anonymous
  • anonymous
The cross section of a trough is an inverted isosceles triangle. Prove that the trough has maximum capacity when the vertex angle is pi/2rad.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Define the cross sectional area in terms of the vertex angle (assuming the sides are a constant length. Differentiate to find the stationary points and prove pi/2 is a max.
anonymous
  • anonymous
Note that the area of a triangle with sides a,b,c, with the angle C between a and b has an area: \[\text{Area} = \frac{1}{2}\cdot a\ \cdot b\ \cdot \sin C \]
anonymous
  • anonymous
so differentiate 1/2ab sinc? that become 1/2ab cosc??

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