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- Does a right circular cylinder such as an aluminum can have a symmetry with respect to at least one plane? b symmetry with respect to at least one line? c symmetry with respect to a point?Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r = 3, and sketch its graph.
- Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z coordinatesDescribe the surfaces defined by the following equations a. p(the greej letter rho) = 13 b. theta=2pi/3 c. phi=pi/4 This is Calculus 3 Cylindrical and Spherical coordinates.Convert the following quadric surface into spherical coordinates. (x-3)^2+y^2+(z+1)^2 = 1
- Sketch, or describe in words, the following surfaces whose equations are givenin cylindrical coordinates:Which statement about cylindrical coordinates is correct?(a) If θ = 0, then P lies on the z-axis.(b) If θ = 0, then P lies in the xz-planeConsider the plot of the solid r = 1 + Sin[a*phi]*Sin[b*theta]] in a spherical coordinate system. What roles do the parameters a and b play? Pay particular
- Find an equation in cylindrical coordinates for the surface represented by the rectangular equation y = x2Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r^2 + z^2 = 4Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein model, solve: to When X2+Y2<=1, find the point F(x,y) that is the intersection lxy with the sphere E