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3 years ago

Find slope of m and y intercept of the graph of x+5y=20

1 answer:

8 0

The answer is -1/5 because you have to switch the x to the other side making it a negative. Then you have to divide everything by 5 making your answer y=-1/5+4

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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

Can someone explain the altitude of a triangle?

nasty-shy [4]

Answer: In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the extended base of the altitude.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Andrea bought tacos from a food truck and left a 25% tip of $2.00.

yan [13]

Answer:

$8.00

Step-by-step explanation:

This is the price because 25% is basically 1/4. We know that 2.00 is 1/4 of 8.00. So the price of the tacos before the tip is $8.00.

5 0

3 years ago

Which angle is adjacent to A. B. C. D.

DaniilM [7]

Angles A F and E should be the answer

8 0

3 years ago

There are 1,332 people under the age 20 in Pierce City. This represents 14% of the total population. What is the total populatio

MAXImum [283]

Answer:

The total population = 9514.2857143 people.

Step-by-step explanation:

Let the total population be represented by X

In the question, we are told that,1332 people are under the age of 20 and this value = 14% of the total population.

Therefore, the total population is calculated as

14% of X = 1332

14/100 × X = 1332

14X/100 = 1332

Cross Multiply

14X = 1332 × 100

X = 1332 × 100/14

X = 9514.2857143

Therefore, the total population = 9514.2857143 people.

8 0

3 years ago