How to solve a related rates problem with an expanding square?

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Homework Help Overview

The problem involves related rates concerning an expanding square, specifically examining the relationship between the rate of change of the area and the rate of change of the side length.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss differentiating the area formula A = s^2 with respect to time and explore the implications of the given rates of change. There is a focus on the relationship between dA/dt and ds/dt, with one participant questioning the correctness of their derived equation.

Discussion Status

The discussion is ongoing, with participants providing hints and confirming each other's reasoning. There is an exploration of the implications of the differentiation, but no consensus on the final answer has been reached.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the depth of exploration and the information available for solving the problem.

carlodelmundo
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Homework Statement



When the area of an expanding square, in square units, is increasing three times as fast as its side is increasing, in linear units, the side is

a.) 2/3
b.) 3/2
c) 3
d) 2
e) 1

Homework Equations



A = s^2
dA/dt = 3s^2


The Attempt at a Solution



Can anyone give me hints on how to start this problem?
 
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Start by differentiating A=s^2 with respect to time correctly. Use implicit differentiation.
 
Okay, Dick.

I get dA/dt = 2s dS/Dt. Since it's saying that the area is increasing three times as fast as its side is increasing... 2s must equal to 3. or s = 3/2

is this correct?
 
carlodelmundo said:
Okay, Dick.

I get dA/dt = 2s dS/Dt. Since it's saying that the area is increasing three times as fast as its side is increasing... 2s must equal to 3. or s = 3/2

is this correct?

You betcha.
 
Thank you, Sir.
 

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