30 hours to 18 hours express as a fraction in simplest form
1 answer:
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Answer:
The given function symmetric about the y-axis.
Step-by-step explanation:
The given function is
.... (1)
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r,-θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
Put (r, -θ ) in the given function.
Therefore it is not symmetric about x-axis.
Put (-r, -θ ) in the given function.
Therefore it is symmetric about y-axis.
Put (-r,θ ) in the given function.
Therefore it is not symmetric about the origin.
In spherical coordinates, we have
which gives volume element
and so the triple integral is given by
which gives volume element
and so the triple integral is given by