Rates of change involving two or more variables. (1 Viewer)

Carl5 · Apr 23, 2011

Oh, what a surprise, I'm stuck again lol

I think I might redo this exercise later because I'm a bit confused, but I'd like some help first.

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And

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ontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> <w:UseFELayout/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--> A rectangular block of ice with a square base has a height half the side of the base. As it melts, the volume of the block of ice is decreasing at the rate of 12 cm<sup>3</sup>s<sup>-1</sup>. Find the rate at which its surface area will be decreasing when the side of its base is 2.1 cm.

I actually have a few more questions, but they're of a similar structure (as far as I can tell).

Please and thank you! <3

Drongoski · Apr 23, 2011

For Q1:

You let x = length of side of cube so that:

V(x) = x³ and S(x) = 6x²

You are given dV/dt = 23

You want to find dS/dt

You use the chain rule:

$\frac {dV}{dt} = \frac{dV}{dS} \times \frac {dS}{dt} = \frac {dV}{dx} \times \frac {dx}{dS} \times \frac {dS}{dt}$

using

$\frac {dx}{dS} = \frac {1}{\frac {dS}{dx}}$

Carl5 · Apr 23, 2011

Sweet!!! Got it! Many thanks to you Drongoski. I'm now attempting another question similar to the first.

joeblow1 · Apr 23, 2011

really disappointing me drongoski ...

Carl5 · Apr 23, 2011

Disappointing??

Carl5 · Apr 23, 2011

Alright, I just got the second question I posted and another question right.

Now moving onto a question that requires pythagoras' theorem, but I'll try it first.

joeblow1 · Apr 23, 2011

remember pythagoras's therom is (a+b)^2 = c^2

Carl5 · Apr 23, 2011

uhhuhh...

jamesfirst · Apr 23, 2011

joeblow1 said:
really disappointing me drongoski ...

hey joe blow. Do you go to a school in Dundas??

Drongoski · Apr 23, 2011

joeblow1 said:
really disappointing me drongoski ...

Pierre, I'm secretly and vainly hoping Carl5 will hire me.

Drongoski · Apr 23, 2011

jamesfirst said:
hey joe blow. Do you go to a school in Dundas??

Don't think so. He belongs to the elite Eastern Suburbs.

Carl5 · Apr 24, 2011

Drongoski said:
Pierre, I'm secretly and vainly hoping Carl5 will hire me.

Hahaha, nice

Anyway, I'm calling it a night. Thank you so much for the help. I was having trouble with writing out all the variables, but for some reason that one example you gave me made the lightbulb light up.

Thank you!

joeblow1 · Apr 24, 2011

Drongoski said:
Don't think so. He belongs to the elite Eastern Suburbs.

damn right, we have beaches , the city, the airport , unsw ( I literally live within 30min combined walk and bus trip, sucks to be all u guys in western sydney on a bloody train for 3hrs to get to unsw ) bondi junction etc .. and you guys out west have shit train stations and hobos robbing and stabbing you.

Rates of change involving two or more variables. (1 Viewer)

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