A radioactive substance has a half-life of one month, which means that at the end of each month, the level of radioactivity is h
alf the level that it was at the beginning of the month The substance was discovered in the soil
near a high school football field. The table shows the relationship between the radioactivity level found in the soil, r(t)and the number of months since discovery, 2.
2
10
5
25
125
4
Which statement correctly interprets the initial value?
near a high school football field. The table shows the relationship between the radioactivity level found in the soil, r(t)and the number of months since discovery, 2.
2
10
5
25
125
4
Which statement correctly interprets the initial value?
1 answer:
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The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when 
.
We can parameterize the spherical cap in spherical coordinates by
where
and 
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
We can parameterize the spherical cap in spherical coordinates by
where
Now the surface area of the cap is given by the surface integral,