Help with math.

[Dulrough]

You know you're bored and want to do some calculus.

Consider the cross section of the house below.

We want to minimize the perimeter of the house while keeping the area at 30 meters square.

a) Solve this minimiztion problem by the mthod of lagrange multipliers. Use the Pythagorean theorem, a^2 + b^2 = c^2.
To eliminate one of the variables, reducing the problem to three variables with one constraint and one multiplier.

b)
In part (A), the calculations were difficult because of the expressions involving radicals. To avoid these difficulties, solve this problem again by leaving a^2+b^2=c^2 as a second constraint. Begin by extending the theory of Lagrange multipliers to allow for a second constraint and a second multiplier. Then solve the specific problem above using this idea.

:rolling:

     /|\
   / a|  \ c
 /____|____\
|       b  |     
|          |
|          |
|__________|

 

[xombine]

Idk + that's ghey = Gtfo, kthxbai.

 

[<RJMC>]

I cant understand why people like maths

maths is too much for my brain

I will become the anti maths guy cuz maths hates me

 

[Ennui]

I cant understand why people like maths

maths is too much for my brain

I will become the anti maths guy cuz maths hates me

rofl.

my calculus knowledge:

 

[Raeven0]

I cant understand why people like maths

The sheer logic of the numbers is astounding. A hundred people can give you two hundred different interpretations of a single verse in Genesis or a single line of The Raven, but a mathematical theorem comes in a single concise package, and if you disagree with it, you are wrong. Gleeeeeee!

What concerns me is the curiously high number of people who think an Internet message board is a valid source of mathematical assistance...

 

[Hazar]

a better picture would help

 

[_Z_Ryuken]

I think geometrically yet I am at a loss to understand how to reduce the perimiter of an area whilst maintaining it's area.

 

[dfc05]

Well, I'd help you except I forgot most of multivariable calculus. And Lagrange multipliers sucked anyways.

 

[TheSomeone]

I think geometrically yet I am at a loss to understand how to reduce the perimiter of an area whilst maintaining it's area.

Seems pretty obvious to me.

5 x 5 square vs 1 x 25 rectangle.

 

[_Z_Ryuken]

Ha, ok yes, I was thinking backwards. I was thinking "perimiter" while picturing "area" in my head.

Makes perfect sense now.

 

[Glirk Dient]

Seems pretty obvious to me.

5 x 5 square vs 1 x 25 rectangle.

5x5 = 25

1x25 = 25

...?

 

[_Z_Ryuken]

5x5 = 25

1x25 = 25

...?

Haha you are doing what I did. In the problem we want to find and shrink the outside perimiter and keep the area the same. (see next post)

Probably involves losing the triangle and squaring the thing off somehow.

I looked up Lagrange multipliers and was completely lost in math terms I do not comprehend. :[

 

[Feath]

But the perimeters are different

5 x 5 square has a perimeter of 5 + 5 + 5 + 5 = 20
1 x 25 rectangle has a perimeter of 25 + 25 + 1 + 1 = 52

 

[99.vikram]

Standard minimisation, right? Boooring.

 

[Ikerous]

Minimum perimeter is 21.115
With
A = 1.324
B = 2.5781
C = 2.8232

In all likelyhood, thats completely wrong, but it's what I got

 

[TheSomeone]

Minimum perimeter is 21.115
With
A = 1.324
B = 2.5781
C = 2.8232

In all likelyhood, thats completely wrong, but it's what I got

i got the same answers

but we dont know if we understood the prompt right. This is just for the cross section right?

I got this equation: 6b + sqrt((60/b + 8b)^2 + b^2)
then since i dont know calc i graphed it and found the vertex and got 21.115

 

[the_rebel_medic]

From some random movie
Teacher "Whats your favorite subject?"
Girl "Maths"
Teacher "Why"
Girl "Because it's the same in every language"
Class "LOL"

 

[Steven]

What concerns me is the curiously high number of people who think an Internet message board is a valid source of mathematical assistance...

qft

 

[Ikerous]

What kind of ppl are most likely to frequently visit internet message boards?
Nerds. What do nerds know? Math.

 

[Steven]

On average there too immature to give you the correct answer or will just post some random O RLY image.

 

[Ikerous]

I sat down for five minutes and worked it out
But i suck at life..

 

[DreadLord]

I sat down for five minutes and worked it out
But i suck at life..

How did I know you'd be the one to find the answer? Right when I saw the thread title I was like, Ikerous will be in here.

 

[Hazar]

On average there too immature to give you the correct answer or will just post some random O RLY image.

 

[DreadLord]

 

[Raeven0]

What do nerds know? Math.

Read this thread again and try to tell me that with a straight face. If you're still not convinced, I can probably dig up some of the utterly dumbfounded responses I got to this tutorial, which involves basic algebra.

 

[Dan]

But the whole point of the question was to use Lagrangian multipliers to optimize it. You guys are all solving it the wrong way. Lagrandian optimization means you use Lagrangian variables and partial derivatives . So your volume is 4b^2 + a*b = 30. Flip that around so that it's 30 - 4b^2 - a*b and then add it to the perimeter equation.

So the perimeter is 4*b + 2*c, but c^2 equal a^2 + b^2

So the final value equation is 4*b + 2*sqrt(a^2+b^2) + lambda(30 - 4b^2 - a*b).

Lambda is the lagrangian variable. Now take the partial derivative of each variable.

d/dlambda = 30 - 4b^2 - a*b
d/da = 2a/sqrt(a^2+b^2) - lambda*b
d/db = 4 + 2b/sqrt(a^2+b^2) - 8*lambda*b - lambda*a

Set each of those equal to 0 and solve for the variables

Then for the 2nd part instead of substituting for c, you add the constraint that c^2-a^2-b^2 = 0

 

[Kamikazie]

On average there too immature to give you the correct answer or will just post some random O RLY image.

The irony in that post is to strong for my sensors, the needle flew straight off!

 

[Ikerous]

But the whole point of the question was to use Lagrangian multipliers to optimize it.

Ya.. i didn't do so well on that test...

 

[TheSomeone]

But the whole point of the question was to use Lagrangian multipliers to optimize it. You guys are all solving it the wrong way.

I'm in precalc.

 

[Steven]

The irony in that post is to strong for my sensors, the needle flew straight off!

Wasn't supposed to be offensive, it's just the truth. I don't think low of anyone if thats what they do and I don't see why you would seen as there replying to someone who asked for math and/or emotional help from people on the internet, I'm one of the people who does it. My initial thought was that you just quoted me randomly and said that. I'm not saying that there aren't people who won't give any help, there just hard to find.

Ya.. i didn't do so well on that test...

The irony in that post is to strong for my sensors, the needle flew straight off!

Hard to understand people are really saying on message boards.

 

[Kamikazie]

Wasn't supposed to be offensive, it's just the truth. I don't think low of anyone if thats what they do and I don't see why you would seen as there replying to someone who asked for math and/or emotional help from people on the internet, I'm one of the people who does it. My initial thought was that you just quoted me randomly and said that. I'm not saying that there aren't people who won't give any help, there just hard to find.

I ment the latter part of your post. Whoops

 

[Steven]

I ment the latter part of your post. Whoops

It's one sentance long and only has one subject. :|

 

[Ravioli]

Isnt that a polynomial? A trinomial

 

[Kamikazie]

It's one sentance long and only has one subject. :|

On average there too immature to give you the correct answer or will just post some random O RLY image.

zomg.

 

[Steven]

teh hax

I don't see how that's supposed to be offensive either, pretty much the same thing but let's nevermind.

 

[<RJMC>]

holy shit I thought the maths freak nerd was a myth