March 2nd, 2018, 06:40 AM  #1 
Newbie Joined: Sep 2017 From: xxxx Posts: 8 Thanks: 0  Substitution
Hi All, Im running into the following problem The equation is something like this: $\displaystyle dv=(1/s^2*s)$ and s = 1/v How do I substitute 1/v (v^1) into the equation? Can someone explain that to me in simple steps? I thought: $\displaystyle dv=(1/v^1*v^1)$ But I think that is wrong. Thanks!!! Last edited by New123; March 2nd, 2018 at 06:43 AM. 
March 2nd, 2018, 06:47 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  Quote:
$s = \dfrac{1}{v} \implies v = \dfrac{1}{s} \implies dv = \dfrac{1}{s} = v$  
March 2nd, 2018, 09:08 AM  #3  
Newbie Joined: Sep 2017 From: xxxx Posts: 8 Thanks: 0  Quote:
$dv = \dfrac{1}{s} = v$ Can you explain the above? I simply do not understand why $dv = \dfrac{1}{s}$ becomes $v$  
March 2nd, 2018, 12:11 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  Quote:
$s = \dfrac{1}{v} \implies v=\dfrac{1}{s}$ you are given $s = \dfrac{1}{v}$ algebraically ... (1) multiply both sides by $v$ $v \cdot s = v \cdot \dfrac{1}{v}$ $v \cdot s = \cancel{v} \cdot \dfrac{1}{\cancel{v}}$ $v \cdot s = 1$ (2) divide both sides by $s$ ... $\dfrac{v \cdot s}{s} = \dfrac{1}{s}$ $\dfrac{v \cdot \cancel{s}}{\cancel{s}} = \dfrac{1}{s}$ $v = \dfrac{1}{s}$  

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