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BigorU [14]
3 years ago
5

} } " alt=" \sqrt{28 - \sqrt{7} } " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
kogti [31]3 years ago
6 0
The answer is 5.0353
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MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t
ioda

Answer:

We would have

                                    l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}

where " l " is  length, " w"  is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

         Surface area for a box with no top = lw+2lh+2wh = 64

where " l " is  length, " w"  is width and "h" is height.

 Step 2.

Remember as well that

                              Volume of the box = l*w*h

Step 3

 We can now use lagrange multipliers.  Lets say,

                                    F(l,w,h) = lwh

and

                                g(l,w,h) = lw+2lh+2wh = 64

By the lagrange multipliers method we know that                            

 

                                                     \nabla F  = \lambda \nabla g

Step 4

Remember that

                          \nabla F  = (wh,lh,lw)

and

                      \nabla g = (w+2h,l+2h , 2w+2l)

So basically you will have the system of equations

                              wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

                                   lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)

Then you would get

                      l\lambda (w+2h) = w\lambda (l+2h) =  h\lambda (2w+2l)

You can get rid of \lambda from these equations and you would get

                         lw+2lh = lw+2wh =  2wh+2lh

And from those equations you would get

                                             l = w =2h

Now remember the original equation

                                    lw+2lh+2wh = 64

If we plug in what we just got, we would have

                                 l^{2} + l^{2} + l^2   =  64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}

                       

                                                 

7 0
3 years ago
If rectangle is 12 inches long and 8 inches wide, what is the ratio of its length to its width?help
Kamila [148]
12:8
or you can simplify it to
3:2
3 0
3 years ago
which expression shows the result of applying the distributive property to 12 (5y + 4) ? A. 60y + 48 B. 5y + 48 C. 17y + 16 D. 6
PSYCHO15rus [73]
A because you just distribute the 12 to both
7 0
3 years ago
Read 2 more answers
The equatorial circumference of Earth is 4.01 x10^4 kilometers. One kilometer is equivalent to 3.94 x10^4 inches. What is the eq
krok68 [10]

The answer is 1,57,940,000

\sf\blue{hope\:it\:helps}

5 0
2 years ago
Yolanda, Hong, and Ahmad served a total of 70 orders Monday at the school cafeteria. Yolanda served 6 fewer orders than Ahmad. H
irina [24]

Answer:Yolanda served 13 orders.

Ahmad served 19 orders.

Hong served 38 orders.

Step-by-step explanation:

Let x represent the number of orders that Ahmad served.

Yolanda served 6 fewer orders than Ahmad. This means that the number of orders that Yolanda served is x - 6

Hong served 2 times as

many orders as Ahmad. This means that the number of orders that Hong served is 2x

Yolanda, Hong, and Ahmad served a total of 70 orders Monday at the school cafeteria. This means that

x - 6 + x + 2x = 70

4x - 6 = 70

4x = 70 + 6 = 76

x = 76/4 = 19

Hong served 2 × 19 = 38

Yolanda served 19 - 6 = 13

5 0
3 years ago
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