15. A rectangular wooden gate with two diagonal boards across the front is shown below. If the length of one of the diagonals is 14 feet, find the
closest value of x, the width of the gate.
Х
11 feet

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

assuming this is from a math graphing problem.

7 would be on the x-axis which is the horizontal line on the graph

84 would be on the y-axis which is the vertical line on the graph