An irrigation canal is the shape of a trapazoid. x = the bottom width, y = height and theta = angle of inclination of the sides from the vertical.

I derived the area and perimeter from the first half of the question, and as such
Area A = y(x + ytan(theta)) and perimeter p = x + 2y/cos(theta)

The question asks: It is known that the best design for a fixed inclination is found by minimizing P subject to the constraint that the area A = Ao is constant. Show that this implies that y^2 = (AoCos(theta)) / ( 2 - sin(theta))

Question

An irrigation canal is the shape of a trapazoid. x = the bottom width, y = height and theta = angle of inclination of the sides from the vertical.

I derived the area and perimeter from the first half of the question, and as such
Area A = y(x + ytan(theta)) and perimeter p = x + 2y/cos(theta)

The question asks: It is known that the best design for a fixed inclination is found by minimizing P subject to the constraint that the area A = Ao is constant. Show that this implies that y^2 = (AoCos(theta)) / ( 2 - sin(theta))

anonymous · Answer

attachment

anonymous · Answer

can anyone confirm this?

anonymous · Answer

hey I did that exact question two night ago?

anonymous · Answer

something like that.

someone deleted the other one I answered which was literally the same, word for word, came from a user called "alleycat" pretty sure.

do you have multiple accounts :|

anonymous · Answer

I don't

anonymous · Answer

I found that answer on cramster but wasn't cure of its quality.

anonymous · Answer

I found their profile but like you said, they deleted it.