Refer to the diagram shown below.
The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x² (1)
The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²
The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x
The total cost is
C = 20x² + 180/x
The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.
The total cost is
C = 20(1.651)² + 180/1.651 = $163.54
Answer: $163.54
Answer:
n = 36
Step-by-step explanation:
The opposite sides of a parallelogram are congruent , that is
AB = DC , substitute values
n - 5 = n + 7 ( multiply through by 3 to clear the fractions )
2n - 15 = n + 21 ( subtract n from both sides )
n - 15 = 21 ( add 15 to both sides )
n = 36
Answer:
x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(x) = 1.5
1.5 = 3/2:
sin(x) = 3/2
Take the inverse sine of both sides:
Answer: x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Step-by-step explanation:
2 2/3
=><em>If</em> 8/3 = 1/6
x =1
1/6x = 8/3 ( Divide both sides by <em>1</em><em>/</em><em>6</em><em> </em>)
___ ___
1/6 1/6
(By cross-multiplying the numerators and denominators)
=> 1×6 8×6
___ x = ___
6×1 3×1
Cancelling out , we have
x = 8×2
____ = 8×2 = 16
1 × 1
<em>The</em><em> </em><em>final</em><em> </em><em>answer</em><em> </em><em>becomes</em><em> </em><em>1</em><em>6</em>
<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em>