The constant variation for the relationship being shown is 4
The smallest region that can be photographed is
5*7 = 35 square km
so we want to know how long it takes to zoom out to an area of
35 * 5 = 175 square km.
Notice that the length and width increase at the same rate, 2 km/sec, and they start out with a difference of two, so when the width has increased from 5 to x, the length will have increased from 7 to x+2. At the desired coverage area, then,
x(x+2) = 175
x^2 + 2x = 175
x^2 + 2x + 1 = 176 [completing the square]
(x+1)^2 = 176
x+1 = ±4√11
x = -1 ±4√11
Since a negative value for x is meaningless here, x must be
-1 + 4√11 = about 12.27 km
and the time it took to increast to that value was
(12.27 - 5) km / (2 km/sec) = about 3.63 seconds
Answer:
Step-by-step explanation:
6 + 12 + 24 + 48 + 96 =
= 6 + 6 * 2 + 6 * 4 + 6 * 8 + 6 * 16
= 6 + 6 * 2^2 + 6 * 2^2 + 6 * 2^3 + 6 * 2 * 4
= 6 * 2^(n - 1)
