Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
A) 9 : 5
B) 5( 36/9) which is 20 ounces of lemonade concentrate
Unlikely because certain would be 100% which is wrong
Answer:
Divide 12 by 4 first to figure out how many gallons are in each 1/4 of the tank.
12/4=3
So if I added another 1/4 to the capacity:
It could hold 15 gallons.
All you have to do to find how many half bottles can be filled is to times 15 by two since we are filling half gallon bottles.
15x2=30
30 bottles.
