Help needed please!
A rectangle made of elastic material will be made into a cylinder by joining edges AD and BC. To support the structure, a wire of fixed length L is placed along the diagonal of the rectangle. Find the angle that will result in the cylinder of maximum volume.
see attached picture
thank you very much!
unfortunately i cannot attach a picture
so here is a shot at it...
theta is angle a, in the triangle cab
i got it so far, but just a quick question on the optimization. when u differentiate would you factor out the (L^3)/4 pi and then differentiate the trig functions, or would you differentiate the entire thing?
I think it's better factorising, less obstruction, more visibility :D
what do i do next?
so i got the derivative to be...
then i set it equal to zero and i get
what do i do from here?
Hm... No... You have to keep the factor L^3/4pi for the whole thing (correction in red)
Originally Posted by doctorgk
The derivative will be :
then i do
so then the derivative is
then i can factor out a cosine and get
i know u have to solve for theta, but i kinda forgot how to solve trig equations
You can factor out only if it's ;)
The better way to do is to factorise, and solve...
how do u then solve it?
im sure you can factor out the L^3/4 pi because it cannot be zero
Here, yes, you can factor it out.
Now, replace by and then solve for it.
thank you very much for the help!