Answer:
Un batido de proteínas cuesta $ 5,25.
Step-by-step explanation:
El sistema de ecuaciones descrito al final del enunciado coincide con lo descrito al comienzo del mismo, de modo que podemos concentraron casi exclusivamente en la resolución del sistema en cuestión, la cual se describe a continuación:
Este es el sistema a resolver:
(1)
(2)
Donde 
es el coste de un batido de fresa y 
corresponde al coste de un batido de proteínas:
1) Despejamos en (1):
2) Eliminamos en (2):
3) Simplificamos y despejamos :
Un batido de proteínas cuesta $ 5,25.
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,
Answer: v = 13920 cm cubed
