Answer:
453 cm²/s
Explanation:
You want the rate of change in area of a rectangle initially 6 cm by 7 cm after 23 s when the side lengths are each increasing at 3 cm/s.
Rate of change
The area is given by ...
A = LW
Then the rate of change of area is ...
A' = L'W +LW'
Values
The length and width after 23 seconds are ...
L = 6 +3·23 = 75 . . . . cm
W = 7 +3·23 = 76 . . . cm
So, the rate of change of area is ...
L' = W' = 3 cm/s
A' = (3 cm/s)(76 cm) +(75 cm)(3 cm/s) = (151)(3) cm²/s = 453 cm²/s
The area of the rectangle is increasing at 453 cm²/s after 23 s.
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