Afarmer will build a rectangular pen for his sheep. a wall will form one side of the pen. the farmer has 28 m of fencing to form the other three sides. the farmer plans to build the pen so that it has its maximum possible area. what will be the dimensions of the farmer’s sheep pen? enter your answers in the boxes.

Answer with explanation:

→The farmer want to build a rectangular pen for his sheep.

→A wall will form one side of the pen.

→The farmer has 28 m of fencing to form the other three sides.

Let length of rectangle = x m

and, Breadth of rectangle = y m

Perimeter of rectangle = ( 2 x + 2 y) meter

Let the side through which wall has been built is along breadth.then equation can be written as

→ 2 x+ 2 y= 28+y

2 x+y=28

y=28-2 x(1)

Area of rectangle = A=Length ×Breadth

A= x y

A= x×(28-2 x)

A= 28 x -2 x²

Differentiating with respect to x, we get

A'=28 -4 x

For Maximal or Minimal value,

A'=0

→28 - 4 x=0

4 x= 28

→→Dividing both side by ,4, we get

x=7

putting the value of x , in equation 1

→y=2 8-2×7

→y=28-14

→y=14

So, length= 7 m

Breadth = 1 4 m

if wall has been side opposite to length, then Dimension of rectangle will be,then equation can be written as

 2 x + 2 y= 28+x

x+2 y=28

→x=28-2 y

Applying same method done above,we will get

Length= 14 m

Breadth = 7 m

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%