# If V=1.5*t+0.0080*t^2 has the units millions of cubic feet per month, how would you rewrite the equation if you wanted the result in cubic feet per second?

Mar 19, 2016

$V = 3.888 \cdot t + 5 , 374.8 \cdot {t}^{2}$

#### Explanation:

The volume, $V$, is given as ${10}^{6}$ cubic feet. Converting this to just cubic feet requires us to divide $V$ by a factor of ${10}^{6}$.

Converting months to seconds requires several multiplying factors

$\left(30 \cancel{\text{ days"))/(1 " month")xx(24 cancel(" hours"))/(1 cancel(" day"))xx(60 cancel(" min"))/(1 cancel(" hour"))xx(60 " sec")/(1 cancel(" min}}\right)$
$= 2.592 \times {10}^{6} \text{sec"/"month}$

Multiplying the volume, $V$, and time, $t$ by these factors gives

$\frac{V}{10} ^ 6 = 2.592 \times {10}^{6} \cdot 1.5 \cdot t + {\left(2.592 \times {10}^{6}\right)}^{2} \cdot 0.008 \cdot {t}^{2}$

$V = {10}^{-} 6 \left(2.592 \times {10}^{6} \cdot 1.5 \cdot t + {\left(2.592 \times {10}^{6}\right)}^{2} \cdot 0.008 \cdot {t}^{2}\right)$
$V = 2.592 \cdot 1.5 \cdot t + {10}^{-} 6 \cdot {\left(2.592 \times {10}^{6}\right)}^{2} \cdot 0.008 \cdot {t}^{2}$
$V = 2.592 \cdot 1.5 \cdot t + {\left(2.592\right)}^{2} \cdot 0.008 \times {10}^{6} {t}^{2}$
$V = 3.888 \cdot t + 5 , 374.8 \cdot {t}^{2}$