If anything there might be an eraser icon (modification notes) so you might want to click on that and read it. If not, post what it says or give the math teacher a call. I hope this helps!

6 0

4 years ago

Read 2 more answers

a farmer has 100m for fence avaibiable, with which he intends to build a pen for his sheep. he intends to create a rectangular p

Reika [66]

The perimeter of the area of the pen the farmer intends to build for his

ship includes the length of the permanent stone wall.

Response:

i) The length and width of the rectangular pen are; x, and $\dfrac{100 - x}{2}$ , therefore;

The area is; $A = \dfrac{1}{2} \cdot x \cdot (100 - x)$

$ii) \hspace{0.5 cm}\dfrac{dA}{dx} = 50 - x$

$\dfrac{d^2A}{dx^2} = -1$

iii) The value of x that makes the area as large as possible is x = 50

<h3>How is the function for the area and the maximum area obtained?</h3>

Given:

The length of fencing the farmer has = 100 m

Part of the area of the pen is a permanent stone wall.

Let x represent the length of the stone wall, we have;

2 × Width = 100 m - x

Therefore;

Width, w, of the rectangular pen, $w = \mathbf{\dfrac{100 - x}{2}}$

Area of a rectangle = Length × Width

Area of the rectangular pen, is therefore;

$A = x \times \dfrac{100 - x}{2} = \underline{\dfrac{1}{2} \cdot x \cdot (100 - x)}$

$ii) \hspace{0.5 cm} \mathbf{\dfrac{dA}{dx}}$ , and $\mathbf{\dfrac{d^2A}{dx^2} }$ are found as follows;

$\dfrac{dA}{dx} = \mathbf{\dfrac{d}{dx} \left( \dfrac{1}{2} \cdot x \cdot (100 - x) \right)} = \underline{50 - x}$

$\dfrac{d^2A}{dx^2} = \mathbf{ \dfrac{d}{dx} \left( 50 - x\right)} = \underline{-1}$

iii) The value of x that makes the area as large as possible is given as follows;

Given that the second derivative, $\dfrac{d^2A}{dx^2} =-1$ , is negative, we have;

At the maximum area, $\dfrac{dA}{dx} = \mathbf{0}$ , which gives;

$\dfrac{dA}{dx} = 50 - x = 0$

x = 50

The value of x that makes the area as large as possible is x = 50

Learn more about the maximum value of a function here:

brainly.com/question/19021959

7 0

2 years ago

Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).

White raven [17]

Answer:

A. y + 1 = -2(x – 5)

Step-by-step explanation:

For a line with slope m through point (h, k), the equation is ...

y -k = m(x -h)

Fill in your values of m=-2, h=5, k=-1 and you have ...

y -(-1) = -2(x -5)

y +1 = -2(x -5) . . . . . . simplify. Matches selection A.

6 0

3 years ago