The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

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The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

Mathematics
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start by assigning a variable to represent the side length of the square. lets call it x. now, what would be the area of the square in terms of x?
100?
no - what is the area of a square if its side length is equal to x?

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I don't get it
|dw:1350248149705:dw|
Oh, A=x^2
:)
good, so now you just need to differentiate both sides with respect to time (t). Do you know how to do that?
Derivative, right?
yes
dA/dt=2x(dx/dt)
perfect! almost there now...
now, when the area is 150 cm^2, then what would the side length of the square equal?
i.e. what is the length of the side of a square if its area is 150 cm^2?
sq rt of 150?
yes
So you would plug in x and dx/dt to get dA/dt?
now, in the equation you derived, you got:\[\frac{dA}{dt}=2x\frac{dx}{dt}\]Your questions tells you how fast the side length is increasing, so this gives you the value for:\[\frac{dx}{dt}=10\]
yes - you have it now - well done! :)
Yay, thank you! :)
yw :)
I would ask for more help, but it's okay.
?
I don't really understand related rates.
What you should do is find a specific example and then post that as a question. Otherwise it becomes difficult to explain in general terms.
For example, in this question, the rate of increase of side length is RELATED to the rate of increase of area by the formula you just derived.
Well, I'm just doing this packet. I understand some, but not all. http://tutorial.math.lamar.edu/ProblemsNS/CalcI/RelatedRates.aspx
In that case I would advise you to pick one that you don't understand and post it as a question. If you also include what parts of it you DO understand then it becomes easier for others to focus on the parts that you are having difficulties with.
Okay, thanks again :D

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