Let[tex]Let \\ \displaystyle\sf S = \sum_{k=1}^n \dfrac{n}{n^2+kn + k^2} [/tex] and ,[tex]\displaystyle \sf T_n =\sum_{k=0}^{n-1}\dfrac{n}{n^2+kn+k^2}[/tex] , [/tex]where n = 1,2,3,4..... Then ,[tex]A)\quad S_n < \dfrac{\pi}{3\sqrt3} \qquad \qquad B)\quad S_n >\dfrac{\pi}{3\sqrt3}\\\\ C)\quad T_n >\dfrac{\pi}{3\sqrt3}\qquad\qquad D)\quad T_n < \dfrac{\pi}{3\sqrt3}[/tex]

Mathematics College

Let
[tex]Let \\ \displaystyle\sf S = \sum_{k=1}^n \dfrac{n}{n^2+kn + k^2} [/tex] and ,
[tex]\displaystyle \sf T_n =\sum_{k=0}^{n-1}\dfrac{n}{n^2+kn+k^2}[/tex] ,
[/tex]
where n = 1,2,3,4..... Then ,
[tex]A)\quad S_n < \dfrac{\pi}{3\sqrt3} \qquad \qquad B)\quad S_n >\dfrac{\pi}{3\sqrt3}\\\\ C)\quad T_n >\dfrac{\pi}{3\sqrt3}\qquad\qquad D)\quad T_n < \dfrac{\pi}{3\sqrt3}[/tex]

Answers

Answer 1

Answer:

A, D

Step-by-step explanation:

You want to know the bound for the values of Sn and Tn, given their definitions as ...

[tex]\displaystyle S_n=\sum_{k=1}^n{\dfrac{n}{n^2+kn+k^2}}\\\\T_n=\sum_{k=1}^{n-1}{\dfrac{n}{n^2+kn+k^2}}[/tex]

Values

All we need to do to determine the correct answer choices is evaluate the sums for some value of n.

For n=2, the value of S2 is ...

S2 = 2/(4+2+1) +2/(4+4+4) = 2/7 +2/12 = 19/42 ≈ 0.4524

For n=2, the value of T2 is ...

T2 = 2/(4+2+1) = 2/7 ≈ 0.2857 . . . . . 1/(3n) less than the value of Sn

Both of these values are less than π/(3√3) ≈ 0.6046.

The correct answer choices are ...

A) Sn < π/(3√3)

D) Tn < π/(3√3)

Additional comment

For the purpose here, it is not necessary to determine the limiting value of either Sn or Tn. It is only necessary to demonstrate which side of the given value the terms of either sequence lie.

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$Let[tex]Let \\ \displaystyle\sf S = \sum_{k=1}^n \dfrac{n}{n^2+kn + K^2} [/tex] And ,[tex]\displaystyle$

Related Questions

and
8. A rhombus has an area of 28 square inches.
The length of each side is increased to twice its
original length, and the height is increased to
twice its original length. What is the area of
the larger rhombus?

Answers

Answer:

the area of the rhombus is 56 square inches

You are the head seamstress at a boutique that specializes in making prom dresses. You are supervising the construction of a new style of dress that will take 180 hours of work to complete. Twenty percent of this time is for beading. Thirty-five percent of this time is for adding ruffles. The remaining time is divided equally between embroidery and sewing. When pricing this style, hourly labor and material costs are $40 for beading, $35 for ruffles, $20 for embroidery, and $18 for sewing. The dress is then sold in the showroom for 25% more than the cost of labor and materials. How much will this dress sell for in the boutique?

Answers

The amount at which the dress will sell for in the boutique is $6716.25.

What is the sellig price of the dress?

The total cost of beading = 180 x 25% x $40 = $1800

The total cost of ruffles = 35% x 180 x $35 = 2205

Time left for making embroidery and sewing = (100% - 35% - 25%)/2 = 20%

The total cost of embroidery = 20% x 180 x $20 = $720

The total cost of sewing = 20% x 180 x $18 = $648

Total cost = 5373

Selling price = 1.25 x 5373 = $6716.25

To learn more about percentages, please check: https://brainly.com/question/25764815

can someone help me solve this?

Answers

Answer:

[tex]\dfrac{7\pi}{18}[/tex]

Step by step explanation:

[tex]70^{\circ}=\dfrac{70\pi}{180}~~\text{radians}=\dfrac{7\pi}{18}~~\text{radians}[/tex]

Divide.

3/7 ÷ 4/7 = ???
A.
1 1/3
B.
5/14
C.
9/11
D.
3/4

Answers

Answer:

3/4

Step-by-step explanation:

Give brainliest if it helped...(:

A function of x containing four ordered pairs of
the form (x, y) is shown below.
{(2,0),(4,0), (6,0), (8,0)}
What is the domain of the function?

Answers

Answer:

{2, 4, 6, 8}

Step-by-step explanation:

The domain refers to all the possible x values of a function.

Our ordered pairs :

(2,0)(4, 0)(6, 0)(8, 0)

As they are in the form (x, y), the domain is :

⇒ {2, 4, 6, 8}

HELP PLEASEEEEEEEEEWEEEEEEEE

Answers

Answer:

x = 27° , <EAF = 27°

Step-by-step explanation:

63° + x° = 90°

x = 27°

63° + <EAF = 90°

<EAF = 27°

Find the exact perimeter of quadrilateral ABCD plotted below. A(-3, 2) B(6,–2) D(0, –6) C(3,-6)

Answers

Answer:

See below ~

Step-by-step explanation:

Distance Formula

D = √(x₂ - x₁)² + (y₂ - y₁)²

Finding the side lengths

AB = √(6 + 3)² + (-2 - 2)² = √81 + 16 = √97BC = √(3 - 6)² + (-6 + 2)² = √9 + 16 = √25 = 5CD = √(3 - 0)² + (-6 + 6)² = √9 = 3DA = √(0 + 3)² + (-6 - 2)² = √9 + 64 = √73

Perimeter

AB + BC + CD + DA√97 + 5 + 3 + √738 + √97 + √73 units [radical form]8 + 9.85 + 8.5426.39 units (decimal form)

pls help me on this i dont get it i wasnt trached this aswell

Answers

Answer:

answer below.

Step-by-step explanation:

1. 1/5----0.2

2. 1/3---0.3 repeating

3. 1/2---0.5

4. 7/10---0.7

5. 3/4---0.75

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Answers

Answer:

152 sq in

Step-by-step explanation:

Surface area just means to find the area of all of the sides of a shape. This triangular prism has been flattened so you can see both bases (triangles) and all three lateral sides (rectangles)

Area of a triangle is:

A = 1/2 b•h

= 1/2 •8•4

= 16

There are 2 of these triangles.

A_bases = 32

Then there are 3 rectangle sides, area of a rectangle is:

A = l × w (or b•h)

6 × 5 = 30

6 × 8 = 48

6 × 7 = 42

Add up all the areas.

32 + 30 + 48 + 42

Total surface area is:

A = 152 sq in

Answer:

152

Step-by-step explanation:

find the measure of angle m and give your reasons for each step

Answers

Answer:

m=56

Step-by-step explanation:

So look at the angles. I learned this in geometry like 2 years ago. I believe it was the opposite angle theorem or the alternate exterior or interior angles. You should look on the internet about that.

Find the points on the ellipse
3x2 + y2 = 3
that are farthest away from the point (1, 0).

Answers

This question has to do with the Mathematical sub-topic in Geometry called Ellipse.

What is an Ellipse in Maths?

An ellipse is a circle that has been stretched in one direction so that it is no longer symmetrical but oval in shape.

How does one find the points on the ellipse?

Let us assume that the points on the ellipse is (cosθ, √3 sinθ)

Next let's minimize their distance squared from (-1, 0) taking a point on the ellipse as (cos θ- -1)² + (√3 sin θ)² =

cos²θ + 2cos θ + 1 + 3 sin² θ

(Substituting sin² θ + cos² θ = 1)

2 + 2 cos θ + 2 sin² θ

The derivative is given as

-2 sin θ + 4 sin θ cos θ =

-2 sin θ (2 cos θ - 1)

The above translates to 0 at sin θ = 0 or cos θ = 1/2, which results in 0°, 180°, 60°, 300°

Assuming we re-write the first derivative as - 2sin θ+ 2sin 2θ, the second derivative becomes:

-2 cos θ + 4 cos 2 θ

At 0°, 180°, 60°, 300°, we get 2, 6, -3, -3.

Therefore, our relative minima is given at 0°, 180°, while the relative maxima at 60°, 300°.

It is safe to declare, therefore that due to the nature of the function, the global minima and maxima will be among the four locations indicated above.

In addition to that,, 180° is the global minimum. This is because it is at the actual point, while 60° and 300° give the same value of the distance squared, thus both will each be maxima.

(cos θ, √3 sin θ) at 60°, 300° is (1/2, 3/2) and (1/2, -3/2)

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See the definition of a circle here:
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Video One, a Blu-ray disc player manufacture, produces two model of Blu-ray players. The mini-blue,
which can only play a Blu-ray disc and the media-blue that plays Blu-ray disc and contains a
personal DVR. The players are assembled on two different assembly lines. Line 1 can assemble 2
units of the mini-blue model and 12 units of the media-blue model per hours, and Line 2 can
assemble 5 units of the mini-blue model and 5 units of the media-blue model per hours. The
company needs to produce at least 20 units of the mini-blue model and 70 units of the media-blue
model to fill an order.
Let x = the number of hours for Line 1
Let y = the number of hours for Line 2.
Write the system of inequalities that represents the minimum number of Blu-ray disc player that
need to be produced to fill the order.

Answers

Answer:

This question is very big, you should shorten your question a bit so that I can answer it quickly, the rest is just that I did not understand the question a bit

Mega Movers charges $19.50 per day for truck rentals, plus an additional mileage fee of $0.95 per mile. U-Move-It charges $42.00 per day for truck rentals, plus an additional mileage fee of $0.45 per mile for mileage over 20 miles. Which of the following systems of equations could be used to find the total mileage, m, that will make the cost, p, of renting a moving truck for one day equal at each rental company, assuming m≥20, is greater than or equal to, 20?

Answers

The equation used to find the total mileage, m, that will make the cost, p, of renting a moving truck for one day equal at each rental company is 45 miles

Equation

Total mileage = mCost = p

Mega movers:

Fixed cost per day = $19.50

Additional cost per mileage = $0.95

p = 19.50 + 0.95m

U-move:

Fixed cost per day = $42.00

Additional cost per mileage =$0.45

p = 42.00 + 0.45m

Equate the cost of both company

19.50 + 0.95m = 42.00 + 0.45m

0.95m - 0.45m = 42.00 - 19.50

0.50m = 22.50

m = 22.50 / 0.50

m = 45 miles

Learn more about equation:

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#SPJ1

PLEASE HELP PLEASE HELPP

Answers

Answer:

Step-by-step explanation:

Coordinates are (x,y) so just look at the table on how the x-value compares.

Answer:

answer is B

pls give me branlist

x is bigger than y. The difference between x and y is 18. Find x and y.

Answers

Answer:

x can be 20

y can be 2

Step-by-step explanation:

i hope i will help you

A store sold 200 cell phone covers in April. The circle graph shows the
percent of each color sold in that month. How many more black covers
were sold than blue covers?

Answers

Answer:

Step-by-step explanation:

Given

Total is 200

From the attachment, we have:

Required

Black- 35%

Blue-23%

How many more of black than blue were sold

First, calculate the difference in percentage sold

Multiply by the total phones sold;

Hence, 24 more blacks were sold than blue

Hope this helps

Brainliest appreciated :)

Answer:

The answer is 24

Step-by-step explanation:

The total amount of phone covers were 200.

35% of those were black. So, 200 x 35% (or 200 x .35) = 70.

70 of the phone covers sold were black.

23% of the covers were blue. So, 200 x 23% (or 200 x .23) = 46

46 of the phone covers sold were blue.

How many more black covers sold than blue covers means we subtract.

70 black covers - 46 blue covers = 24 more black covers sold.

What is the mode of the data represented in this line plot?

Enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

The mode is 3 because it is the most commonly repeating number in the data set.

The mode of the data represented in this line plot is 3

How to determine the mode?

From the line plot, we have the following frequency table

Data Frequency

1 2

2 3

3 4

4 3

In the above frequency table, the entry 3 has the highest frequency of 4

Hence. the mode of the data is 3

Answers

Answer:

[tex]the \: volume \: of \: a \: rectangular \: prism \: is \\ l \times w \times h \\ in \: this \: graph \: \\ l = 2 \frac{1}{4} \\ w = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: h = 4 \\ 2 \frac{1}{4} \times 2 \times 4 \\ 4 \frac{1}{2} \times 4 = 18 \\ the \: volume \: is \: 18 {in}^{3} [/tex]

Find the length of the midsegment of the trapezoid.

Answers

Answer:

MN=66.5

Step-by-step explanation:

Add 57 and 76, then divide by 2.

1.Find the perimeter of the polygon with the given vertices
D(-3, 2), E(4,2), F(4, -3)

Answers

Answer:

perimeter = 12 + √74

area = 17.5

Step-by-step explanation:

See the drawing below.

This is a right triangle.

The legs have lengths 5 and 7.

We can find the length of the hypotenuse using the Pythagorean Theorem.

5² + 7² = e²

e² = 74

e = √74

perimeter = 5 + 7 + √74

perimeter = 12 + √74

area = bh/2

area = 5 × 7/2

area = 17.5

The recursive formula for an arithmetic sequence is:
{a1 = -6
{an-an-1+2
What is the 3rd term in the sequence?
A. - 2
B. -4
C. -10
D. -18

Answers

the answer is A so pick that

4 + (x + y) = (4 + x) + y =
what are the properties?

Answers

Answer:

Distributive

Step-by-step explanation:

For questions 4 – 6, name all of the radii of the circle shown in the figure.
For questions 7 – 10, find the measure of the radius of the circle. 7. 8.

Answers

For questions 4 – 6, name all of the radii of the circle shown in the figure.

For questions 7 – 10, find the measure of the radius of the circle. 7. 8.

Answer:

center(-2,5) r=6

Tom has 267 marbles, He shares the marbles out between himself and his two friends How many marbles does
each get? How many left over ?

Answers

Answer:

Each get 89 marbles and the leftovers are 0

Step-by-step explanation:

We have to ditribute the 267 marbles for 3 people so divide 267 by 3:

[tex]\frac{267}{3}[/tex] = 89

So each one gets 89

The leftovers are 0 because 267 is divisible by 3, means that if we divide 267 by 3 we will get a natural number ( no decimal part/ remainder=0)

remainder=0 → leftovers=0

match the function equations to their graphs. please help!

Answers

Answer:

y goes from the top to the bottom postive to negative. Then x is from left to right. The left is negative the right is postive.

Step-by-step explanation:

charlie stands at point A while holding the control line attached to a model airplane. the plane travels 120 feet counterclockwise from point b to point c about how long is the control line

Answers

The counterclockwise direction of the airplane implies that it moves in the opposite direction

The control line could be 60 feet long

How to determine the length of the control line?

The question is incomplete, as the figure that represents the control line and other parameters are not given.

However, a possible solution is as follows.

From the question, we understand that the airplane travels 120 feet counterclockwise.

The counterclockwise direction could represent that points B and C are on either sides of point A, such that:

AB = AC = 0.5* BC

So, we have

AB = 0.5* 120

AB = 60 feet

Hence, the control line could be 60 feet long

Answers

Answer:

333.3 years

Step-by-step explanation:

The formula

I = Prt

Condition

I needs to equal 10 x P

Solving

I = Prt10P = Prt10 = 0.03 x tt = 10/0.03t = 10/3 x 100 = 1000/3 = 333.3 years

Which expression represents y to the 4th power -36 in simplest factored form?

Answers

Answer:

(y^2 + 6)(y^2 - 6)

Step-by-step explanation:

First, substite variable x for y^2:

FOR x = y^2:

y^4 - 36

= (y^2)(y^2) - 36

= (x)(x) - 36

= x^2 - 36

Now, use the formula a^2 - b^2 = (a + b)(a - b):

x^2 - 36

= x^2 - 6^2

= (x + 6)(x - 6)

Finally, since the expression is factored for x, not y, substite y^2 in for x:

(x + 6)(x - 6)

= (y^2 + 6)(y^2 - 6)

[tex]= (y^2 + 6)(y^2 - 6)[/tex]

A solid has volume 7 cubic units. The equation k =
represents the scale factor of k by which
the solid must be dilated to obtain an image with volume V cubic units. Select all points which are
on the graph representing this equation.
a. (0,0)
e. (14,2)
b. (1,1)
f. (49,2)
C. (1,7)
(
g. (56,2)
(71)
h (27,3)

Answers

The volume of the solid is the amount of space in it.

The points on the graph are (0,0) and (1,7)

How to determine the points?

The volume is given as:

V1 = 7

The scale factor is given as:

Let the new volume be V.

So, we have:

V = V1 * k^3

Substitute 7 for V1

V = 7k^3

Divide both sides by 7

k^3 = V/7

Take the cube root of both sides

k = (V/7)^1/3

Next, we test the options

a. (0,0)

k = (0/7)^1/3

k = 0 --- this is true

b. (1,1)

k = (1/7)^1/3

k = 0.05 --- this is false

c. (1,7)

k = (7/7)^1/3

k = 1 --- this is true

d (7, 1)

k = (1/7)^1/3

k = 0.05 --- this is false

e. (14,2)

k = (2/7)^1/3

k = 0.10 --- this is false

f. (49,2)

k = (2/7)^1/3

k = 0.10 --- this is false

g. (56,2)

k = (2/7)^1/3

k = 0.10 --- this is false

h (27,3)

k = (3/7)^1/3

k = 0.14 --- this is false

Hence, the points on the graph are (0,0) and (1,7)

Answers

The critical value becomes 2.584 for two tailed test since we have to reject the null hypothesis, t >2.584 or t < -2.584 test stat lie in the rejection region.

Test-Static t

Data;

mean = 5.82s = 4.93n = 600

Let's calculate the t-value

[tex]t = \frac{x - \mu}{\frac{s}{\sqrt{n} } }[/tex]

Substitute the values into the equation and solve;

[tex]t = \frac{x - \mu}{\frac{s}{\sqrt{n} } } \\t = \frac{5.82 - 5}{\frac{4.93}{\sqrt{600} }} \\t = \frac{0.82}{0.201} \\t = 4.079[/tex]

The t-value is 4.079

The allowed significance value = 0.01

The degree of freedom is n -1, which becomes 600 - 1 = 599.

The critical value becomes 2.584 for two tailed test since we have to reject the null hypothesis, t >2.584 or t < -2.584 test stat lie in the rejection region, we have to reject the null hypothesis or claim incorrect.

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