Sets in cylindrical coordinates Identify and sketch the following sets in cylindrical coordinates.
11.
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- Describe the set in cylindrical coordinates. (Enter 0 values between 0 and 27.) x² + y2 + z2 = 9, x 2 0, y 2 0, z 2 0 z = f(r) = sosarrow_forward-> Evaluate F.dr, where F (x, y, z) = - yi + xj + z²k and C is the curve of C intersection of the plane y + z = 2 and the cylinder x? + y? = 1.arrow_forward2. Use parametric equations to derive the formula for the lateral surface area of a right circular cylinder of radius a and height b (e.g. the set of all points (x, y), where x2 + y? = a² and 0 < z < b.)arrow_forward
- Change from rectangular to cylindrical coordinates. Select such set of cylindrical coordinates as 0 € [0, 2л). (a) (2√3, 2, -2). (r, 0, z) = ( (b) (5, -2, 2). (r, 0, z) = ( ).arrow_forwardV1-x2 (16 2. Sv2 x2 dzdydx By changing to cylindrical coordinate, evaluatearrow_forward1) Express in cylindrical and spherical coordinate systems. Cylindrical Spherical Coordinates Coordinates The XZ plane The Y axis The Z axis The line Y = X on the XYarrow_forward
- Identify the center and radius for each. r? + y? = 49 x² + y? = 324 x² + (y + 2) = 64 (r + 2)² + y² = 64 (1 – 5)² + (y – 3)² = 144 (z+1) + (y – 10)? = 100 :: Center: (0, 2), r = 8 : Center (-1, 10), r = 10 : Center: (-2, 0), r = 8 :: Center: (1, – 10), r = 10 :: Center: (0, 0), r = 18 : Center: (5, 3), r = 12 : Center: (2, 0),r = 8 : Center. (0, 0), r = 7 : Center (-5,-3), r = 12 : Center (0, -2), r = 8arrow_forwardThe following points are given in cylindrical coordinates; express each in rectangular coordinates and spherical coordinates. Cylindrical (r, 0, z) (1, 45°, 9) (3, 1,-4)|( 2 (0, 45°, 9) (5,, 12) ( 6 (1,2,0) 3π 4 -1 -6 Rectangular (x, y, z) DIC DIC DIC DIC DIC DIC Spherical (ρ, θ, φ) Crookarrow_forward2 Sketch the parametric surface x = Vu“ +v , y = u, z = v. luarrow_forward
- Convert the following point from cylindrical to rectangular coordinates: (10.-) 4 (x, y, z) Usage: To enter a point, for example (x, y, z), type "(x, y, z)".arrow_forwardFind a parametric representation of the cone /3x² + 3y² Z. = in terms of parameters p and 0, where (p, 0, p) are spherical coordinates of a point on the surface. X = Edit y = Edit Edit =2arrow_forwardConvert the point (x, y, z) = ( − 5, 2, 3) to cylindrical coordinates. Give answers either as expressions, or decimals to at least one decimal place, with positive values for and r. (r, 0, z) = -arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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