Ika_Kim
somebody please help me..got test tonight but still dunn how to solve this...
The base of a triangle increases at the rate 2cm per second, and height decreases at the rate of 1/2cm per second.Find the rate of change f its area when the base and height are of length 5cm... ? T.T helpp
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Ika_Kim
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anybody ??? :(
Ika_Kim
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you know agent00smith ?
agent0smith
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hmm.... we know \[A = 0.5 b h\] \[\frac{ db }{ dt } = 2 (cm/s)\] \[\frac{ dh }{ dt }= -0.5 (cm/s)\] We need \[\frac{ dA }{ dt } = ?\]
Ika_Kim
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chain rule ?
Ika_Kim
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but we have t differentiate A with respect to ??
agent0smith
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Yeah that's what i'm trying to think of...
Ika_Kim
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o.O ok ... i really dunno how to relate that
zepdrix
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Hmm are we assuming this is a `right` triangle? :o
zepdrix
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I guess it would have to be, otherwise we need more information. :)
Looks like agent was on the right track.
Both \(\large b\) and \(\large h\) are variables.
Just apply the product rule! :D
zepdrix
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Differentiate with respect to time*
agent0smith
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Yeah that's what I was thinking... differentiate A wrt t
Ika_Kim
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huh ??? yeahh differentiate wrt time . that is wwhat we want to find
Ika_Kim
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im not clear with that
agent0smith
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But then that seems to make the actual values of the base and height unnecessary, but maybe that's okay....
\[\frac{ dA }{ dt} = 0.5 \frac{ db }{ dt}\frac{ dh }{ dt}\]
zepdrix
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Woops, product rule! :O
zepdrix
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\[\large A=\frac{1}{2}bh\]\[\large A'=\frac{1}{2}b'h+\frac{1}{2}bh'\]Something like that, yes? :D
Ika_Kim
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huhh ????? how can...i dont undrstand...
Ika_Kim
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urmmm let me try that
Ika_Kim
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wow.....yeahh!!! correct answer !!! greatt !! thank you so much guys ! love uollsz!! :D
zepdrix
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yay team \:D/
Ika_Kim
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my mentors :)
agent0smith
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ah yes, my bad