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## Homework Statement

## Homework Equations

## The Attempt at a Solution

V=20 S=6 E=2 H=20/12 (from V=SEH?)

[itex]\frac{dS}{dt}=-.2[/itex] <--- + OR -?

[itex]\frac{dE}{dt}=.3[/itex] <--- + OR -?

V=SEH

Product rule for 3 variables:

[itex]\frac{dV}{dt}=SE\frac{dH}{dt}+EH\frac{dS}{dt}+SH \frac{dE}{dt}[/itex]

[itex]0=SE\frac{dH}{dt}+EH(-.2)+SH(.3)[/itex]

[itex]-EH(-.2)-SH(.3)=SE\frac{dH}{dt}[/itex]

[itex]\frac{-EH(-.2)-SH(.3)}{SE}=\frac{dH}{dt}[/itex]

[itex]\frac{-(2)(\frac{20}{12})(-.2)-(6)(\frac{20}{12})(.3)}{SE}=\frac{dH}{dt}[/itex]

[itex]\frac{-7}{36}=\frac{dH}{dt}[/itex]

Negative, therefore decreasing.

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