Alright, quick background... This problem is a "look back" for my Calculus class & for some reason, I cannot figure out where to go...
Question:
"A cattle rancher has 2300 feet of fencing that will be used to enclose a rectangular feed lot. If one of the dimensions of the feed lot is x , find a formula for the area y of the feed lot (in square feet) as a function of x."
My proposed Answer (not yet complete, but this is what i have so far)
2x+2y=2300
x+y=1150
x*y= ?
now what??
Please help! Thank you!
2007-08-31 20:18:46 · 8 answers · asked by Sum Girl 4 in Science & Mathematics ➔ Mathematics
2x+2L=2300
x+L=1150
L=1150-x
y=xL
y=x(1150-x)
y=1150x-x²
Bye.
p=p
2007-08-31 20:26:19 · answer #1 · answered by PIERRE 6 · 1⤊ 0⤋
I think this is how it works :
2x + 2y = 2300
2y = 2300 - 2x
So y = (2300 - 2x) / 2 = 1150 - x
Since the area of the feed lot is xy,
Substitute y = 1150 - x into the above statement.
xy = x(1150 - x)
= 1150x - x^2
Umm so I think that the formula is this :
(1150x - x^2) square feet.
I hope this helps.
2007-09-01 05:25:59 · answer #2 · answered by Answerer 2 · 1⤊ 0⤋
To Dragon's Fire: she doesn't need to find the dimension, she needs to find a formula of the area as a function of x.. big difference!
So errrr.. been a while since I did this sort of thing. But I *think* (not sure) what you need to do is put y in terms of x:
x + y = 1150, therefore
y = 1150 - x
then you take the last of your listed equations and substitute:
Area(x) = x * (1150 - x)
or A(x) = 1150x - (x^2)
mind, it's been a while since I did this sort of thing.. hope that answers your question, haha, good luck :)
edit: oh, a bunch of people already answered.. nevertheless I feel proud for having answered. correctly.
2007-09-01 03:32:55 · answer #3 · answered by Kate the Irate 2 · 1⤊ 0⤋
I find it hard to write it all on computer, but essentially you need to derive the formula you created.
okay you know 2 sides are x.
so that must mean the other two sides are: (2300 - 2x)/2 = 1150 -x
Therefore the area must be x(1150 -x) which opens up to 1150x - x^2
therefore area = y = 1150x - x^2
=]
2007-09-01 03:32:12 · answer #4 · answered by pRinceT 1 · 1⤊ 0⤋
Let:
x = one side of the rectangular feed lot
r = the other side of the rectangular feed lot
The perimiter of a rectangle is equal to the sum of the lengths of all sides:
2x + 2r = 2300
2r = 2300 - 2x
r = 1150 - x
The area of a rectangle is equal to the product of the two sides Y as a function of x:
Y = xr where r = 1150 - x
Y= x (1150 - x)
Y = 1150x - xsquared
2007-09-01 03:37:23 · answer #5 · answered by Kiriblu 1 · 1⤊ 0⤋
You are on the right track! but be careful with y, they used it for the Area, and you used it for length, that is where the confusion sets in. I will use z for the length and y is the area.
2x+2z=2300
Area = x*z
and z =( 2300 - 2x )/2 from the first equation, so:
Area = x(1150-x) = y
Area = y =1150x-x²
2007-09-01 03:48:36 · answer #6 · answered by 037 G 6 · 1⤊ 0⤋
the two sides would be x and (2300-2x)/2
so y = x(2300-2x)/2 = 1150x - x^2
Hope this helps!
2007-09-01 03:29:40 · answer #7 · answered by disposable_hero_too 6 · 1⤊ 0⤋
You have to know one of the dimentions, either width or length to find the other.You have to know either x or y.then it's
2300 -2xdevided by 2, or 2300 -2y devided by 2
2007-09-01 03:25:20 · answer #8 · answered by Dragon'sFire 6 · 0⤊ 0⤋