Mathematics, 14.04.2020 23:37 aaqa3735

A rectangular piece of land is to be fenced using two kinds of fencing. Two opposite sides will be fenced using standard fencing that costs $6 m, while the other two sides will require heavy-duty fencing that costs $9 m. What are the dimensions of the rectangular lot of greatest area that can be fenced for a cost of $9000?

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Answer from: levy72

Therefore the dimension of the rectangular piece of land is 375 m by 250 m.

Step-by-step explanation:

Given that,

Two opposite sides of rectangular land will be fenced using standard fencing that costs $6 per m while the other two side will require heavy duty fencing that costs $9 per m.

Let the length and width of the rectangular x and y respectively.

Then total cost for fencing = $\$(2x\times 6+2y\times 9)$

=$(12x+18y)

Then,

12x+18y= 9,000

⇒ 2x+3y=1,500 [ cancel out common factor 6]

⇒3y= 1500 - 2x

$\Rightarrow y=\frac{1500-2x}{3}$ ....(1)

The area of the rectangular land is = Length × width

= xy

Let,

A=xy

Putting the value of y

$A=x.\frac{1500-2x}{3}$

$\Rightarrow A=\frac13(1500x-2x^2)$

Differentiating with respect to x

$A'=\frac13(1500-4x)$

Again differentiating with respect to x

$A''=-\frac43$

Now we have to determine the critical value of A.

For critical value set A'=0

$\frac13(1500-4x)=0$

⇒1500-4x=0

$\Rightarrow x=\frac{1500}{4}$

$\Rightarrow x=375$ m

Since, $A''|_{x=375}=-\frac43$ . at x=375 m the area of the rectangular piece of land is maximum.

From equation (1) we get when x=375

$y=\frac{1500-2\times 375}{3}$

⇒y=250 m

Therefore the dimension of the rectangular piece of land is 375 m by 250 m.

Answer from: Quest

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

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