What is the rate of change of the width (in ft/sec) when the height is 10 feet, if the height is decreasing at that moment at the rate of 1 ft/sec.A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 60 square feet?

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Answer 1 · 2015-03-16T18:20:52

The rate of change of the width with time #(dW)/(dt)# = #0.6"ft/s"#

#(dW)/(dt)=(dW)/(dh)xx(dh)/dt#

#(dh)/(dt)=-1"ft/s"#

So #(dW)/(dt)=(dW)/(dh)xx-1=-(dW)/(dh)#

#Wxxh=60#

#W=60/h#

#(dW)/(dh)=-(60)/(h^2)#

So #(dW)/(dt)=-(-(60)/(h^2))=(60)/(h^2)#

So when #h=10#:

#rArr# #(dW)/(dt)=(60)/(10^2)=0.6"ft/s"#