ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: shinny on November 09, 2008, 05:33:11 pm
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Chances are I'm wrong somehow since VCAA and iTute go against what I think here, but in that case someone point me in the right direction if I am wrong. In the wine glass question:
(http://img233.imageshack.us/img233/3417/wineglasseg6.jpg)
Once the question asks:
"At time t = 0 seconds wine begins to be poured into the upright glass so that its depth (x cm in the graph opposite) is increasing at a rate of 2 cm/sec."
I interpreted that as 
yet VCAA and iTute have 
, but since the wine glass is tilted on its side, once you start pouring stuff into it, it'll be filling from five to zero; not the other way around. Hence negative?
-2 seems to make even more sense when you start subbing in values into the consequent 
equation (where A is the surface area of the wine), because you end up with these values being negative at values beyond the turning point on the above graph (e.g. x=2,4 etc) and positive below the turning point, when it clearly should be the other way around. So is VCAA wrong? I don't see how their answer makes sense unless I'm looking at this wine glass from the wrong way, but 'upright' is meant to be in the negative x-direction isn't it?
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It says that the wine glass is upright when wine is poured into it.
Therefore you have to imagine as if the inverse was rotated around the y axis - the volume of wine that goes into the glass increases.
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Yeh but if it's upright when wine is being poured into it, that means liquid is collecting on the positive x-axis side and building up towards 0. Doesn't that mean x is decreasing i.e. negative rate of change? I don't quite get what you mean by taking the inverse and rotating, hows that even relevant? You need to fix the x and y co-ordinates don't you? I mean, we're still working with them as they are on the graph.
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Isn't it building up from 0 towards 5?
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You're right about pouring water into the negative x-direction, but where would that water collect? It doesn't start at x=5 because that's the rim of the glass.
It'd start at x=0 and work its way up to x=5, therefore x increases as time increases, therefore dx/dt is positive.
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OH WAIT. OK nah don't worry. I just misinterpreted the graph. I thought it was sitting the other way -_-" Fail@visualising. Yeh, I thought it was one of those wine glasses where it was more like a V shape on top, and then they just truncated the rest of it. Yeh dw now I get it <_<
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Aha, :(
Was my initial explanation bad?
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Ahah not that it was bad, it just didn't address my misunderstanding =P Had the idea locked into my head that 'upright' was the negative x-direction all along so yeh.
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OH WAIT. OK nah don't worry. I just misinterpreted the graph. I thought it was sitting the other way -_-" Fail@visualising. Yeh, I thought it was one of those wine glasses where it was more like a V shape on top, and then they just truncated the rest of it. Yeh dw now I get it <_<
lol
how the hell do you drink from that!
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well i suppose you tip it so it's not upright anymore :9