Answer:
The area is changing at 2 m²/d.
Step-by-step explanation:
The area of a rectangle is given by:
[tex] A = l*w [/tex]
Where:
l is the length
w is the width
We have that the length is increasing at a rate:
[tex] \frac{dl}{dt} = 1 \frac{m}{d} [/tex]
And the width is decreasing at a rate:
[tex]\frac{dw}{dt} = -2 \frac{m}{d}[/tex]
The change in the rectangle's area is the following:
[tex] \frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt} [/tex]
When the length is 8 meters and the width is 18 meters we have:
[tex] \frac{dA}{dt} = 18 m*1\frac{m}{d} + 8 m(-2 \frac{m}{d}) [/tex]
[tex] \frac{dA}{dt} = 18 \frac{m^{2}}{d} - 16 \frac{m^{2}}{d} [/tex]
[tex] \frac{dA}{dt} = 2 \frac{m^{2}}{d} [/tex]
Therefore, the area is changing at 2 m² per day.
I hope it helps you!
