Help me please. I really need it, explain to me how it is done too, I’d really really appreciate that.
1 answer:
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Answer:
15% off
Step-by-step explanation:
We know we paid $25.50 of the original $30. We can divide these two numbers . This is means we paid 85% of the original price. The discount percentage is the remaining percentage from 85 to 100 which is 15. The pants were 15% off.
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,