Brian, a scientist, is writing a research paper on projectile motion. during one of his experiments, he throws a ball from a point marked as point a, with a certain velocity in the horizontal direction. the ball travels a total horizontal distance of 0.6 meter after 1 second, 1.2 meters after 2 seconds, 1.8 meters after 3 seconds, and so on. it hits the ground on the 8th second. brian marks the point where the ball landed as point b. calculate the distance between point a and point b.

2500

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)