The town of West Fortuna has a population of 10,000 people. On Friday night, 10,000 more people from out of town come to west fortuna to attend a football game, the number of people in the Town decrease exponentially. One hour after the end game, there are 16,000 people in town. Use the point tool to plot points showing, to the nearest 500 people, how many people are in West Fortuna: at the end of the football game, 2 hours after the game ends, and 6 hours after the game ends.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

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)