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# Lagrange Multipliers Q watch

1. Hey guys

Question is above. I can't seem to derive the correct expression for mass (which we want to minimise subject to fixed volume).

I can solve using lagrange multipliers fine - just the first step of writing down the equations I am having trouble with. What's the best way to put these worded questions into algebraic expressions?

2. (Original post by fkhan100)
Hey guys

Question is above. I can't seem to derive the correct expression for mass (which we want to minimise subject to fixed volume).

I can solve using lagrange multipliers fine - just the first step of writing down the equations I am having trouble with. What's the best way to put these worded questions into algebraic expressions?

What is the volume of the cylinder, given its base radius and height? What is the mass of the shell given those dimensions?
(Eep, spoilers for the 2013 paper which I'm leaving as a mock :P )
3. (Original post by Smaug123)
What is the volume of the cylinder, given its base radius and height? What is the mass of the shell given those dimensions?
(Eep, spoilers for the 2013 paper which I'm leaving as a mock :P )
So obviously V = pi(h)(r)^2, where h is height and r is radius of the disc at the end of the cylinder.

We have mass = volume*density => mass = k(p)*pi(r)^2 + k*pi*d (where d is diameter). Is that right? Not sure..
4. (Original post by fkhan100)
So obviously V = pi(h)(r)^2, where h is height and r is radius of the disc at the end of the cylinder.

We have mass = volume*density => mass = k(p)*pi(r)^2 + k*pi*d (where d is diameter). Is that right? Not sure..
Yes, that's right. Now extremise the mass subject to V remaining constant.
5. (Original post by Smaug123)
Yes, that's right. Now extremise the mass subject to V remaining constant.
Yep done. So you're keeping all four 2013 papers as mocks? That's 12 hours of mock examinations which is quite long . Which years are you doing for supervisions then?
6. (Original post by fkhan100)
Yep done. So you're keeping all four 2013 papers as mocks? That's 12 hours of mock examinations which is quite long . Which years are you doing for supervisions then?
In general I'm doing 09/10/11 for supervisions, although Met+Top was *really* hard in those years so I'm pushing that back to 06/07 (IIRC). For CA (which I've not started yet) I think my supervisor wants me to do 2013 :/

Yeah, that's nearly two weeks of mocks, I suppose - hadn't thought of that! Better get started soon…

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