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August 24th, 2017, 07:20 AM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 109 Thanks: 0  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. 
August 24th, 2017, 07:49 AM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
You are correct , probably a typo. The exponent should be between the parenthesis and bracket. 
August 24th, 2017, 07:57 AM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 109 Thanks: 0 
Thanks, I appreciate the reassurance.

August 24th, 2017, 10:52 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,422 Thanks: 1462 
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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