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slava [35]
3 years ago
14

A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle.

As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Mathematics
1 answer:
Lesechka [4]3 years ago
6 0
So we know that the formula for the area of a rectangle is A = lw.
Now both the length and width of the rectangle increase at 3 km/s, therefore, A(t) = (3t+l)*(3t+w). Since the initial length = initial width = 4 km, then the initial area = 16 [tex]km^2. We want to know the time when the area is four times its original area, therefore, our new formula is: 4A(t) = (3t+l)*(3t+w). Plugging in our known values we have:

64 [km^2] = (3t + 4 [km])*(3t + 4 [km])
t =  \frac{4}{3} s

The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.
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