A person wishes to design a rain collection system using the roof of their small shed as the collection surface. She finds that the distance along the slant of the roof is 11 feet 1 in, and the distance across the front of the shed is 14 ft and 9 in. She estimates the pitch of the roof is about 30 degrees. How many gallons of water will the roof collect for each inch of rain that falls

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

step-by-step explanation: hi!