-9.75 + 3.25x
= -3.25(3) + 3.25(x)
= -3.25(3) - -3.25(x) <em>notice they have the same factor of -3.25</em>
= -3.25(3 - x)
Answer: A
Answer:
52feet
Step-by-step explanation:
The set up will be a right angle
Let the angle of depression be 30°
The height above the sea level will be the opposite
The distance of the ship from the base is x (adjacent)
Using TOA
Tan theta = opposite/adjacent
Tan 30 = 30/x
x = 30/tan 30
x = 30/0.5774
x = 51.96
x ≈ 52 feet to the nearest foot
Answer:
2 3/4
Step-by-step explanation:
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
