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:
19 ft
Step-by-step explanation:
The perimeter of a rectangle is given by ...
P = 2(L +W)
Filling in the given values, we have ...
78 = 2(20 +W)
39 = 20 +W . . . . . divide by 2
19 = W . . . . . . . . subtract 20
The width of the rectangular pen is 19 feet.
Answer:
de from a shuffled pack, you win $9.
Find the expected value you win (or lose) per game.
Step-by-step explanation:
to join in his game. The rules are: To play you must pay him $2. If you pick a spade from a shuffled pack, you win $9.
Find the expected value you win (or lose) per game.
The y-intercept is "equal to", "y=1", "x=0".
_____
The y-intercept is the "+1" part of the equation y=2x+1.