Answer:
The answer would be Igneous rock
Explanation:
a. I've attached a plot of the surface. Each face is parameterized by
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with
and
;
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with
and
;
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with
and
;
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with
and
; and
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with
and
.
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.
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Hope that helps!
You just multiply these two numbers, it's 1250J
Answer:
a) 2.41 km
b) 38.8°
Questions c and d are illegible.
Explanation:
We can express the displacements as vectors with origin on the point he started (0, 0).
When he traveled south he moved to (-3, 0).
When he moved east he moved to (-3, x)
The magnitude of the total displacement is found with Pythagoras theorem:
d^2 = dx^2 + dy^2
Rearranging:
dy^2 = d^2 - dx^2


The angle of the displacement vector is:
cos(a) = dx/d
a = arccos(dx/d)
a = arccos(3/3.85) = 38.8°