- #1

biochem850

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## Homework Statement

"At a given instant the legs of a right triangle are 8in. and 6in., respectively. The first leg decreases at 1in/min and the second increases at 2in/min. At what rate is the area increasing after 2 minutes?"

## Homework Equations

A=[itex]\frac{1}{2}[/itex]bh

[itex]\frac{db}{dt}[/itex]=-1

[itex]\frac{dh}{dt}[/itex]=2

## The Attempt at a Solution

A=[itex]\frac{1}{2}[/itex]bh

[itex]\frac{dA}{dt}[/itex]=[itex]\frac{1}{2}[/itex]([itex]\frac{db}{dt}[/itex]*h+b*[itex]\frac{dh}{dt}[/itex])

[itex]\frac{dA}{dt}[/itex]=[itex]\frac{1}{2}[/itex](-1*10+6*2)

[itex]\frac{dA}{dt}[/itex]=[itex]\frac{1}{2}[/itex](2)=1

Therefore the area is increasing at a rate of [itex]\frac{1in^{2}}{min}[/itex] after 2 minutes. Is my reasoning sound (I'm pretty sure my answer is correct but I want to be sure that my work is logical)?

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