Mathematics, 10.10.2019 22:50 bryce99

Farmer alex has 32 llamas each of whom needs 1 square feet of grazing area. he wants to enclose a rectangular pen along a straight river, where he does not need fence. what is the minimum amount of fencing he must use to build his pen?

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Answer from: caprisun1491

The minimum amount of fencing must be used to build his pen is $505.96\; \text {ft}$ .

Step-by-step explanation:

Given information:

Farmer Alex has 32 llamas each of whom needs 10000 square feet.

Now the area of rectangle is A=x.y

Where, length of grazing field

And width of the grazing field

Now, the total required area

$32000=x.y\\\\y=32000/x$

Now, find the equation of perimeter of the rectangular pen:

The perimeter P=2x+2y

As, the one side of pen is along with the river

P=x+2y

Now, find the minimum area of fencing:

So for minimum perimeter:

P=x+2(32000/x)

Using a graphing tool (see attached figure)

The vertex of the graph is the point of minimum perimeter.

The vertex is point (252.98,505.96)

That means :

x=252.98

And , minimum perimeter is $505.96\; \text {ft}$

Now the value of

$y=32000/x\\y=32000/252.98\\y=126.49\\$

Hence, The minimum amount of fencing must be used to build his pen is $505.96\; \text {ft}$ .

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Farmer alex has 32 llamas each of whom needs 1 square feet of grazing area. he wants to enclose a re

Answer from: pesinaic

Step 1

we know that

the area of a rectangle is equal to

A=xy

where

x is the length side of the rectangle

w is the width side of the rectangle

Find the total required area

$32*10,000=32,000\ ft^{2}$

32,000=xy

y=32,000/x ------> equation A

Step 2

Find the equation of the perimeter of the rectangular pen

we know that

the perimeter of the rectangle is equal to

P=2x+2y

Remember that one side of the pen is along a straight river

so the perimeter is equal to

P=x+2y ------> equation B

Step 3

Find the minimum amount of fencing

we know that

the minimum amount of fencing is when the perimeter is a minimum

Substitute equation A in equation B

P=x+2*(32,000/x)

Using a graphing tool

see the attached figure

The vertex of the graph is the point for a minimum perimeter

the vertex is the point (252.98,505.96)

that means

for $x=252.98\ ft$

The minimum perimeter is equal to $505.96\ ft$

Find the value of y

y=32,000/x

y=32,000/252.98

$y=126.49\ ft$

therefore

The answer is

the minimum amount of fencing he must use to build his pen is

$505.96\ ft$

Answer from: Quest

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3

Answer from: Quest

step-by-step explanation:

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