pts) https://webwork.math.ohio-state.edu/...045bebae81.png

A covered metal triangular trough is constructed as follows:

A square shaped sheet of metal which is 200 centimeters wide and long square is folded along the center. Next, two pieces of metal in the shape of isosceles triangles are are welded to the ends. (See picture above). Finally, a metal cover is attached to the top (not shown).

We want to find the smallest and largest surfaces area https://webwork.math.ohio-state.edu/...575ddb21c1.png that a so constructed trough can have, and at what opening angle https://webwork.math.ohio-state.edu/...9b8ccd6cf1.png of the triangular pieces it is attained. Proceed as follows:

Find the surfaces area as a function of the angle. (Be sure to include all five sides of the trough).

https://webwork.math.ohio-state.edu/...5b662fc5f1.png

The natural domain of https://webwork.math.ohio-state.edu/...fbc39b2671.png is an interval with left endpoint https://webwork.math.ohio-state.edu/...4f6c767fe1.png and right endpoint https://webwork.math.ohio-state.edu/...4f6c767fe1.png.

On its domain https://webwork.math.ohio-state.edu/...eb479d0001.png has one stationary point https://webwork.math.ohio-state.edu/...7d610c7571.png. Although there is no explicit formula for the value of https://webwork.math.ohio-state.edu/...25e85dc621.png itself, it is possible to derive the exact value of the cosine of https://webwork.math.ohio-state.edu/...25e85dc621.png. Find it:

https://webwork.math.ohio-state.edu/...88d04e42c1.png

Find from this the surfaces area at the stationary point:

https://webwork.math.ohio-state.edu/...0e50ebde01.png Find also the global minimal value of https://webwork.math.ohio-state.edu/...575ddb21c1.png on its natural domain:

https://webwork.math.ohio-state.edu/...7a3e4ac791.png

Ok I have tried doing the first part and was pretty confident that I had the right answer but the computer was telling me that I was wrong. I know that 0 is the endpoint of the domain of w. Please Help