Help me please multiple choice math

a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

xenn [34]

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83. $\underline{\overline 3}$ feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

$\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x$

$y = \mathbf{250 - \dfrac{3}{2} \cdot x}$

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

$\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2$

$\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}$

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, $\dfrac{dA}{dx} = 0$

Finding the value of x at the maximum point, we get;

$\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0$

Therefore;

$\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}$

$\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125$

The length of the plot that will give the most area, y = 125 feet

Learn more here:

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6 0

3 years ago

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 lette

dybincka [34]

The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.

Mr. McMillan has already taught his class 8 letters.

The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.

Mr. McMillan plans to teach his class 4 new letters per week.

Ms. Burke intends to cover 3 new letters per week.

Eventually, the students in both classes will know how to write the same number of letters.

Then the number of weeks by which the students in both classes will know how to write the same number of letters will be

Let x be the number of the weeks and y be the total number of the letters.

Then the equation will be

y = 4x + 8 …1

y = 3x + 12 …2

Then by solving the equations 1 and 2, we have

x = 4 and y = 24

More about the linear system link is given below.

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#SPJ1

4 0

2 years ago

Given the figure below, find the values of x and z

Dafna1 [17]

Answer:

my bad it was a mistake .

Step-by-step explanation:

7 0

3 years ago

What is the slope of the line (-3, 3) and (-1, -1)?

Anna [14]

Answer:

m= -2

Step-by-step explanation:

8 0

3 years ago

Can someone help me with this? Thanks.

marin [14]

Answer:

7.38461538462

Step-by-step explanation:

1/2x6/5=3.25

24/3.25=7.38461538462

7 0

1 year ago

Read 2 more answers