1. ## 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 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.

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Determine the positions of the bends in the sheet metal as a function of . Based on Figure B, find the values of and as varies. ( is used in place for )

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Write a function of the volume depending on .
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2. 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 $\displaystyle \theta$.