Need a little help with this related rates problem

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The discussion revolves around a related rates problem involving the area of a circle and the rate of change of its radius. The user initially calculates the derivative of the radius and arrives at 1/2π, while the expected answer is 1/2. There is an emphasis on the importance of unit management to avoid mistakes in calculations. Participants encourage the user to seek help and recognize that making errors is a part of the learning process. The conversation highlights the value of humility and the willingness to learn from mistakes in mathematics.
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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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