My Math Forum Provided solution isn't simplified and is wrong?

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 August 24th, 2017, 06:20 AM #1 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 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 06:41 AM.
 August 24th, 2017, 06:49 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, 06:57 AM #3 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Thanks, I appreciate the reassurance.
 August 24th, 2017, 09:52 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,847 Thanks: 1568 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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