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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?

A.) 4.94 sec
B.) 3.28 sec
C.) 9.7 sec
D.) 1.33 sec

Respuesta :

metchelle
Given:

L1 = original length = 4 km
W1 = original width = 4 km
A1 = original area = 4*4 = 16 km^2
A2 = 4(16) = 64 km^2

Given the second area, we can conclude that the lengths and widths of the zoomed out photograph should both be 8 km.

Given that the zooming occurs at 3 km/sec, the amount of time needed for the lengths and widths to zoom out from 4 km to 8 km is shown below:

8km - 4km / 3km/s = 4 / 3 = 1.33 seconds

Therefore, the correct answer is D.

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