问题标题：
【一道英文数学题(微积分)Thedimensionsofarectanglearechanginginsuchawaythatthearearemains24in^2.Atwhatrateistheperimeterchangingattheinstantwhenonesideis6in,longandisincreasingattherateof0.3inchperminu】
问题描述：
一道英文数学题(微积分)
Thedimensionsofarectanglearechanginginsuchawaythatthearearemains24in^2.Atwhatrateistheperimeterchangingattheinstantwhenonesideis6in,longandisincreasingattherateof0.3inchperminute?
陈善文回答：
Letldenotetheperimeter,aoneside
(l-2a)/2*a=24,thatisla-2a^2=48
differentiate(l-2a)/2*a=24respecttothetimet
a*dl/dt+l*da/dt-4a*da/dt=0
a=6,da/dt=0.3insertwehave(l=(24/6+6)*2=20)
6dl/dt+20*0.3-4*6*0.3=0
dl/dt=0.2istheanswer
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