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the length of a rectangle increases at a rate of 0.5 cm/sec and the width decreases at a rate of 0.5 cm/sec at the time when the length is 10cm and the width is 7 cm what is the rate of change in the area of the rectangle?

Respuesta :

Answer:

Step-by-step explanation:

let length=x

width=y

area A=xy

[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]

area is decreasing at the rate of 1.5 cm^2/sec