
Determine the equation
Hi, I need help in finding the equation for x(t), h(t), and V(t). So far from what I understand 2x+h=W. I just don't know how to write it all out. If anyone can, please help.
W=45
For this trough the sheet metal is bent into a right trapezoid with the left side always making a right angle with the bottom and the right side bent such that it makes an angle http://webwork.sdsu.edu/webwork2_fil...631e7925d1.png with a line perpendicular to the bottom. Unlike the first trough, where the strip is bent evenly into thirds, you need to determine where the bends are made such that the bottom and the right side are equal and the left side is exactly the height needed to make the top parallel to the bottom.
(link to picture, Figure B)
Untitled Document
Determine the positions of the bends in the sheet metal as a function of http://webwork.sdsu.edu/webwork2_fil...631e7925d1.png. Based on Figure B, find the values of http://webwork.sdsu.edu/webwork2_fil...dd0b8b8e91.png and http://webwork.sdsu.edu/webwork2_fil...11a2eaba01.png as http://webwork.sdsu.edu/webwork2_fil...631e7925d1.png varies. ( http://webwork.sdsu.edu/webwork2_fil...5b59f2bc11.png is used in place for http://webwork.sdsu.edu/webwork2_fil...631e7925d1.png)
http://webwork.sdsu.edu/webwork2_fil...66fdefb981.png .
http://webwork.sdsu.edu/webwork2_fil...a88d633741.png .
Write a function of the volume depending on http://webwork.sdsu.edu/webwork2_fil...631e7925d1.png.
http://webwork.sdsu.edu/webwork2_fil...0270ccc131.png .

According to the picture, $\displaystyle h$ is the leg of the triangle with angle $\displaystyle \theta$ and hypotenuse $\displaystyle x$, so $\displaystyle h=x\cos\theta$. Using $\displaystyle 2x+h=45$, you should be able to isolate $\displaystyle x$ and $\displaystyle h$ as functions of $\displaystyle \theta$.