. At a certain instant, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. At the same instant, the width is 2 inches and is decreasing at the rate of .5 inches per minute. Is the area increasing or decreasing

Area is increasing

Step-by-step explanation:

Let x be the length of rectangle and y be the width of rectangle

We are given that

x=3 in

dx/dt=1 in/min

y=2 in

dy/dt=-0.5/min

We know that

Area of rectangle,

Differentiate w.r.t t

Substitute the values

Hence, the area  of rectangle is increasing.

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answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb