Question

Help Precalculus!
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 (1 point)

4.94 sec
3.28 sec
9.7 sec
1.33 sec

Answer 1

@SolomonZelman

Answer 2

@satellite73

Answer 3

original size = 16 km^2

Answer 4

after 1 sec:

Area = (4+3)(4+3) = 49 km^2

Answer 5

I don;t understand how to solve the time.

Answer 6

4 times the original size = 4*16 = 64 km^2

Answer 7

after 3 seconds:

A = (4 + 3 +3) * (4 +3 + 3) = 10 * 10 = 100 km^2

Answer 8

2 seconds i mean

Answer 9

so you want this equation:

Answer 10

Area = length * Width

64 = (4+3t)(4+3t)

Answer 11

both Length and Width are initially 4 and increase at a rate of 3 per second

Answer 12

but there isn't answer 2 seconds. I also got that before.

Answer 13

right, you have to solve
64 = ( 4 + 3t )^2
for t

Answer 14

so I need to divide 4 by 3?

Answer 15

no

Answer 16

\[64 = (4 + 3t)^2\]

Answer 17

square root both sides first

Answer 18

well yeah the answer is 4/3

Answer 19

ok thank you so much. the answr is 1.33 right?

Answer 20

yeah, you can check by using that time, and running through the original question again

Answer 21

area is length times width,
They both start at 4 and increase by 3 every second
time is 1.3333 seconds

A = (4+1.33*3)*(4+4.33*3) = ?

if it is 64 then good