Which best explains why a hot air balloon rises into the air?

A. As the air is cooled, it becomes more dense and the balloon rises.
B. As the air is cooled, it becomes less dense and the balloon rises.
C. As the air is heated, it becomes less dense and the balloon rises.

C. As the air is heated, it becomes less dense and the balloon rises.

Step-by-step explanation:

A is wrong. The denser cold air would cause the balloon to drop.

B is wrong. As the air is cooled, it becomes less dense.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)