a. I've attached a plot of the surface. Each face is parameterized by
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with
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with
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b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.





Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.










c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.

where <em>R</em> is the interior of <em>S</em>. We have

The integral is easily computed in cylindrical coordinates:


as expected.
It is typically 30 km to 50 km thick.
Answer:
The slope of a graph of position vs time
Shadows are the absence of light, they are created when an object blocks light. In other words, shadows are the product of light particles, known as photons. These particles “bounce off” of the object without reaching the other side. Therefore light by itself will not form a shadow.