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16.684 x a

---------             >16

14b x (10a)      

Guest Nov 3, 2015
 #1
avatar+92919 
+5

\(\frac{16.684*a}{14b*(10a)}>16\\ \frac{16.684a}{140ba}>16\qquad a\ne0\quad and \quad b\ne0 \\ \frac{16.684}{140b}>16\\ \frac{16.684}{b}>16*140\\ \frac{16.684}{b}>2240\\ \frac{16.684}{b}*\frac{b^2}{1}>2240*\frac{b^2}{1}\\ 16.684b>2240b^2\\ 0>2240b^2-16.684b\\ b(2240b-16.684)<0\)

 

Consider y=b(2240b-16.684)

This is a concave up parabola  

The roots are b=0 and   2240b-16.684=0

The roots are b=0 and   b=16.684/2240

The roots are b=0 and   b=417/56000

The parabola will have negative y value when b is between 0 and 417/56000

 

That is                          

 

\(0 < b < \frac{417}{56000}    \qquad and \;\;a\in R \;\;\;where\;\;\;\; a\ne0\)

Melody  Nov 3, 2015

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