Professional football field is 160 feet wide what's the width of the field in yards

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

To find the sum of 4 and -5.

Katen [24]

Answer:

-1

Step-by-step explanation:

-5 + 4 = 1

5 0

3 years ago

In how many ways can a designer chose from 3 summer dresses,2 purses, a hat, 3 scarfs, 2 belts if she chooses one of each?

butalik [34]

Answer:

I'm pretty sure it's 32

Step-by-step explanation:

hope this helpsb

4 0

3 years ago

Evaluate the expression 43 + 2(3 − 2).

Vedmedyk [2.9K]

Answer:

It's 45, and it appears none of them are right.

Step-by-step explanation:

43 + (6 - 4)

43 + 2 =

45

Hope that helps!

4 0

3 years ago

Read 2 more answers

Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? A. She showed that an explicit formul

Step2247 [10]

Answer:

Option D is correct

Step-by-step explanation:

Option D is correct

Being an arithmetic sequence there will be common difference between the consecutive terms

Option A is incorrect because it is not necessary that explicit formula is an arithmetic sequence we can create explicit formula for any sequence

Option B is incorrect because recursive formula can be created for any sequence for geometric series also.

Option C is incorrect because the sequence that has constant ratio is the geometric sequence not an arithmetic sequence.

6 0

3 years ago

Read 2 more answers