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#1 NeoTifa  Icon User is online

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Optimization Problems

Post icon  Posted 01 June 2009 - 07:23 AM

Halp! Ajudame!

There's 2 that are giving me problems, actually. I keep getting funky answers.

Find the area of the largest rectangle that can be inscribed in the ellipse x^2/a^2 + y^2/b^2 = 1. I keep getting 0 and I just redid it and got 1 :(



A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector adn joining the edges CA and CB. Find the max capacity of such a cup. ((The drawing looks like a sideways Pacman with the corner of his mouth C and the upper lip A and lower lip B XD))

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#2 Nikhil_07n  Icon User is offline

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Re: Optimization Problems

Posted 01 June 2009 - 09:45 AM

Still solving..

haven't solved these since January.
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#3 NeoTifa  Icon User is online

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Re: Optimization Problems

Posted 01 June 2009 - 09:49 AM

Thanks in advance. <3
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#4 Nikhil_07n  Icon User is offline

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Re: Optimization Problems

Posted 01 June 2009 - 09:59 AM

Found the first one in last year's notes and copied from there :D

---Check Attachment---

Now, just find y.

I'll do the second problem later.

YOU CAN'T RUIN MY HOLIDAYS FOR THAT!! :D

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  • Attached Image

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#5 NeoTifa  Icon User is online

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Re: Optimization Problems

Posted 01 June 2009 - 10:03 AM

Thanks I tried it 3 different ways. <3 Now hows about the cup?
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#6 Nikhil_07n  Icon User is offline

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Re: Optimization Problems

Posted 01 June 2009 - 01:44 PM

It's 2 AM here.
I'll do that tomorrow morning.

It's easier then the first one.. I think.. but I'm feeling sleepy now.
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#7 NeoTifa  Icon User is online

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Re: Optimization Problems

Posted 02 June 2009 - 06:14 AM

Thanks. I got x = Sqrt(a^2/2) <3 awesome. See, I started by getting the common denominator. I think they were just algebra mistakes. :\ 4th times the charm, eh?
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#8 Nikhil_07n  Icon User is offline

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Re: Optimization Problems

Posted 02 June 2009 - 10:50 AM

:D

Now, the second one.

This was one tricky problem. I was wondering since today morning that how the hell could anyone create a drinking cup from a sector.

I figured out it was the remaining circular part that was being used.

here R(as given in the question) = x

Attached Image

Now just put the values and differentiate the equation.
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#9 Nikhil_07n  Icon User is offline

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Re: Optimization Problems

Posted 02 June 2009 - 11:13 AM

OMG, I got it wrong!!

Here's the correction..

The first equation shold be

2*(pi)*r = 2*(pi)*x - (theta)*x

Now, put the value of r in the below solution accordingly.

And since I'm watching Star Wars series again these days..

May the Force be with you..
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#10 NeoTifa  Icon User is online

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Re: Optimization Problems

Posted 02 June 2009 - 11:58 AM

Thanks. I got something totally janky.
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