartesian coordinates (x, y) = (V2, -V2) ? ㅇ…

A: Given cartesian coordinates:x,y=2,-2To find: polar coordinates r,θ

Q: Find the formula for the distance between the points P1(a1,b1,c1) and P2(a2,b2,c2) given in…

A: First write the given coordinates in spherical coordinates. a1=r cosθsinϕb1=r…

Q: 3. What are the rectangular coordinates of the point with polar coordinates (r, 0)= ( 2, ? 4 (x, y)…

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Q: If the cartesian coordinates of a point are given by (3, y) and its polar coordinates are (r, 60°),…

A: This question can be solved using the concept of polar coordinates.

Q: Convert the point P(x, y) = P(-2,2) to polar coordinates. %3D P (r, 0) = (2/2, ) 57 P(r,0) = (2/2, )…

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Q: Change the following rectangular equations to polar form. Show work on separate paper. 14. x² +y°…

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