Need a little help with this related rates problem

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SUMMARY

The discussion revolves around solving a related rates problem involving the area of a circle, where the area A is defined as A=πr². The user initially calculated the rate of change of the radius (dR/dt) as 1/2π, but the correct answer is 1/2. The conversation highlights the importance of unit management in mathematical problems and the value of seeking help when encountering difficulties. Participants emphasize that recognizing mistakes is a crucial part of the learning process.

PREREQUISITES
  • Understanding of calculus concepts, specifically related rates
  • Familiarity with the formula for the area of a circle (A=πr²)
  • Basic knowledge of differentiation and derivatives
  • Ability to manage and interpret units in mathematical equations
NEXT STEPS
  • Study the application of the chain rule in related rates problems
  • Learn how to derive and apply the formula for the area of a circle in various contexts
  • Practice solving related rates problems with different geometric shapes
  • Review techniques for unit conversion and management in calculus
USEFUL FOR

Students studying calculus, particularly those struggling with related rates problems, and educators looking for insights on common student misconceptions in mathematical applications.

MrDickinson
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Can someone help me with this?
(dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections).
A=pir^2
(dA/dt)=2pir(dR/dt)
Multiply through by (1/2pir)
(dA/dt)/(2pir)=dR/Dt
What is the rate of change of the radius for a circumfrance of 2
I just used the related rates formula that I derived for dR/dt to find the derivative of of the radius and I get 1/2pi, the problem is that the answer is 1/2... gosh I suck at this. Can someone please help me?
 
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I moved your thread to our homework section.
MrDickinson said:
(dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections).
Taking care of units allows to avoid many mistakes in homework problems.
MrDickinson said:
What is the rate of change of the radius for a circumfrance of 2
I just used the related rates formula that I derived for dR/dt to find the derivative of of the radius and I get 1/2pi, the problem is that the answer is 1/2... gosh I suck at this. Can someone please help me?
What did you get as value for r?
 
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mfb said:
I moved your thread to our homework section.
Taking care of units allows to avoid many mistakes in homework problems.
What did you get as value for r?
Thanks. I understand the value of checking units, but in math they are useless. I understand where you are going though, as I once had a chemistry TA make the statement "numbers without units are useless" as in... I think he was getting at something like "math without application is useless." But for me, it turns out that they usually don't do anything other than tell me what I already know; namely, I am wrong.

I think I see where I went wrong... how stupid of me... I mean, I should feel shame and dishonor over this...
 
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MrDickinson said:
... gosh I suck at this.

MrDickinson said:
I think I see where I went wrong... how stupid of me... I mean, I should feel shame and dishonor over this...

I think you might be a bit hard on yourself. You recognized that you needed help and sought it out from those who are likely to be more knowledgeable. No one got hurt, and no one died as a result of your failure in solving this math problem. In general as well, having the humility to recognize your mistakes and actively seek to correct them is absolutely nothing to be ashamed of.
 
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Tallus Bryne said:
I think you might be a bit hard on yourself. You recognized that you needed help and sought it out from those who are likely to be more knowledgeable. No one got hurt, and no one died as a result of your failure in solving this math problem. In general as well, having the humility to recognize your mistakes and actively seek to correct them is absolutely nothing to be ashamed of.
Thank you.
 

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