Question

Write the equations in cylindrical coordinates.

(a) 8x^{2} − 7x + 8y^{2}
+ z^{2} = 1

(b) z = 4x^{2} − 4y^{2}

Answer #1

Write the equations in cylindrical coordinates.
9x2 − 3x + 9y2 + z2 = 9
// I keep getting z^2=9-3r(3r-cos (theta))

Write the equations in cylindrical coordinates.
(a)
7x2 − 3x + 7y2 + z2 = 1
(b)
z = 7x2 − 7y2
Evaluate the integral by making an appropriate change of
variables. 9(x + y) ex2 − y2 dA, R where R is the rectangle
enclosed by the lines x − y = 0, x − y = 3, x + y = 0, and x + y =
9

- write N-S equations for incompressible flows in cartesian
coordinates in long form (in x,y,z coordinates) (1 point)
- also write continuity equation and N-S equations for
incompressible flows in polar coordinates in long form (in r,θ,z)
(since one of your friends ask you can find it easily in online
resources or in books) (1 point)
- Write down N-S equations in x direction for Planar Couette-
Pouseille flow and derive an equation for velocity variation using
boundary layer conditions...

Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z =
x2 + y2
and the sphere
x2 + y2 + z2 = 128.

(1) Sketch the given surfaces ( for Question (a) and (b) graph
x=0, y=0 and z=2 traces)
(a) x2-4y2=z
(b) y2-4x2-z2=4
(2) state the type of the quadric surface and describe the trace
obtained by intersecting with the given plane.
(x/2)2+(y/5)2-5z2=1, x=0

1. a) Sketch the surface. 9x2 +
4y2 + z2
= 36. Identify the surface.
b) Sketch the surface. z = 4 −
y2. Identify the surface.
c) Sketch the surface. y =
5z2 −
5x2. Identify the surface.
d) Sketch the surface. 6x2 −
y2 + z2 =
0 . Identify the surface.
e) Sketch the surface. 6x2 +
4y2 + z = 0 .
Identify the surface.

A
particle moves in a potential field V(r,z)=az/r, a is constant. Use
the cylindrical coordinates as the general coordinates.
1)Determine the Lagrangian of this particle.
2)Calculate the generalized impulse.
3)Determine the Hamiltonian of this particle and the
Hamiltonian’s equations of motion.
4)Determine the conserved quatities of this system.

Find the spherical coordinates of a point P with cylindrical
coordinates (r,θ,z). Draw a figure.

Write down a cylindrical coordinates integral that gives the
volume of the solid bounded above by z = 50 − x^2 − y^2 and below
by z = x^2 + y^2 . Evaluate the integral. (Hint: use the order of
integration dz dr dθ.)

Sketch the graphs of the quadratics surfaces defined by the
equations x = z2 - y2 and y2 -
x2 - z2 = 1 on the coordinates systems
below.

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