Micah constructs a rectangular prism with a volume of 360 cubic units. The height of his prism is 10 units and the base has an area of 36 square units. Micah claims that the base of the prism must be a square. Is it possible that the base is a rectangle instead? What would its dimensions be?

answer:

your answer is: c. 196 7/8 in^3.

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)

60: 45 =12: 9 =4: 3 so the answer is 4: 3

step-by-step explanation: