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# another differentiation question watch

1. a)
I get 40 m² as well.

b)
The bits of fence labelled as x would be replaced on one side by the existing (permanent) fence, thus doubling the value of x an the other side of the pen. i.e the area doubles!
2. can u explain it more please?
3. i understand part b) but i dont quite know how to calculate part a)....
can you show me please? cheers
4. (Original post by ronnie)
can u explain it more please?
Let L be the length of fencing.
Let A be the area of all the pens together.
let a be the area of a single pen.
Then,
a)
L = 80
A = 4xy
a = xy

L = 5 lots of y plus 2*(4 lots of x)
L = 5y + 8x
5y + 8x = 80
y = 16 - 1.6x

A = 4x(16 - 1.6x)
A = 64x - 6.4x²
dA/dx = 64 - 12.8x = 0 for max or min
64 - 12.8x = 0
:. x = 5
======
& y = 8
======
a = 5*8 = 40 m²
============
b)
When the permanent fence is used, The fencing is only used on the 5 lots of y and on only 4 lots of x, not 8 lots like in part a).
So,
L = 5y + 4x
5y + 4x = 80
y = 16 - 0.8x
A = 4x(16 - 0.8x)
A = 64x - 3.2x²
dA/dx = 64 - 6.4x = 0 for max or min
64 - 6.4x = 0
:. x = 10
=======
& y = 8
======
a = 10*8 = 80 m²
=============
5. cheers fermat! unfortunately part a) came to me in my sleep. but thanks anyway! tis a rather easy question in the end.
6. maybe if i put it like this, would be better to understand.

Let L be the length of fencing.
Let A be the area of all the pens together.
Then,
a)
L = 80
A = 4.x.y

L = 5 y's plus 2 rows of 4 x's
therefore, L = 5y + 8x
and total length is 80 so
5y + 8x = 80
make it y equals
y = 16 - 1.6x

them put y=16-1.6x into the A=4.x.y
A = 4x(16 - 1.6x)
A = 64x - 6.4x²
differentiating and get
A'=64 - 12.8x
make it equal 0 for max or min
64 - 12.8x = 0
then find x
:. x = 5
======
then u put it into this equation that u found earlier, y = 16 - 1.6x
y=8
======
then u put it into the equation u got in first step
A = 4.x.y
A=4x5x8
=160 (which is the area of all 4 boxes/pens)
do u divide 160 by 4 =40

read mine and fermats and keep looking at the diagram and good luck !

cheers !
7. (Original post by ronnie)
maybe if i put it like this, would be better to understand.

Let L be the length of fencing.
Let A be the area of all the pens together.
Then,
a)
L = 80
A = 4.x.y

L = 5 y's plus 2 rows of 4 x's
therefore, L = 5y + 8x
and total length is 80 so
5y + 8x = 80
make it y equals
y = 16 - 1.6x

them put y=16-1.6x into the A=4.x.y
A = 4x(16 - 1.6x)
A = 64x - 6.4x²
differentiating and get
A'=64 - 12.8x
make it equal 0 for max or min
64 - 12.8x = 0
then find x
:. x = 5
======
then u put it into this equation that u found earlier, y = 16 - 1.6x
y=8
======
then u put it into the equation u got in first step
A = 4.x.y
A=4x5x8
=160 (which is the area of all 4 boxes/pens)
do u divide 160 by 4 =40

read mine and fermats and keep looking at the diagram and good luck !
thanks! but as i said (in post6), i already got it. thanks anyway.
and part b) is 80 as x is doubled (so x=10, y remains 8, so A=80).
8. i know how to do part b now but don't really understand, why is the answer doubled ?(lol, math is not really my thing)
9. ronnie send me your email add and i will send you an explanation. i have it written on Word (which is much easier to explain on!)

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