Question

Test the equation for symmetry with respect to the polar axis, to the line ?=, ", or to the pole. ? =3+2sin?

Answer #1

1. Write an explanation of how to test the
symmetry with respect to the line y = - x.
2. You Decide. Alicia says that any
graph that is symmetric to the origin and to the y-axis must also
be symmetric to the x-axis. Chet disagrees. Who is
correct? Support your answer graphically and algebraically.

determine symmetry with respect to the x -axis and y -axis for
the graph: |y| = 3x

find the coordinates of the vertex and the equation of
the axis of symmetry for the parabola given by the equation.
y = 2x^2 - x - 5
vertex (x,y) = ( ? )
axis of symmetry ?
y = x^2 + 2x
vertex (x,y) = ( ? )
axis of symmetry ?

Sketch the polar cuve and find the polar of the
tangent line to the cuve at the pole r=2cos(3θ)

Answer all the following
1a.
Find any intercepts. (Order your answers from smallest to
largest x, then from smallest to largest y.)
y = x2 − 9x + 18
y-intercept
(x, y) =( , )
x-intercepts
(x, y)= ( , )
(x,y)= ( , )
1b.
Test for symmetry with respect to each axis and to the origin.
(Select all that apply.)
y = x2 + 5x
The equation is symmetric with respect to the
x-axis.
The equation is symmetric...

Write the standard polar equation for a hyperbola with one focus
at the pole and vertices at points (1, pi) and (30, pi).

3) Find a polar equation of the conic in terms of r
with its focus at the pole. ( r=???)
a)(4, π/2) (parabola)
b) (4, 0), (12, π) (eclipse)
c) (8,pi/2), (16,3pi/2) (eclipse)

Do the following
a) Find the equation of the cylinder having radius 1 and axis of
symmetry is the line x=t+1, y=t-1, z=-t
b) What is the trace of this cylinder with the y-z plane?

Classical Mechanics problem:
A bucket of water is set spinning about its symmetry axis with
an angular velocity of magnitude Ω. What is the shape of the water
surface after it has reached equilibrium? HINT: The surface of the
water is an equipotential under the combined effects of gravity and
the centrifugal force. The shape is one you are familiar with
(circle) and using cylindrical polar coordinates will make
it easier.

Sketch the curve with the given polar equation by first
sketching the graph of r as a function of θ in Cartesian
coordinates.
r=3sin2θ
and
r= cos3θ
and
r= 4cos(2θ)
Please show symmetry tests
Thank you in advance!

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