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anonymous
 5 years ago
Calculus 2 HelpA rancher has property along a river that he needs to divide into three separate,
equalsized regions: one for the cows, one for the horses, and one for the sheep. The
rancher has 1000 ft of available fencing with which to divide up the land. There will need
to be enough fencing for three outer sides of the property as well as two lengths of
fencing to divide the region into three parts. Determine the values of x and y, and the
area of an individual pen so that its area is maximized. Be sure to use calculus to
justify you have found a maximum.
anonymous
 5 years ago
Calculus 2 HelpA rancher has property along a river that he needs to divide into three separate, equalsized regions: one for the cows, one for the horses, and one for the sheep. The rancher has 1000 ft of available fencing with which to divide up the land. There will need to be enough fencing for three outer sides of the property as well as two lengths of fencing to divide the region into three parts. Determine the values of x and y, and the area of an individual pen so that its area is maximized. Be sure to use calculus to justify you have found a maximum.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So i got that the equation will be F=1000ft=4x+y and A=1/3xy

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Is the river included as one side of the pens? cause in alot of problems it is..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you dont need fence for the river part

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then we need 4x + y = 1000, right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea the 2 equations i set up are my up top

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good, but I need to work it thru in my head too:)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and the area of each pen is x(y/3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Since y = 1000  4x, can we use that in the area?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the deriviate and solve for max right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0esxucse typos, my keyboard hates me:)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i get (3000  24x)/9 for a derivative...what about you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hold on, did you set it up first by substituting?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x = 3000/24 = 1500/12 = 750/6..... yeah substitute in y=10004x.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so A(x)=1000x4X^2 all over 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x = 375/3...x = 125 for me

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its ok...gives me time for my mind to wander :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Your A(x) was correct...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then you took the derivative?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, the derivative tells us where we can find bends inthe graph that are our max and min values.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0You remember your quotient rule?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea let me do it one sec

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep; and theres another way we could have approached it. 1/3 is a constant so we can pull it out and just derivative (1000x4x^2). Either way is the same

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0y did i get x=27000/24

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0solve for y' = 0. What makes (300024x)/9 = 0?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the top has to equal 0 for ay of it to matter; so throw away the 9

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0300024x = 0 what is x?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01000  8x = 0...is the same thing

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, now reduce it or use it as is if you want :) Good job

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(500)(125)/3 is more accurate, but yeah...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.020833ft^2, that seems large?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when talking about football field measurements, I imagine it would be :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh ok , now the other part is the maximum

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02nd derivative right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0total inclosed area is 62500 ft^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0they just want individual

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we already found the maximum... there is only one hump in a quadratic..

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you can second derive it if you want, just to prove it to yourself, but it aint needed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i need to do all steps she takes off for everything

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is this 100% right, she had like inequality equations and domain stuff on her examples. I am confused

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol..when y'' is (+) we have a concave down which is an upside down bowl on the graph. And that is the max.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its right....so far :) use the math luke.....the maaatthhhh...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0might wanna double check that concavity thing, I never use it enough to remember if Im right :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it should be negative to be a max <0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0remember CAVE....CAVE UP is (+) and CAVE DOWN is () or the other way around..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i mean in concavity relation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if its >0, its concave up oh okay

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol....ill trust you on that :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do you have a max then

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0picture the graph of (x^2) thats all this is.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hold up is the second derivative 8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats right, so the cave is down. its an upside down bowl.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x^2) ... y'=(2x)....y'' = (2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, lol i am so bad at optimization

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do the domains work

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0she wants us to show that too D:(0, )

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0there is nothing limiting our domain, so it canbe any real number (R)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0look at the fractions we made, if anything makes the bottom a 0, throw it out. Nothing matters, so keep it all

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I suppose we should focus on positive numbers to make sense of it all, so yeah. except it should be [0,inf) 0 is included.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0wait....just had athought

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we only have so much fencing to work with... so make the D [0,1000]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or you might wanna think about like this: we need 4 amounts of x so ...maybe...[0,1000/4] ? take a gander at it and see :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0my gut tells me that we do [0,1000]..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my friend said the domain is 0 to 250

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0does your friend tell you how to find the max area :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0He said solve 1000x4x^2 for x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and thats your A( )>0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which is your max by the Extreme value theorem

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats fine.....well use 0 to 250......its as good as anyother I can think of :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no he said solve the inequality 10004x>0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats what the 250 is

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01000/4 = 250....i know iknow...yeahyeahyeah....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can we walk through it step by step, I am so confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is 125 okay because it falls in the domain?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0step 1: we are given certian rules that govern our equations...did we use them right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0A'' in that case is <0 and negative which is why its a max?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we Know: 4x + y = 1000 and we KNow : Area per pen = xy/3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes, since it is <0 it is a max

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we want max area per pen so we substitute y in our area formula and get the derivative.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when y' = 0 we have a bend, a max OR a min.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which we just say is 10008x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes.... and y'' tells us how the graph behaves at certain points. () = CAVE DOWN = max point (+) = CAVE UP = min point (0) = point of inflection.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0tells us it is always concave DOWN becasue its always (8)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you still confused? or feeling more confident?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea im getting it a little. He said since x fits in the open interval, you take the 2nd derivative

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahhhh where do I plug in our x in our second derivative?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0why would you need to pluu it in? the only reason to plug in an x in the secondD is to figure out where is changes sign. x^2 never changes concavity so it is always, and I mean ALWAYS cavedown

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^3 changes....so that youd check :) but we aint messin with no x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is A'' of (1000x4x^2)/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets see if it works anyway

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0A' = (10008x)/3 A'' = 8/3 A''' = 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you say this is calc 2 stuff?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0cause im only in trig at the moment.....and it is sooooo boring there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how are you helping me so well then?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i dunno, maybe I is smart ? I taught myself calculus in intermediate algebra to pass the time....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha nice yea this is college calc 2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I still need alot of practice with integrals tho..... and word problems. I loathe word problems :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea you are still decent

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Im gonna get my masters in math...and teach college math

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i bet you can do it! easy 4 u

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0easy as....should I?......PI lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0no prob... keep up the good work :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my friend confirmed everything
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