Anonymous
Anonymous asked in 科學及數學數學 · 5 years ago

# math help

Rating

Suppose x and h are numbers

a)

Method1：

Perimeter of base triangle=x+x+x=3x (m)

Area of the base triangle

=√[3x/2 (3x/2 - x)(3x/2 - x)(3x/2 - x)]

=√(3x⁴/16)

=(√3)x²/4 (m²)

Method2：

In the base triangle

Since 3 sides are also equal,

then 3 angles are also equal(=60°) (property of equil Δ)

Area of the base triangle

=(x)(x)(sin60°)/2

=(√3)x²/4 (m²)

b)

The volume of the prism

=Area of the base triangle * hight

=(√3)x²h/4 (m³)

c)

Area of a rectangle

=xh (m²)

C

=12*2*(√3)x²/4 + 8*3*xh

=(6√3)x² + 24xh

d)

Since the prism volume=100 (m³)

(√3)x²h/4=100

h=400/[(√3)x²]

C=(6√3)x² + 24xh

C=(6√3)x² + 24x{400/[(√3)x²]}

C=(6√3)x² + (3200√3)/x

dC/dx

=d[(6√3)x² + (3200√3)/x]/dx

=d[(6√3)x²]/dx + d[(3200√3)/x]/dx

=(12√3)x - (3200√3)/x²

d²C/dx²

=d[(12√3)x - (3200√3)/x²]/dx

=d[(12√3)x]/dx - d[(3200√3)/x²]/dx

=12√3 + (6400√3)/x³

e)

dC/dx=0

(12√3)x - (3200√3)/x²=0

12x=3200/x²

x=(800/3)^(1/3)

Sub x=(800/3)^(1/3) into d²C/dx²

d²C/dx²>0

∴If x=(800/3)^(1/3), the cost is the minimum.

f)

The minimum cost

=(6√3) (800/3)^(2/3) + (3200√3)/[(800/3)^(1/3)]

=240 * 3^(5/6) * 10^(1/3)

=\$ 1292 (corr to the nearest dollar)

• 5 years ago

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2015-07-06 22:05:52 補充：

無救啦～　你剛剛刪了我的帖子啦～

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