Answer:
k = 0.02278
Step-by-step explanation:
Given that:
The population P = 1674.7e^kt
where;
t represents the year,
if year 2000 represents t = 0
Then, the year 2007 represents = 7; &
year 2006 represents = 6
In 2006, population recorded in the city was about 1,920 thousand
Therefore;
Taking the logarithm of both sides, we get:
7.560080465= 7.423389324 + 6k
7.560080465 - 7.423389324 = 6k
0.136691141 = 6k
k = 0.136691141/6
k ≅ 0.02278
Answer:
3/2
Step-by-step explanation:
slope=rise/run=30/20=3/2
Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
Answer:
C.
Step-by-step explanation:
Answer:
1 1/2
Step-by-step explanation:
9/10 ÷ 3/5
Copy dot flip
9/10 * 5/3
Rewriting
9/3 * 5/10
3 * 1/2
3/2
1 1/2
