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?

1 Answer
Mar 19, 2016

V=3.888*t + 5,374.8*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

(30 cancel(" days"))/(1 " month")xx(24 cancel(" hours"))/(1 cancel(" day"))xx(60 cancel(" min"))/(1 cancel(" hour"))xx(60 " sec")/(1 cancel(" min"))
=2.592xx10^6 "sec"/"month"

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

V/10^6=2.592xx10^6*1.5*t+(2.592xx10^6)^2*0.008*t^2

V=10^-6(2.592xx10^6*1.5*t+(2.592xx10^6)^2*0.008*t^2)
V=2.592*1.5*t+10^-6*(2.592xx10^6)^2*0.008*t^2
V=2.592*1.5*t+(2.592)^2*0.008xx10^6t^2
V=3.888*t + 5,374.8*t^2