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astra-53 [7]
3 years ago
8

A box is contructed out of two different types of metal. the metal for the top and bottom, which are both square, costs $5 per s

quare foot and the metal for the sides costs $4 per square foot. find the dimensions that minimize cost if the box has a volume of 15 cubic feet.
Mathematics
1 answer:
patriot [66]3 years ago
3 0
Total cost, C = 8x^2 + 12xz 
volume, V = (x^2)*z = 10 
C = 8x^2 + 12x*10/x^2 
= 8x^2 + 120/x 
dC/dx = 16x - 120/x^2 = 0 
16x = 120/x^2 
x^3 = 120/16
 x = 1.957 ft

d^2C/dx^2 = 16 +240/x^3 = +ve for x = 1.957 
so, C is minimum when
x = 1.957 ft z = 2.61 ft

Length of the base x is 1.957 ft and height of side z is 2.61 ft
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schepotkina [342]

Answer: B.

4x - 2y = 8\\-4x + 2y = -8

Step-by-step explanation:

Let's solve your system by elimination.

4x−2y=8;−2x+2y=6

Add these equations to eliminate y:

   4x-2y=8  

 -2x+2y=6    

  2x=14

Substitute 7 for x in 4x−2y=8:  

(4)(7)−2y=8

−2y+28=8  (Simplify both sides of the equation)  

−2y+28+−28=8+−28  (Add -28 to both sides)

−2y=−20  

−2y/−2=−20/−2  (Divide both sides by -2)  

y=10

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2 years ago
7/8 - 5/12 ayudaaa por favor es para mañana​
RUDIKE [14]
7/8 = 21/24
5/12 = 10/24

21/24-10/24 = 11/24
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5 cm<br> Find the total surface area of the<br> cylinder.<br> 10 cm
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(b)The graph of y = g(x) is shown. Draw the graph of g(2x). Will award 100 Brainly points
ivanzaharov [21]

Using the stated transformation, the graph of g(2x) is given at the end of the answer.

<h3>Horizontal stretch and compression</h3>

An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:

g(x) = f(ax).

The definition of stretch or compression depends on the value of the constant a, as follows:

  • If a > 1, it is a compression by a factor of 1/a.
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In this problem, the rule is:

f(x) = g(2x).

Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:

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That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.

More can be learned about transformations at brainly.com/question/28725644
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