.
be a subset of 
such that no sum of three distinct elements of 
.
.
that satisfy the equation 
.
be a circle, and let a line 
intersect 
and 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
and 
Prove that
.
Prove that
and 
Prove that
,
,
is not greater than 
.
.
.
Y by samrocksnature
The company produces sets of 
tennis balls in two types of packaging: a long cylinder with a thickness of 
ball and a flat cylinder with a height of ball, as shown in the picture. The balls touch each other and the walls so that they do not dangle. The empty space is filled with plastic chips.
a) In filling a package - the long or flat, - requires more chips?
b) How many grams of crumb does it take to fill a flat pack if it takes
grams to fill a long one ?
To solve (b), you will need an interesting fact, which Archimedes already knew: the ball occupies exactly
of the volume the cylinder in which it is inscribed (the ball touches the walls, bottom and cover of the cylinder).
tennis balls in two types of packaging: a long cylinder with a thickness of 
ball and a flat cylinder with a height of ball, as shown in the picture. The balls touch each other and the walls so that they do not dangle. The empty space is filled with plastic chips.a) In filling a package - the long or flat, - requires more chips?
b) How many grams of crumb does it take to fill a flat pack if it takes
grams to fill a long one ?To solve (b), you will need an interesting fact, which Archimedes already knew: the ball occupies exactly
of the volume the cylinder in which it is inscribed (the ball touches the walls, bottom and cover of the cylinder).This post has been edited 2 times. Last edited by parmenides51, Jun 16, 2021, 5:46 PM
