Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
The correct answer is B. If you drop the parenthesis and collect like terms you get 8-3i.
Answer:
3520 ft/min
Step-by-step explanation:
40 mi/h = (40 mi/h)×(5280 ft/mi)×(1 h)/(60 min) = 3520 ft/min
_____
Each conversion factor has a value of 1 (numerator = denominator), so changes the units without changing the speed.
Answer:
m<G = 71
Step-by-step explanation:
Find x first
7x + 1 + 6x - 6 + 55 = 180
Combine like terms:
13x + 50 = 180
- 50 - 50
13x = 130
/13 /13
x = 10
Then apply to problem
7 (10) + 1
70 + 1
= 71
81, if you mean 9 Squared.
