Homework Help: calc

Posted by bekah on Sunday, January 2, 2011 at 11:32am.

can you just show me how to set this up? or a formula that could help? im confused.
The length of a rectangle is increasing at 3 ft/min and the width is decreasing at 2 ft/min. When the length is 50 ft and the width is 20 ft, at what rate is the rectangle decreasing?

calc - Reiny, Sunday, January 2, 2011 at 12:00pm
Let the width of the rectangle be x ft
let the length of the rectangle be y ft

Area = xy
d(Area)/dt = x dy/dt + y dx/dt

given: dx/dt = -2 and dy/dt = 3
so when x = 20 and y = 50

d(Area)/dt = 20(3) + 50(-2)
= -40

At that moment, the area is decreasing at a rate of 40 ft^2/min
calc - bekah, Sunday, January 2, 2011 at 12:06pm
thank you so much!!!!

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