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3 years ago

Which of the sequences is an arithmetic sequence

Mathematics

2 answers:

Kipish [7]3 years ago

6 0

B because arithmetic mean that they are add g or subtracting each time the same amount

Verizon [17]3 years ago

4 0

Answer:

Step-by-step explanation:

Alright, lets get started.

Arithmetic sequence is when a certain number is added in each term to get the next term of sequence.

The first term is given as -20 in option B

When we add -7 in it, we will get -27

When we add -7 in -27, we will get -34

When we add -7 in -34, we will get -41

When we add -7 in -41, we will get -48

It means this is a arithmetic sequence with common differnce -7.

hence the sequence is -20, -27, -34, -41, -48 : Answer

Hope it will help :)

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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be $F=L+2W$ .

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

$LW=80,000...(1)$

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be $C=20L+5(2W)\Rightarrow 20L+10W$ .

From equation (1), we will get:

$L=\frac{80,000}{W}$

Upon substituting this value in cost equation, we will get:

$C=20(\frac{80,000}{W})+10W$

$C=\frac{1600,000}{W}+10W$

$C=1600,000W^{-1}+10W$

To minimize the cost, we need to find critical points of the the derivative of cost function as:

$C'=-1600,000W^{-2}+10$

$-1600,000W^{-2}+10=0$

$-1600,000W^{-2}=-10$

$-\frac{1600,000}{W^2}=-10$

$-10W^2=-1,600,000$

$W^2=160,000$

$\sqrt{W^2}=\pm\sqrt{160,000}$

$W=\pm 400$

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

$C''=-2(-1600,000)W^{-3}$

$C''=3200,000W^{-3}$

$C''=\frac{3200,000}{W^3}$

Now, we will substitute $W=400$ in 2nd derivative as:

$C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05$

Since 2nd derivative is positive at $W=400$ , therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting $W=400$ in $L=\frac{80,000}{W}$ , we will get:

$L=\frac{80,000}{400}\\\\L=200$

Therefore, the side parallel to the river will be 200 feet.

4 0

3 years ago

5x (-2w-4) I need this asap

ira [324]

Hello from MrBillDoesMath!

Answer:

-10w - 20

Discussion:

5 ( -2w - 4 ) =

5(-2w) - 5(4) =

-10w - 20

Thank you,

MrB

4 0

3 years ago

Find the general form of the complete partial fraction decomposition of the integrand. use it to determine whether or not a term

zhuklara [117]

The answer is int(x^2-4x / X = 3).

8 0

3 years ago

The length of a rectangle picture frame is 2 centimeters more than twice it’s width. If the area of the frame is 364 square cent

sergeinik [125]

Answer:

Length:28 cm

Width: 13 cm

Step-by-step explanation:

Let

x ---> the length of a rectangle picture frame

y ---> the width of a rectangle picture frame

we know that

The area of a rectangle picture frame is equal to

$A=xy$

we have

$A=364\ cm^2$

$364=xy$ ----> equation A

The length of a rectangle picture frame is 2 centimeters more than twice it’s width

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

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (28,13)

see the attached figure

therefore

Length:28 cm

Width: 13 cm

5 0

3 years ago

3. Determine which ordered pair is not a solution of y = –5x – 4.

erastovalidia [21]

Answer:

Step-by-step explanation:

Let's try choice A.

y = -5x-4

(10, -52)

-52 = -5(10)-4

-52 = -50-4

-52= -54

-52 is not equal to -54, so A is the answer.

5 0

3 years ago