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Alecsey [184]
3 years ago
11

What is the answer to this question

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0
A is false in this question.



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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
Bill and matt are discussing their children. bill tells matt that he has 3 kids, and the product of their ages is 72. he also te
zloy xaker [14]
Bill tells Matt that he has 3 kids. This means that in this item, we have three unknowns, those are the ages of the three kids. First, the product of the ages is 72.
                            (x)(y)(z) = 72
Also, for the sum of their ages, we have
                              x + y + z =?

There are three variables in the equation which means that 3 equations should also be presented to determine the ages of the three children. 
4 0
3 years ago
18 ≥ -2x <br> i cant solve this
Bumek [7]

Answer:

x\geq -9

Step-by-step explanation:

7 0
3 years ago
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Susie ordered her sister a get well card from a company that randomly selects a card from their inventory. The company has 50 to
Hunter-Best [27]
If you want it in fraction form it would be 4/5 but if you wanted it in the percentage it would be there is a 80% chance it will not be a get well card. Work: 4/5 x 2= 8/10 which converted into a percentage would be 80/100, or 80%. Hope this helped!
3 0
3 years ago
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What the base and formula v
Dmitriy789 [7]

Answer:

length x width x height and 25

8 0
3 years ago
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