Mathematics: A farmer wants to fence a rectangular pasture using a river as one side. The pasture must contain 180,000 square meters of space for the herd to frolic. What is the least amount of fencing required to enclose such a pasture?

It is just a very simple substitution operation...let x= 2so the function f(x) would be:That is for the first oneand so on for the other twocan you follow this and do the other two??f(5)-f(4)=81-49=32...

A farmer wants to fence a rectangular pasture using

Ответ:

Dillpickle3322

23.01.2022

Mathematics

1200 m

Step-by-step explanation:

We are given that

Area of pasture,A=180000 square meter

We have to find the least amount of fencing required to enclose such a pasture.

Let length of pasture,=x

Width of pasture,b=y

Area of pasture= $l\times b=xy$

xy=180000

$y=\frac{180000}{x}$

Fencing required=2x+y

$P=2x+\frac{180000}{x}$

Differentiate w.r.t x

$\frac{dP}{dx}=2-\frac{180000}{x^2}$

$\frac{dP}{dx}=0$

$2-\frac{180000}{x^2}=0$

$\frac{180000}{x^2}=2$

$x^2=\frac{180000}{2}=90000$

$x=\sqrt{900000}=300$ m

It is always positive because length cannot be negative.

$y=\frac{180000}{300}=600$ m

Again differentiate w.r.t x

$\frac{d^2P}{dx^2}=\frac{360000}{x^3}$

Substitute x=300

$\frac{d^2P}{dx^2}=\frac{360000}{27000000}=0.0130$

The fence is minimum at x=300

Therefore, fencing required to enclose such a pasture

P=2x+y=2(300)+600=1200 m

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A farmer wants to fence a rectangular pasture using a river as one side. The pasture must contain 180,000 square meters of space for the herd to frolic. What is the least amount of fencing required to enclose such a pasture?

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