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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; and
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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.
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Answer:
1/4 times your earth's weight
Explanation:
assuming the Mass of earth = M
Radius of earth = R
∴ the mass of the planet= 4M
the radius of the planet = 4R
gravitational force of earth is given as = 
where G is the gravitational constant
Gravitational force of the planet = 
=
=
recall, gravitational force of earth is given as = 
∴Gravitational force of planet = 1/4 times the gravitational force of the earth
you would weigh 1/4 times your earth's weight
Answer:
the angle of incidence θ is 45.56 º
Explanation:
Given data
strikes the mirror before wall x = 30.7 cm
reflected ray strikes the wall y = 30.1 cm
to find out
the angle of incidence θ
solution
let us consider ray is strike at angle θ so after strike on surface ray strike to wall at angle 90 - θ
we will apply here right angle triangle rule that is
tan( 90 - θ) = y /x
tan( 90 - θ) = 30.1 / 30.7
90 - θ = tan^-1 (30.1/30.7)
90 - θ = 44.4345
θ = 45.56 º
the angle of incidence θ is 45.56 º
magnetic materials will produce magnetic field near it
All magnets are made up of small magnet type atoms which are known as domains
These all atoms will align itself so that they all produce strong magnetic field along the axis
this magnetic field will become more strong as more number of atoms are aligned.
Now if we break the magnet into small piece then the magnetic field strength will start decreasing and at the end when only one atom will remain then the magnetic field strength will reduce to the field of one atom only.