Any members on here able to do Calculus?

[flyfisher117]

Going out on a limb here but I need help with two Calculus questions, If anyone can help it would be greatly appreciated. I just dont know where to start on these.

#1 If 1200cm of materials is available to make a box, and the manufacturer needs the box to have a square base and an open top, find the largest pssible volume of the box.

#2 A farmer wants to fence an area of 1.5 million sqaure feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What dimensions should he use to minimize his cost in building the fence?

Thanks

 

[threetrees]

Re: Any members on here able to do Calculus?

without warranty or anything:

starting with #2 because that looks simple:

rectancle of the form:

. ____b______
. |.....|.....|
a |.....|.....|
. |____|____|

(okay, seems that ascii drawing is not that easy here)

we'll put the splitting fence directly on the short side, as this is obviously the ideal approach to minimize the length of the total fence for the total (halfed) field.

total area of the field: A

-> in math term:
minimize 3*a + 2b
subject to a*b = A
(subject to a, b elem R_{>0}, but i guess you won't have to be that precise)

-> b = A/A
-> minimize 3*a + 2 (A/a)
-> derivation by a and set it equal to zero, which is the minimum (the derivation of a function at its maximum/minimum is always zero for 'well behaving' problems)

-> 3 - 2 A/a^2 == 0
-> 3 a^2 = 2 A -> a = sqrt(2/3) sqrt(A)
-> b = A/a = sqrt(3/2) sqrt(A)

 

[threetrees]

Re: Any members on here able to do Calculus?

similar to #2:

problem #1

maximize V = a^2 * h
subject to 4*a*h + a^2 = A
(subject to a,h elem R_{>0})

with:
a = side length of quadratic bottom
h = height of box
V = volume
A = surface, consisting of 4* (a*h) side areas + bottom (a^2) (and the top missing)

-> from the side condition
-> h = (A-a^2)/(4a)
-> V = a^2 * (A-a^2)/(4a)
-> derivation of V to a, set it equal to zero and solve for a
-> (i get, half an hour past midnight) a=sqrt(A/3)
-> get h from h=(A-a^2)/(4a)

i hope that there are now remaining errors, but it should be about fine. at least the dimensions come out correctly, so it can't be too wrong

 

[Maggot]

Re: Any members on here able to do Calculus?

Nice work, 3. Its really not calc, though, simple algebra can do those equations.....though I must admit Ive been away from it to o long to work them.

 

[armorpl8chikn]

Re: Any members on here able to do Calculus?

The real nice work is by Noobie who just got someone on SH to do his homework for him.

 

[The Mechanic]

Re: Any members on here able to do Calculus?

http://www.wolframalpha.com/

 

[flyfisher117]

Re: Any members on here able to do Calculus?

Thank you ThreeTrees, the part that makes these problems the hardest for me is just getting my equations all sorted out and solve for making it so that I can solve for the answers.

Wether this is truly Calc or not I cant argue. I just know that im in a Highschool calc class, have a test tomorrow and its over stuff like above and they are throwing me for loops.


@Mechanic, not sure where that website has been all year but I LIKE IT!


@Armorpl8 In all honesty No I did not just get my homework done for me... I was having trouble getting the Equations set up and ThreeTrees helped me there but I still actually have to plug everything in and get the answers, then I have to go back and check over ThreeTrees work to make sure he didnt just give me random equations to work with. THEN I still have to write a paragraph explaining each of my answers. Top that off I still have 5 more questions similar to the two shown above that I must do all of that again too. My math teacher would have given me the same help but he doesnt live with me so my next best helper is the internet.

 

[flyfisher117]

Re: Any members on here able to do Calculus?

ThreeTrees I was wondering if you have the answers that you got so I could compare.

For #1 I got that the maximum volume of the box would be 4000 cm^3

for #2 Im still working on it But I got that the base of the field would be 1,500 ft and the height would be 1000 ft. That just seems WAYY to easy and simple haha.

 

[The Mechanic]

Re: Any members on here able to do Calculus?

I really should have linked to the example page so you can see what the web site is all about. It is incredible and has been around for 5 or 6 years I think. It is the nerds nerd of websites.
http://www.wolframalpha.com/examples/

 

[shootist2004]

Re: Any members on here able to do Calculus?

www.khanacademy.org

this site will help you with any homework no matter what level you are at....

 

[Killer Spade 13]

Re: Any members on here able to do Calculus?

Does that take into account the kerf loss for the saw cuts???