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I am Lyosha [343]
2 years ago
14

Which of these numbers is prime? large 11, 15, 21, 27, 56

Mathematics
2 answers:
gizmo_the_mogwai [7]2 years ago
6 0
11 is the only prime number. It's only multiples are 1 and itself
vaieri [72.5K]2 years ago
5 0
11 because only 1 times 11 = 11 and it has no other factors 
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denpristay [2]

Answer:

Length = 2 ft

Width = 2 ft

Height = 5 ft

Step-by-step explanation:

Let the square base of the box has one side = x ft

Therefore, area of the base = x² ft²

Cost of the material to prepare the base = $0.35 per square feet

Cost to prepare the base = $0.35x²

Let the height of the box = y ft

Then the volume of the box = x²y ft³ = 20

y=\frac{20}{x^{3} } -----(1)

Cost of the material for the sides = $0.10 per square feet

Area of the sides = 4xy

Cost to prepare the sides of the box = $0.10 × 4xy

                                                             = $0.40xy

Cost of the material to prepare the top = $0.15 per square feet

Cost to prepare the top = $0.15x²

Total cost of the box = 0.35x² + 0.40xy + 0.15x²

From equation (1),

Total cost C=0.35x^{2}+(0.40x)\times \frac{20}{x^{2} }+0.15x^{2}

C=0.35x^{2}+\frac{8}{x}+0.15x^{2}

C=0.5x^{2}+\frac{8}{x}

Now we take the derivative of C with respect to x and equate it to zero,

C'=0.5(2x)-\frac{8}{x^{2}} = 0

x-\frac{8}{x^{2}}=0

x=\frac{8}{x^{2} }

x^{3}=8

x = 2 ft.

From equation (1),

(2)^{2}y=20

4y = 20

y = 5 ft

Therefore, Length and width of the box should be 2 ft and height of the box should be 5 ft for the minimum cost to construct the rectangular box.

8 0
2 years ago
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