ashleynguyenx3
  • ashleynguyenx3
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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asnaseer
  • asnaseer
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?
ashleynguyenx3
  • ashleynguyenx3
100?
asnaseer
  • asnaseer
no - what is the area of a square if its side length is equal to x?

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More answers

ashleynguyenx3
  • ashleynguyenx3
I don't get it
asnaseer
  • asnaseer
|dw:1350248149705:dw|
ashleynguyenx3
  • ashleynguyenx3
Oh, A=x^2
asnaseer
  • asnaseer
:)
asnaseer
  • asnaseer
good, so now you just need to differentiate both sides with respect to time (t). Do you know how to do that?
ashleynguyenx3
  • ashleynguyenx3
Derivative, right?
asnaseer
  • asnaseer
yes
ashleynguyenx3
  • ashleynguyenx3
dA/dt=2x(dx/dt)
asnaseer
  • asnaseer
perfect! almost there now...
asnaseer
  • asnaseer
now, when the area is 150 cm^2, then what would the side length of the square equal?
asnaseer
  • asnaseer
i.e. what is the length of the side of a square if its area is 150 cm^2?
ashleynguyenx3
  • ashleynguyenx3
sq rt of 150?
asnaseer
  • asnaseer
yes
ashleynguyenx3
  • ashleynguyenx3
So you would plug in x and dx/dt to get dA/dt?
asnaseer
  • asnaseer
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:\[\frac{dx}{dt}=10\]
asnaseer
  • asnaseer
yes - you have it now - well done! :)
ashleynguyenx3
  • ashleynguyenx3
Yay, thank you! :)
asnaseer
  • asnaseer
yw :)
ashleynguyenx3
  • ashleynguyenx3
I would ask for more help, but it's okay.
asnaseer
  • asnaseer
?
ashleynguyenx3
  • ashleynguyenx3
I don't really understand related rates.
asnaseer
  • asnaseer
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.
asnaseer
  • asnaseer
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.
ashleynguyenx3
  • ashleynguyenx3
Well, I'm just doing this packet. I understand some, but not all. http://tutorial.math.lamar.edu/ProblemsNS/CalcI/RelatedRates.aspx
asnaseer
  • asnaseer
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.
ashleynguyenx3
  • ashleynguyenx3
Okay, thanks again :D

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