A cell phone plan costs $39 a month. The plan includes 2 gigabytes (GB) of free data and charges $15 per gigabyte for any additional data used. The monthly charges are a function of
the number of gigabytes of data used, given by
C (x) = (x)
39, if 0 ⩽ x ⩽ 2
39 + 15 (x − 2), if x > 2
(a) Find C(0.5), C(2), and C(4) .
(b) What do your answers in part (a) represent?
(c) Is C(x) continuous at x = 2?

250

step-by-step explanation:

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)