From a thin piece of cardboard 40 in by 40 in, square corners are cut out so that the sides can be folded up to make a box. what
dimensions will yield a box of maximum volume? what is the maximum volume?
1 answer:
The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deep
The maximum volume is
(80/3 in)²(20/3 in) = 4740 20/27 in³
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deep
The maximum volume is
(80/3 in)²(20/3 in) = 4740 20/27 in³
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Answer:
1035.33 feet
Step-by-step explanation:
OBH is a triangle and the sum of the angles of a triangle = 180
∠OBH = 90°
∠OHB = 180 -(49 + 90) = 41°
The law of sines that the ratio of each side of a triangle to the sin of the angle opposite it is the same
Thus
A/sinα = B/sinβ = C/sinγ
where A, B and C are the three sides of the triangle and α, β, γ corresponding respectively to the angles opposite them.
Using the law of sines
Therefore BH which is the height the helicopter is flying at is
≈ 1035.33 feet