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?

Question

5174 views around the world

You can reuse this answer
Creative Commons License

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"#