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
Answer:
B
Step-by-step explanation:
<em>Let's multiply this out and combine like terms:</em>
So there are 2 terms.
Answer choice B is right.
9514 1404 393
Answer:
(a) = 7 +3·5
Step-by-step explanation:
The given expression evaluates to ...
6 +2^4 = 6 +16 = 22
The offered choices evaluate to ...
7 +3·5 = 7 +15 = 22
4·10^3 +96 = 4·1000 +96 = 4096
7^2 = 49
3·10 +2 = 30 +2 = 32
The only choice that will form a proper equation is the expression that evaluates to 22:
6 +2^4 = 7 +3·5
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Answer:
80
Step-by-step explanation:
720/P = 9/1
Cross multiply.
9P = 720
P = 720/9
P = 80
