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August 24th, 2017, 07:20 AM   #1
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Exclamation Provided solution isn't simplified and is wrong?

Observe the following problem:



Notice that the answer doesn't seem right. Shouldn't K be C*(4*pi)*(3/(4*pi))^(2/3) rather than C*((4*pi*3)/(4*pi))^(2/3)? Or am I wrong and I don't understand? If this answer isn't wrong, then why isn't it simplified? What's going on here? This was the provided answer key by my instructor.

Last edited by John Travolski; August 24th, 2017 at 07:41 AM.
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August 24th, 2017, 07:49 AM   #2
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You are correct , probably a typo.

The exponent should be between the parenthesis and bracket.

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August 24th, 2017, 07:57 AM   #3
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Thanks, I appreciate the reassurance.
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August 24th, 2017, 10:52 AM   #4
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Any sphere of radius r has volume r³ and surface area r², so dV/dt = -cV$^{2/3}$,
where c is a positive constant and V is the raindrop's volume at time t.

The above assumes that the raindrop's rate of evaporation means the raindrop's rate of change of volume.
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